What is the integer quantum Hall effect?

And why is it so amazing?

Surprises [about physics in two dimensions] occurred in the 1980s when it became possible to study Landau levels [the quantised energy levels of electrons in a magnetic field] in Flatland. This happens when the electrons are completely constrained to move in only two dimensions. The surface within which the electrons move needs to be extremely flat and free from defects and impurities. Advances in semiconductor technology in the 1970s led to two realisations of this Flatland. Both were developed for technological reasons: the desire to have transistors in which the electrons and holes can move extremely fast. One class of device is silicon MOSFETs (Metal Oxide Semiconductor Field Effect Transistors). The second class is heterostructures, where layers of ultrapure semiconductors such as gallium arsenide are grown on top of each other, one layer of atoms at a time. In both classes of device, a fixed density of electrons (or holes) can be injected at the surface. These charge carriers can move freely in Flatland, acting like a fluid. Things get interesting when the number of charge carriers is small enough and the magnetic field is large enough that the number of charge carriers is comparable to the number of quanta of magnetic flux that pass through the system. Then, the quantum state of most of the charge carriers is one of the lowest Landau energy levels. 

To achieve this regime for the cleanest possible systems requires magnetic fields more than a hundred thousand times stronger than that of the Earth. Furthermore, the magnetic field must be spatially uniform in the region where the semiconductor system is located, stable over the time of the measurements, and the interior of the electromagnet producing the field must be large enough to contain a refrigerator that can cool the charge carriers in the system down to a few degrees above absolute zero. By 1980, all these conditions became possible. Klaus von Klitzing was able to perform measurements of the Hall resistance versus magnetic field in a special high magnetic field laboratory in Grenoble, France. The results were surprising and are shown schematically in Figure 35 below. There are four noteworthy features. 

 

Figure 35. The quantum Hall effect. The Hall resistance is shown as a function of the strength of the magnetic field and has a step-like structure. The integer n is related to the quantized energy that the charge carriers have.

First, there are distinct steps in the curve. At small magnetic fields the Hall resistance versus field is a straight line, as expected for the classical Hall effect. However, at larger fields there are plateaus in the curve.

Second, each of the plateaus is extremely flat. Von Klitzing found that the magnitude of the Hall voltage on each plateau did not vary to one part in ten million. As he varied the magnetic field, he noticed that the first seven digits on the voltmeter he was using did not change. He wondered if the voltmeter was broken and had become jammed. But it was working.

Third, the magnitude of the Hall resistance for all the plateaus has a simple relationship to fundamental physical constants. The quantum of resistance is defined as equal to h/2e^2 . When you calculate this quantity, the answer (25,812.827 ohms) is in the units of electrical resistance. The value of the Hall resistance is precisely equal to this value divided by an integer (n=1,2,3 …) which is related to the highest quantized energy (Landau level) that an electron can have at that magnetic field. That is why it is known as the integer quantum Hall effect.

Fourth, the observed value of the Hall resistance for each of the plateaus is independent of many details, including the temperature, the amount of disorder in the material, the chemical composition of system (silicon versus gallium arsenide), or whether the charge carriers are electrons or holes. [This independence is characteristic of the universality associated with emergent phenomena]. 

These four features are similar to those for the steps associated with the macroscopic quantum effects (magnetic flux in superconducting cylinders, circulation in a superfluid, Josephson effects) discussed in the previous chapter. Again, it is astonishing that a macroscopic measurement – of electrical resistance - of a macroscopic system can determine fundamental constants that are normally associated with properties of atomic systems. Just as the Josephson effect led to a new standard measure for voltage, the quantum Hall effect led to a new standard measure for electrical resistance.

Anyone familiar with building electronic circuits will have used resistors of varying values in ohms (Ω), e.g., 10 Ω or 25 kΩ. When these resistors are made, they are calibrated against some standard. For making integrated circuits with billions of transistors this standard needs to be extremely accurate. In 1990 the international standard for the ohm was changed to be that defined by the quantum Hall effect. Previously, the ohm was defined by the electrical resistance of a column of liquid mercury with constant cross-sectional area, 106.3 cm long, a mass of 14.4521 grams and a temperature 0 °C. Like the Josephson voltage standard, the quantum Hall resistance standard has the advantage of precision, portability, reliability, reproducibility, and independence of platform. 

An extract from Topology Matters, Chapter 8, Condensed Matter Physics: A Very Short Introduction.

Topology matters in condensed matter physics

Topology is the field of mathematics describing the properties of geometric objects that do not change when they are smoothly deformed. These properties only change in steps by cutting or gluing. Concepts in topology can be illustrated with everyday objects such as balls, doughnuts, coffee cups, and pretzels. For example, a doughnut can be gradually and smoothly deformed into the shape of a coffee mug (Figure 33). No ripping or cutting is required. In contrast, it is impossible to turn a ball into a doughnut without cutting a hole. The number of holes in an object is referred as a topological invariant. For a ball, doughnut, and the simplest pretzel these numbers are zero, one, and two, respectively. Topology is about qualitative differences not quantitative details such as distances, angles, and sizes.

Figure 33. A doughnut can be smoothly deformed into a coffee cup. From the perspective of the mathematical field of topology all the objects above are identical.

In chapter 4 it was noted that in ordered states of matter, some properties are determined by topological defects, such as vortices in superconductors. These are topological objects in the following sense. In a superconductor, there is an electrical current circulating around a vortex and a magnetic field that passes through the centre of the vortex. The magnetic flux is equal to one unit or quantum of the magnetic flux. If the spatial distribution of the electrical current around the vortex is smoothly changed the total magnetic flux remains the same. Furthermore, it is not possible to smoothly deform the system in any way to make the vortex disappear. The magnetic flux associated with the vortex is a topological invariant.

Condensed matter physics is about qualitative difference: states of matter are qualitatively different from one another. Until the 1980s these differences were only associated with different types of symmetry, which in turn reflect the underlying ordering in the state. This chapter describes unanticipated discoveries of new states of matter that could not be described in terms of this traditional symmetry picture. But they can be described in terms of topology. These states exhibit macroscopic quantum effects, reminiscent of superconductors and superfluids. Understanding these states of matter involves venturing back into Flatland and also into some abstract mathematical spaces. Remarkably, these abstractions can be related to practical questions about international standards for electronic circuits.

An extract from Topology Matters, Chapter 8, Condensed Matter Physics: A Very Short Introduction 

Macroscopic quantum effects in superconductors and superfluids

Quantisation of magnetic flux in a superconductor

Magnets and electrical currents produce magnetic fields, regions of space where other magnets and electrical wires experience a mechanical force. For a circle of wire in the presence of a magnetic field the magnetic flux is defined as the strength of the magnetic field passing through the circle multiplied by the area of the circle. A law of electromagnetism states that if the field varies with time, then a voltage is produced in the wire with a magnitude that is proportional to the rate at which the magnetic flux through the circle changes. This is the physics behind all electrical motors and electrical generators. In the everyday world magnetic flux can have any value and can be varied continuously by changing the strength of magnetic field. In the quantum world that is not the case. Magnetic flux is quantised.

In 1961, two experimental groups independently reported the first observation of a macroscopic quantum effect, the quantisation of the magnetic flux passing through a superconducting cylinder (Figure 30). One team was Bascom Deaver and William Fairbank and the other Robert Doll and Martin Nabauer. A tall thin cylinder made of tin was placed in a magnetic field and cooled down to a low enough temperature that it entered the superconducting state. The magnetic flux passing through the cylinder was then measured as the magnetic field was varied. The resulting graph has four noteworthy features. First, there are clear steps, showing that the magnetic flux has discrete values. In contrast, in the normal metallic state the graph was a straight line. Secondly, the magnitude of the steps was the same, to within about one per cent, suggesting quantisation of a single unit of magnetic flux. Thirdly, the value of this quantum of magnetic flux was equal to the value of h/2e. Thus, it was completely determined by the two fundamental constants, h and e, Planck’s constant and the charge on an electron, respectively. And fourthly, graphs with the same three features noted above were later observed in other superconducting materials and cylinders. This showed that flux quantisation is independent of details such as the chemical composition and dimensions of the cylinder. This flux quantisation is a macroscopic quantum effect. It is macroscopic because the system is macroscopic, and the magnetic flux is a macroscopic property. It is quantum as and the magnitude of the quantisation is determined by Planck’s constant.

                                                                       (b)

Figure 30. Quantisation of magnetic flux in a superconducting cylinder. (a) A tall thin cylinder of tin was placed in a magnetic field. (b) The graph shows the value of the magnetic flux passing through the cylinder as the magnetic field was varied. Note the step like structure, showing quantisation of the flux.

The quantum of magnetic flux is denoted Φ0 (= h/2e) and has the value 2.067833848...×10−15   tesla (metre)2. This number also determines the scale of quantum interference effects between two superconductors, as we will see shortly. The flux quantum is also relevant to vortices that form when some superconductors are placed in a magnetic field (Figure 20). A persistent electrical current flows around the vortex and the magnetic field penetrates the core of the vortex. It can also be shown, both theoretically and experimentally, that the magnetic flux associated with each vortex is exactly equal to one quantum of flux. Something similar happens in superfluids.

Macroscopic quantum effects in superfluids

When a cylinder containing a fluid is rotated about an axis passing down the centre of the cylinder the fluid will also rotate. The faster the cylinder is rotated the faster the fluid rotates. A physical quantity known as the circulation is proportional to the speed of rotation and the diameter of the cylinder. With a variable speed motor, the rotation speed can be continuously varied and in normal fluids the circulation has continuous values. But not in a superfluid, as shown in a beautiful experiment done by W.F. Vinen in 1961 using liquid 4He. He observed that when the liquid was cooled below the superfluid transition temperature that the circulation could only take on discrete values. Furthermore, these discrete values are multiples of h/M where h is Planck’s constant and M is the mass of one atom of helium. This value was predicted by Lars Onsager in 1949 who identified h/M with the circulation of a single vortex in the superfluid. This is another macroscopic quantum effect.

The quantisation of magnetic flux in superconductors and of circulation in superfluids showed that both superconductors and superfluids can be classified as quantum states of matter. The close similarity of these quantum phenomena, even though superconductivity occurs in solids and superfluidity in liquids. This indicates a deep underlying unity, demonstrated through the study of condensed matter physics. 

This is an extract from Chapter 7, Quantum Matter, in Condensed Matter Physics: A Very Short Introduction.

What is a quasiparticle?

 An example of emergent entities in condensed matter physics are quasiparticles. The concept can be described with the following analogue. When a horse gallops through the desert it stirs up a dust cloud that travels with it. The motion of the horse cannot be separated from the accompanying dust cloud. They act as one entity. Similarly, in a system consisting of many interacting particles, when one particle moves it carries with it a “cloud” of other particles. This composite entity is referred to as a quasiparticle. It turns out to be easiest to understand the whole system of particles in terms of the quasiparticles rather than in terms of the individual particles.

Quasiparticles are composite objects. Like the constituent particles in the system, quasiparticles each have properties such as charge, mass, and spin. However, these properties of a single quasiparticle may be different from those of the individual particles of which it is constituted. An example is holes in semiconductors; the many electrons in a crystal act collectively to produce a hole (the absence of a single electron), a quasiparticle with the opposite charge to that of a single electron. A more striking example is for the fractional quantum Hall states; the charge of the quasiparticles can be a fraction of the charge on a single electron.

Different musical instruments produce distinct sounds because they are made of different materials, and they vibrate in different ways in response to different stimuli. In general, the vibrations of a medium reflect something about the medium itself. Chapter 3 discussed how in a crystal the number of distinct ways that sound can travel through a crystal reflects the symmetry and ordering of the atoms in the crystal.

When the skin on a drum is hit by a drumstick the skin vibrates at particular frequencies. Similarly, a state of matter responds to external stimuli such as light, sound or heat, by oscillating at particular frequencies. These vibrations travel through the matter as waves. The properties of these waves reflect the particular order present in the state of matter. Here is a specific example. When a neutron with a particular energy and momentum is absorbed by a ferromagnetic crystal the interaction of the magnetism of the neutron with that of the atoms in the crystal produces a collective oscillation of the magnetic state of the crystal in time and space. Known as a spin wave, this oscillation has a particular frequency and wavelength. In quantum theory, waves and particles are equivalent to one another. The energy and momentum of a particle are related to the waves’ frequency and wavelength, respectively. Particles equivalent to light waves are known as photons; particulate equivalents of sound waves are known as phonons. And similarly, the particle equivalent of a spin wave is known as a magnon. These collective excitations are quasiparticles. Whereas the particles in a system may interact strongly with one another, the quasiparticles may interact weakly with one another. This makes analysis and understanding of the relevant theories more tractable.

The quasiparticle concept is a powerful theoretical tool in condensed matter physics. It is the basis for the construction of models that enable emergent phenomena to be understood in terms of the effective interactions between components such as quasiparticles, rather than in terms of the actual constituent particles and their interactions. This approach requires profound physical insight in order to discern what the truly essential components of a system are. Lev Landau was one of the first theoretical physicists to take this approach, introducing the idea of quasiparticles in his theories of superfluidity in 4He and of liquid 3He. This approach was also central to the BCS theory of superconductivity. Phil Anderson was also a master of the approach, using intuition to propose models that were simple enough for analysis and yet complex enough to capture the essential physics associated with a particular state of matter. In 1977 he was awarded the Nobel Prize for work using this approach to understand two specific systems: magnetic atoms in metals and the motion of electrons in materials that are not crystals and are dirty in the sense of containing many impurities.

An extract from Chapter 9, "Emergence: More is Different", in Condensed Matter Physics, A Very Short Introduction

A more detailed and technical discussion is in Section 8.2 of my review article on emergence.

Condensed matter physics in flatland

Adventures in Flatland

In everyday life we think of most objects as having three dimensions. But what would life be like in a two-dimensional world? For one thing, it would be harder to move around. We could no longer step over things but would have to move around them. In 1884 Edwin Abbott published Flatland: A Romance of Many Dimensions, under the pseudonym, A. Square, a satirical novella about social life in Victorian England. People are represented by geometrical objects. Men are represented by shapes such as triangles and hexagons. Women are represented by lines. The social status of men increases with the number sides that their shape has and how many of the sides are of the same length. Abbott’s book created limited interest and was largely forgotten by the 1920s. Interest revived when theoretical physicists started to think about worlds in different dimensions. This interest was stimulated by Albert Einstein’s theories of relativity, that proposed that we live in a four-dimensional world, not a three-dimensional one. Time is the fourth dimension, and there is an intimate and concrete connection between time and space. Attempts to unify gravity with other fundamental forces has led to physicists proposing and studying theories with more than four dimensions.

Changing the number of spatial dimensions leads to different physics because it changes what is mathematically possible. In three dimensions, there were only five highly symmetrical shapes known as Platonic solids (tetrahedron, cube, octahedron, icosahedron, and dodecahedron). In contrast, in two dimensions it is possible to make an infinite number of symmetrical shapes, known as regular polygons, shapes made of straight lines of equal length such as squares or hexagons. Similarly, the number of Bravais lattices differ in two and three dimensions. Changing the number of spatial dimensions changes both what is mathematically possible and what is physically possible.

What would condensed matter physics be like in Flatland? This question received limited attention before the 1970s. Occasionally, theoretical physicists would investigate mathematical models of crystals or magnets in one or two dimensions just because the mathematics was simpler and more tractable than in three dimensions. The goal was to obtain insight into physics in three dimensions. We will consider a famous example, the Ising model. 

In the 1970s, several surprising developments led to significant interest in condensed matter physics in spatial dimensions different from the usual three. First, it became possible to make a wide range of material systems that were two-dimensional. Secondly, theoretical work showed that states of matter, and phase transitions between them, can be qualitatively different in one, two, and three spatial dimensions. And thirdly, considering different numbers of spatial dimensions turned out to be very fruitful for theory, particularly for understanding phase transitions near critical points. 

An extract from "Adventures in Flatland," chapter 5 in Condensed Matter Physics: A Very Short Introduction

Condensed matter physics is about how order emerges from disorder

 The order of things

Life and the world around us sometimes appears chaotic and random. We may feel this way about traffic, weather, economics, social change, politics, or our personal relationships. Perhaps that is why many yearn for regularity, predictability, order, and stability. Science is a search for patterns and order in the natural world. Condensed matter physics is about how order emerges from disorder.

This chapter explores how different states of matter are associated with different types of ordering of the atoms in the material. The symmetry of the state reflects the type of ordering, i.e., the patterns associated with the state. There is also a rigidity associated with the ordering and the rigidity determines the nature of the deviations from perfect ordering and results in entities such as vortices that are central to the physical properties of the state of matter.

The association of a state of matter with a specific type of ordering is illustrated in Figure 15 by an analogue with the dodgem bumper cars at an amusement park. A quiet day at the park is not much fun as collisions between cars are rare. In other words, there is little correlation between the relative locations and speeds of the cars. In comparison, on a busy day at the park the spatial separation of the cars is small, and their positions and speeds are more correlated with one another than on a quiet day. But, in both cases, there is no ordered arrangement of the cars. In contrast, after the park closes the cars are parked and arranged in an orderly manner. There is a rigidity associated with their spatial arrangement. One car cannot be moved without moving others. These three states of the dodgem cars are an analogue of three states of matter: gas, liquid, and crystal. 

Figure 15. A dodgem car analogue for the three states of matter: crystal, liquid, and gas. The only ordered arrangement is for the crystal (car park after hours) and this is associated with a specific symmetry and rigidity. The liquid and gas (busy and quiet day) only differ in density and the amount of correlation between the positions of the different atoms (dodgem cars).

In the dodgem car analogue, there are other possible types of ordering. In some amusement parks there is a track, and the cars are meant to all go in the same direction. The symmetry between clockwise and anti-clockwise of the track is then broken.  In the car park, Figure 15 shows cars that are symmetrical with respect to front and back. However, real cars have a front and back, and so can be parked either front first or back first. Hence, several types of ordering are possible: all cars park back first, all cars park front first, cars are front first or back first at random, alternating patterns of front first and back first as one goes along a row, alternating rows of front first and back first, and so on. These different types of ordering in the car park all have analogues in different solid states of matter.

Liquid crystals involve unique types of ordering. These materials are composed of elongated organic molecules, such as those shown in Figure 16. At high temperatures the material is in a liquid state and the orientations and positions of the molecules are random. The liquid has both continuous translational and rotational symmetry. At low temperatures the molecules form a solid crystal without the continuous translational and rotational symmetry of the liquid state. As the crystal is heated the temperature increases and there is a phase transition to the liquid crystal state, in which all the molecules point in the same direction, but their positions are random. Hence, the liquid crystal state has the continuous translational symmetry of the liquid, but not its continuous rotational symmetry, like the crystal. As the temperature increases further there is a transition to the liquid state (Figure 16). In terms of the dodgem car analogue the liquid crystal state is similar to when cars park in a field all pointing in the same direction but there are no grid lines, and their positions are then random.

The existence of a state in between a liquid and crystal was first proposed in 1888 by botanist and chemist Friedrich Reinitzer who was doing research on cholesterol at the Institute for Plant Physiology in Prague. He performed a heating experiment similar to that described in Figure 4. Instead of one melting transition he observed transitions at two distinct temperatures. 

Figure 16. Liquid crystals. (a) An example of the type of elongate organic molecule found in these materials. Each molecule can be represented by an oval shape. (b) In the nematic liquid crystal state, the molecules tend to point in the same direction, but their positions are random. 

There are multiple alternative orderings for liquid crystals with names such as nematic, smectic, chiral nematic, discotic, and chlorestic. In the smectic phase molecules form layers of oriented molecules. The character of the liquid crystal state can be detected by shining polarised light on the material. Liquid crystal displays (LCDs) in electronic devices use the property that an electric field can orient the molecules, and this changes the interaction of the material with polarised light.

For solid crystals the nature of the ordering and the symmetry associated with a specific crystal structure is clear once the spatial arrangements of the atoms in the crystal are determined, such as by X-ray diffraction. For other states of matter, such as superconductors, superfluids, and antiferromagnets, the nature of the ordering and the symmetry is often not apparent and has only been determined with significant scientific insight. 

An extract from "The order of things," chapter 4 in Condensed Matter Physics: A Very Short Introduction.

Symmetry matters in condensed matter physics

 Snowflakes form incredibly diverse structures, seen when they condense onto a plate of glass. Every snowflake is different. On the other hand, every snowflake is the same. They are all composed of ice, a solid state of water. Every snowflake is composed of units that have a six-fold symmetry (Figure 8). Every snowflake is composed solely of water molecules. This paradox of the particular and the universal is at the heart of condensed matter physics. Although diversity prevails anything is not possible. No snowflake has five-fold symmetry. Snowflakes have enchanted scientists for a long time. The astronomer Johannes Kepler studied them and in 1611 wrote a small book about them as a gift for his patron. Kepler suggested snowflakes provided clues to deeper questions about the composition of matter. Today, Kenneth Libbrecht, a physicist at Caltech, has spent most of his career studying snowflakes and has produced beautiful volumes of photographs of them.

Figure 8. A snowflake shows a six-fold symmetry, just like a hexagon. The snowflake appears identical when it is rotated by an angle of sixty degrees about an axis passing through its centre and perpendicular to the page.

Condensed matter physicists ask several questions about snowflakes. What is the reason for the six-fold symmetry of the snowflake? What is the connection between the macroscopic properties of snowflakes and the properties of the underlying microscopic constituents, molecules of H2O? How is the diversity of snowflake shapes possible? Is there a phase diagram that defines the external conditions under which the different shapes form?

There is a long history in art, architecture, philosophy, and science, of associating symmetry with beauty and perfection. The ancient Greek philosopher Plato was a proponent of this view. He studied a particular class of solid shapes: cube, tetrahedron, octahedron, icosahedron, and dodecahedron. Plato identified the first four shapes with the four “elements”: earth, wind, fire, and water, respectively, and the fifth with the heavens. Each of these solid shapes is highly symmetric. Every face of a Platonic solid is the same shape (square, triangle, pentagon,...) and each of those shapes has edges of equal length. 

Like Plato, Kepler believed that “God is a geometer” and that God’s creation should reflect the perfection of God. These convictions led Kepler to propose in 1597 that the orbits of the planets around the Sun were circular and that the Platonic solids determined the relative size of the orbits. Later this model for the solar system was shown not to be true. In fact, Kepler himself became famous because he showed that the planets moved in elliptical, not circular orbits. Nevertheless, Kepler’s model was the beginning of a long history of successfully relating physical laws to symmetry and geometry.

A key discovery in physics from the past century is that symmetry is central to understanding a wide range of physical phenomena, whether colliding billiard balls, the allowed energies of an atom, the fundamental forces of nature, or different states of matter. Symmetries determine what is physically possible. For example, that energy cannot be created or destroyed is a consequence of the fact that physical laws do not change with time.

In this Chapter I explore three key ideas. First, transitions between different states of matter are associated with changes in symmetry. Thus, symmetry provides a criterion for specifying the qualitative difference between distinct states of matter. Second, for a specific state of matter the relevant symmetry constrains what is physically possible. Third, symmetry is central to making connections between the macroscopic and microscopic properties of a state of matter. The next chapter will explore how symmetry is associated with the type of ordering that occurs in a state of matter.

An extract from Chapter 3, Condensed Matter Physics: A Very Short Introduction

How many states of matter are there?

Diamond and graphite are distinct solid states of carbon. They have qualitatively different physical properties, at both the microscopic and the macroscopic scale. Condensed matter physics is all about states of matter. In science classes at school, you were probably taught that there are only three states of matter: solid, liquid, and gas. Like other things you were told in school, this is incorrect. There are endless, unlimited, distinct states of matter. 

Consider the “liquid crystals” that are the basis of LCDs (Liquid Crystal Displays) in the screens of televisions, computers, and smartphones. How can something be both a liquid and a crystal? A liquid crystal is a distinct state of matter. Solids can be found in many different states. We have already seen that there are two different solid states of carbon: graphite and diamond. In everyday life ice means simply solid water. But there are in fact eighteen different solid states of water, depending on the temperature of the water and the pressure that is applied to the ice. In each of these eighteen states there is a unique spatial arrangement of the water molecules and there are qualitative differences in the physical properties of the different solid states. Welcome to the world of condensed matter...

Extract from Chapter 1, Condensed Matter Physics: A Very Short Introduction

Classifying objects, people, and societies requires making qualitative distinctions. One book is easy to understand, and another is hard. One person is kind, and another is mean. One society is egalitarian, and another is not. Justifying such qualitative distinctions is hard. Not everyone will agree. Are there definitive criteria to justify a particular quality? Some claim they can quantify qualities such as these but that is contentious. In contrast, in condensed matter physics it is possible to give objective criteria that distinguish different states of matter. A state can only exist under specific external conditions, including defined ranges of parameters such as temperature and pressure. This chapter describes the clear signatures of transitions between different states that are observed as these parameters are varied. Some of the many known states of matter will be introduced including superconductors, superfluids, and magnets. On the way we will learn about “dry ice”, how to convert graphite into diamond, and how freeze-dried food is made.

Abrupt changes in properties

If you put some ice cubes in one empty glass and water in another, the ice does not change its shape, whereas water takes the shape of the glass. Solids are rigid and liquids are not. The distinct change from one state to another can be detected by observing an abrupt change or discontinuity in physical properties. For example, ice (solid water) has a different density to liquid water. This is evident because ice floats. The solid state of water has a lower density than the liquid state. To put it another way, water expands when it freezes. That’s why water pipes can burst if they freeze in cold weather.

A transition between two distinct states of matter is an example of a tipping point: a small change in a system variable can produce large changes in the system. For example, changing the temperature of water from +1 °C to -1 °C can produce a qualitative change in the system's properties. The water changes from liquid to solid. Tipping points occur in a wide range of physical, biological, and social systems. Examples include a stock market crash, the outbreak of an epidemic, and the operation of a room thermostat. Tipping points show that quantitative differences can become qualitative differences.

Extract from Chapter 2, Condensed Matter Physics: A Very Short Introduction

What is condensed matter physics?

 Every day we encounter a diversity of materials: liquids, glass, ceramics, metals, crystals, magnets, plastics, semiconductors, foams, … These materials look and feel different from one another. Their physical properties vary significantly: are they soft and squishy or hard and rigid? Shiny, black, or colourful? Do they absorb heat easily? Do they conduct electricity? The distinct physical properties of different materials are central to their use in technologies around us: smartphones, alloys, semiconductor chips, computer memories, cooking pots, magnets in MRI machines, LEDs in solid state lighting, and fibre optic cables. Consequently, the science of materials attracts researchers in a wide range of disciplines: physics, chemistry, biology, mathematics, and the varieties of engineering (electrical, chemical, mechanical, material…). But why do different materials have different physical properties? 

There are more than one hundred different types of atoms, or chemical elements, in the universe. Any material is composed of a specific collection of different atoms, and they are arranged in a particular spatial pattern within the material. A central question is: 

How are the physical properties of a material related to the properties of the atoms from which the material is made?

Extract from Chapter 1, Condensed Matter Physics: A Very Short Introduction

Quantum states of matter and metrology

Two characteristics of states of matter are associated with them being referred to as quantum. One characteristic is the importance of quantum statistics of particles, i.e., that the system is composed of particles that obey Fermi-Dirac or Bose-Einstein statistics. The second characteristic is that a macroscopic property is quantized with values determined by Planck’s constant. I now discuss each of these with respect to emergence.

Quantum statistics. 

For a system of non-interacting  fermions and bosons at high temperatures the properties of the system are those of a classical ideal gas. As the temperature decreases there is a smooth crossover to low-temperature properties that are qualitatively different for fermions, bosons, and classical particles. This crossover occurs around a temperature, known as the degeneracy temperature, that is dependent on the particle density and Planck’s constant. 

Many of the properties resulting from quantum statistics also occur in systems of strongly interacting particles and this is central to the concept of Landau’s Fermi liquid and viewing liquid 4He as a boson liquid. If liquid 3He and the electron liquid in elemental metals are viewed as a gas of non-interacting fermions, the degeneracy temperature is about 1 K and 1000 K, respectively. Thermodynamic properties are qualitatively different above and below the degeneracy temperature. Low-temperature properties can have values that differ by orders of magnitude from classical values and have a different temperature dependence. In contrast to a classical ideal gas, a fermion gas has a non-zero pressure at zero temperature and its magnitude is determined by Planck’s constant. This degeneracy pressure is responsible for the gravitational stability of white dwarf and neutron stars.  

These properties of systems of particles can be viewed as emergent properties, in the sense of novelty, as they are qualitatively different from high-temperature properties. However, they involve a crossover as a function of temperature and so are not associated with discontinuity. They also are not associated with unpredictability as they are straightforward to calculate from a knowledge of microscopic properties.

Quantised macroscopic properties.

These provide a more dramatic illustration of emergence. Here I consider four specific systems: superconducting cylinders, rotating superfluids, Josephson junctions, and the integer Quantum Hall effect. All of these systems have a macroscopic property that is observed to have the following features.

i. As an external parameter is varied the quantity varies in a step-like manner with discrete values on the steps. This is contrast to the smooth linear variation seen when the material is not condensed into the quantum state of matter.

ii. The value on the steps is an integer multiple of some specific parameter.

iii. This parameter (unit of quantisation) only depends on Planck’s constant h and other fundamental constants. 

iv. The unit of quantisation does not depend on details of the material, such as chemical composition, or details of the device, such as its geometrical dimensions.

v. The quantisation has been observed in diverse materials and devices.

vi. Explanation of the quantisation involves topology.

Superconducting cylinders. A hollow cylinder of a metal is placed in a magnetic field parallel to the axis of the cylinder. In the metallic state the magnetic flux enclosed by the cylinder increases linearly with the magnitude of the external magnetic field. In the superconducting state, the flux is quantized in units of the magnetic flux quantum, Φ0 = h/2e where e is the charge on an electron. It is also found that in a type II superconductor the vortices that occur in the presence of an external magnetic field enclose a magnetic flux equal to Φ0.  

Rotating superfluids. When a cylinder containing a normal fluid is rotated about an axis passing down the centre of the cylinder the fluid rotates with a circulation proportional to the speed of rotation and the diameter of the cylinder. In contrast, in a superfluid, as the speed of rotation is varied the circulation is quantised in units of h/M where M is the mass of one atom in the fluid. This quantity is also the circulation around a single vortex in the superfluid. 

Josephson junctions. In the metallic state the current passing through a junction increases linearly with the voltage applied across the junction. In the superconducting state the AC Josephson effect occurs. If a beam of microwaves of constant frequency is incident on the junction, jumps occur in the current when the voltage is an integer multiple of h/2e. The quantisation is observed to better than one part in a million (ppm).

Integer Quantum Hall effect. In a normal conductor the Hall resistance increases linearly with the external magnetic field for small magnetic fields. In contrast, in a two-dimensional conductor at high magnetic fields the Hall resistance is quantized in units of h/2e^2. The quantisation is observed to better than one part in ten million. Reflecting universality, the observed value of the Hall resistance for each of the plateaus is independent of many details, including the temperature, the amount of disorder in the material, the chemical composition of system (silicon versus gallium arsenide), or whether the charge carriers are electrons or holes.

Other examples of macroscopic quantum effects are seen in SQUIDs (Superconducting Quantum Interference Devices). They exhibit quantum interference phenomena analogous to the double-slit experiment. The electrical current passing through the SQUID has a periodicity defined by the ratio of the magnetic flux inside the current loop of the SQUID and the quantum of magnetic flux.

The precision of the quantisation provides a means to accurately determine fundamental constants. Indeed, the title of the paper announcing the discovery of the integer quantum Hall effect was, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance.” It is astonishing that a macroscopic measurement of a property of a macroscopic system, such as the electrical resistance, can determine fundamental constants that are normally associated with the microscale and properties of atomic systems. 

Laughlin and Pines claimed that the quantisation phenomena described above reflect organizing principles associated with emergent phenomena, and their universality supports their claim of the unpredictability of emergent properties. 

Quantum states of matter and metrology

The universality of these macroscopic quantum effects has practical applications in metrology, the study of measurement and the associated units and standards. In 1990 new international standards were defined for the units of voltage and electrical resistance, based on the quantum Hall effect and the AC Josephson effect, respectively.

Prior to 1990 the standard used to define one volt was based on a particular type of electrical battery, known as a Weston cell. The new standard using the AC Josephson effect allowed voltages to be defined with a precision of better than one part per billion. This change was motivated not only by improved precision, but also improved portability, reproducibility, and flexibility. The old voltage standard involved a specific material and device and required making duplicate copies of the standard Weston cell. In contrast, the Josephson voltage standard is independent of the specific materials used and the details of the device. 

Prior to 1990 the international standard for the ohm was defined by the electrical resistance of a column of liquid mercury with constant cross-sectional area, 106.3 cm long, a mass of 14.4521 grams and a temperature 0 °C. Like the Josephson voltage standard, the quantum Hall resistance standard has the advantage of precision, portability, reliability, reproducibility, and independence of platform. The independence of the new voltage and resistance standards from the platform used reflects the fact that the Josephson and quantum Hall effects have the universality characteristic of emergent phenomena.

This post is an adaptation of material in Condensed Matter Physics: A Very Short Introduction

What symmetries distinguish liquids, crystals, glasses, and isotropic solids?

 One of the most important ideas in condensed matter physics is that different states of matter are associated with different symmetries. These different symmetries result in different types of elementary excitations such as the Goldstone bosons associated with continuous symmetry breaking. The symmetries of the low-lying excited states reflect the symmetries of the ground state.

For example, consider the transition from a liquid to a cubic crystal. The continuous rotational and translational symmetry of the liquid is broken to the discrete rotational and translational symmetry of the crystal. Long-wavelength sound waves reflect these changes in symmetry. In the crystal, there are three distinct sound waves: one longitudinal and two shear modes. In contrast, in the liquid, there are only longitudinal modes. 

An isotropic solid, such as studied in elasticity theory, supports two types of distortions: compression and shear. Consequently, there are three types of sound waves (longitudinal and transverse phonons. The latter can have two different polarisations). The isotropic solid has continuous, not discrete, rotational and translational symmetries. A glass is an example.

This leads to a fundamental question:

What is the difference between liquids and solids at the level of fundamental symmetries?

In different words, what is the order parameter for the liquid-solid transition? A possible answer is the shear modulus G, which vanishes in the liquid state.

A related question is: What is the fate of the transverse phonons upon transitioning from the solid state to the liquid state?

I would have thought that these questions would have been settled decades ago. However, they have not. Just two years ago, Physical Review E published a 22 page article that aims to address the questions above.

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory

Matteo Baggioli, Michael Landry, and Alessio Zaccone

The paper immediately drew a Comment claiming the paper

"contradicts the known hydrodynamic theory of classical liquids." The authors have a Reply.

I do not have the expertise to give insight on the subtle technical issues in this debate. My only comment is that it is amazing how we are struggling to answer such basic questions.

I thank Jean-Noel Fuchs for getting me interested in these subtle questions. This happened when he kindly pointed out an error in Condensed Matter Physics: A Very Short Introduction. On page 40, I erroneously stated that shear sound waves exist in a liquid. This was part of a confused discussion about how sound waves can be used to distinguish different states of matter.  I have drafted a corrected paragraph and inserted it in my post listing the errors in my book.

I welcome any comments about the issues discussed above.

Emergence talk at University of the Philippines

Today I am giving a seminar on emergence at the University of Philippines Los Banos, in the Institute of Mathematical Sciences and Physics.

Here are my slides.

The whole is qualitatively different from the parts: beer, birds, and brains

Pint of Science is an annual event in cities all around Australia. Local scientists give short talks about their research to general audiences. I am speaking tonight, along with my colleague Ben Powell. 

I found the tips to speakers very helpful. This led me to try and make the talk more of a personal story, reduce the amount of text on slides, and aim for engagement rather than focusing on scientific details or on technical details of your own research.

Here is the current version of my slides.

The introduction is based on this video and poem about emergence in economics.

This provides an example of how "free" economic markets can work well sometimes. But I will also point out that they can also fail spectacularly, another emergent phenomenon! 

A light conversation about condensed matter physics

Three weeks ago I did a local book launch for Condensed Matter Physics: A Very Short Introduction.

It was at a wonderful independent bookstore, Avid Reader, It is a vibrant part of the local community and has several author events every week.

I had a conversation about the book with my friend, Dr Christian Heim, an author, composer, and psychiatrist. My wife and daughter were surprised it was so funny. Most people loved it, but a couple of people thought it should have been more technical. I think that is not the point of such an event or of the Very Short Introduction series.

Here is a recording of the conversation, including the Q&A with the audience afterwards.

Many thanks to all the friends who came.

Launching my book in a real physical bookshop

Physical bookstores selling physical books are in decline, sadly. Furthermore, the stores that are left are mostly big chains. Brisbane does have an independent bookstore, Avid Reader, in the West End. It is a vibrant part of the local community and has several author events every week.

My daughter persuaded me to do a book launch, for Condensed Matter Physics: A Very Short Introduction (Oxford UP, 2023) 

 

It is at Avid Reader on Monday, February 26, beginning at 6 pm.

Most readers of this blog are not in Brisbane, but if you are or know people who are please encourage them to consider attending.

The event is free but participants need to register, as space is limited.

 

I will be in conversation about the book with my friend, Dr Christian Heim, an author, composer, and psychiatrist. Like the book, the event is meant for a general audience.

  

Very Short Introductions Podcast on Condensed Matter Physics

The podcast episode where I talk about my book just came out.

It is available on a range of platforms, listed here, including SoundCloud and YouTube.

Condensed matter physics in 15 minutes!

Oxford University Press has a nice podcast on Very Short Introductions. 

In each episode, an author of a specific volume has 10-15 minutes to introduce themself and answer several questions.

What is X [the subject of the VSI]?

What got you first interested in X?

What are the key aspects of X that you would like everyone to know?

The ones I have listened to and particularly liked are Infinity, Philosophy of Science, Evangelicalism, Development, Consciousness, Behavioural Economics, and Modern China.

Tomorrow, I am recording an episode for Condensed Matter Physics: A Very Short Introduction.

Here is a practise version of the audio and the draft text is below. 

I welcome feedback.

VSI Podcast 

I am Ross McKenzie. I am an Emeritus professor of physics at the University of Queensland in Brisbane, Australia. I have spent the past forty years learning, teaching, and researching condensed matter physics. I really love the Very Short Introduction series and so I am delighted to share my experience by writing Condensed Matter Physics: A Very Short Introduction.

What is condensed matter physics? It is all about states of matter. At school, you were probably taught that there are only three states of matter: solid, liquid, and gas. This is wrong. There are many more states such as liquid crystal, glass, superconductor, ferromagnet, and superfluid. New states of matter are continually, and often unexpectedly, being discovered. Condensed matter physics investigates how the distinct physical properties of states of matter emerge from the atoms of which a material is composed.

What first got me interested in condensed matter physics?

After I finished an undergraduate degree in theoretical physics in Australia in 1982, I would not have been able to answer the question, “what is condensed matter physics?”, even though it is the largest sub-field of physics. I then went to Princeton University in the USA to pursue a Ph.D. in and I took an exciting course on the subject and began to interact with students and faculty working in the field. 

At Princeton was Phil Anderson, who had won a Nobel Prize in physics for work in condensed matter. At the time I did not appreciate his much broader intellectual legacy. In his recent biography of Anderson, Andrew Zangwill states “more than any other twentieth-century physicist, he [Anderson] transformed the patchwork of ideas and techniques formerly called solid-state physics into the deep, subtle, and intellectually coherent discipline known today as condensed matter physics.” Several decades later, my work became richer as Anderson gave me an appreciation of the broader scientific and philosophical significance of condensed matter physics, particularly its connection to other sciences, such as biology, economics, and computer science. When do quantitative differences become qualitative differences? Can simple models describe rich and complex behaviour? What is the relationship between the particular and the universal? How is the abstract related to the concrete?

So what are the key aspects of condensed matter physics that I would like everyone to know?

First, there are many different states of matter. It is not just solid, liquid, and gas. Consider the “liquid crystals” that are the basis of LCDs (Liquid Crystal Displays) in the screens of televisions, computers, and smartphones. How can something be both a liquid and a crystal? A liquid crystal is a distinct state of matter. Solids can be found in many different states. In everyday life, ice means simply solid water. But there are in fact eighteen different solid states of water, depending on the temperature of the water and the pressure that is applied to the ice. In each of these eighteen states, there is a unique spatial arrangement of the water molecules and there are qualitative differences in the physical properties of the different solid states.

Condensed matter physics is concerned with characterising and understanding all the different states of matter that can exist. These different states are called condensed states of matter. The word “condensed’’ is used here in the same sense as when we say that steam condenses into liquid water. Generally, as the temperature is lowered or the pressure is increased, a material can condense into a new state of matter. Qualitative differences distinguish the many different states of matter. These differences are associated with differences in symmetry and ordering.

Second, condensed matter physics involves a particular approach to understanding properties of materials. Every day we encounter a diversity of materials: liquids, glass, ceramics, metals, crystals, magnets, plastics, semiconductors, and foams. These materials look and feel different from one another. Their physical properties vary significantly: are they soft and squishy or hard and rigid? Shiny, black, or colourful? Do they absorb heat easily? Do they conduct electricity? The distinct physical properties of different materials are central to their use in technologies around us: smartphones, alloys, semiconductor chips, computer memories, cooking pots, magnets in MRI machines, LEDs in solid-state lighting, and fibre optic cables. Why do different materials have different physical properties? 

Materials are studied by physicists, chemists, and engineers, and the questions, focus, goals, and techniques of researchers from these different disciplines can be quite different. The focus of condensed matter physics is on states of matter. Condensed matter physics as a research field is not just defined by the objects that it studies (states of matter in materials), but rather by a particular approach to the study of these objects. The aim is to address fundamental questions and to find unifying concepts and organizing principles to understand a wide range of phenomena in materials that are chemically and structurally diverse. 

The central question of condensed matter physics is, how do the properties of a state of matter emerge from the properties of the atoms in the material and their interactions? 

Let’s consider a concrete example, that of graphite and diamond. While you will find very cheap graphite in lead pencils, you will find diamonds in jewelery. Both graphite and diamond are composed solely of carbon atoms. They are both solid. So why do they look and feel so different?  Graphite is common, black, soft, and conducts electricity moderately well. In contrast, diamond is rare, transparent, hard, and conducts electricity very poorly. We can zoom in down to the scale of individual atoms using X-rays and find the spatial arrangement of the carbon atoms relative to one another. These arrangements are qualitatively different in diamond and graphite.. Diamond and graphite are distinct solid states of carbon. They have qualitatively different physical properties, at both the microscopic and the macroscopic scale. 

Third, I want you to know about superconductivity, one of the most fascinating states of matter. I have worked on it many times over the past forty years. Superconductivity occurs in many metals when they are cooled down to extremely low temperatures, close to absolute zero (-273 ºC). In the superconducting state, a metal can conduct electricity perfectly; without generating any heat. This state also expels magnetic fields meaning one can levitate objects, whether sumo wrestlers or trains. 

The discovery of superconductivity in 1911 presented a considerable intellectual challenge: what is the origin of this new state of matter? How do the electrons in the metal interact with one another to produce superconductivity? Many of the greatest theoretical physicists of the twentieth century took up this challenge but failed. The theoretical puzzle was only solved 46 years after the experimental discovery. The theory turns out also to be relevant to liquid helium, nuclear physics, neutron stars, and the Higgs boson. New superconducting materials and different superconducting states continue to be discovered. A “holy grail” is to find a material that can superconduct at room temperature. 

I find superconductivity even more interesting when considering quantum effects. By 1930 it was widely accepted that quantum theory, in all its strangeness, describes the atomic world of electrons, protons, and photons. However, this strangeness does not show itself in the everyday world of what we can see and touch. You cannot be in two places at the same time. Your cat is either dead or alive. However, condensed matter physicists have shown that the boundary between the atomic and macroscopic worlds is not so clear cut. A piece of superconducting metal can take on weird quantum properties, just like a single atom, even though the metal is made of billions of billions of atoms. It is in two states at the same time, almost like Schrodinger’s famous cat.

Fourth, condensed matter physics is all about emergence; the whole is greater than the sum of the parts. A system composed of many interacting parts can have properties that are qualitatively different from the properties of the individual parts. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. Condensed matter physics is arguably the field with the greatest success at understanding emergent phenomena in complex systems, particularly at the quantitative level. This is not because condensed matter physicists are smarter than sociologists, economists, or neuroscientists. It is because the materials we study are much “simpler” than societies, economies, and brains. 

Finally, condensed matter physics is one of the largest and most vibrant sub-fields of physics. For example, in the past thirty years, the Nobel Prize in Physics has been awarded thirteen times for work on condensed matter. In the past twenty years, eight condensed matter physicists have received the Nobel Prize in Chemistry. 

I hope I have sparked your interest in condensed matter physics. I invite you to learn more about why I consider this field of science significant, beautiful, and profound. 

Listing mistakes in Condensed Matter Physics: A Very Short Introduction

Someone told me that the day after your book is published you will start finding errors. They were correct.

Here are the first errors I have become aware of.

On Page 2 I erroneously state that diamond "conducts electricity and heat very poorly."

However, the truth about conduction of heat is below, taken from the opening paragraph of this paper.

Diamond has the highest thermal conductivity, L, of any known bulk material. Room-temperature values of L for isotopically enriched diamond exceed 3000 W/m-K, more than an order of magnitude higher than common semiconductors such as silicon and germanium. In diamond, the strong bond stiffness and light atomic mass produce extremely high phonon frequencies and acoustic velocities. In addition, the phonon-phonon umklapp scattering around room temperature is unusually weak.

Figure 2 on page 4 has a typo. Diamond is "hard" not "hand".

On page 82 I erroneously state that for the superfluid transition, the "critical exponent alpha was determined to have a value of -0.0127, that is to five significant figures."  The value actually has three significant figures. 

I thank my engineering friend, Dave Winn, for pointing out the first and third errors.

Update. August 27, 2024.

On page 40, I erroneously state that shear sound waves exist in a liquid. I thank Jean-Noel Fuchs for pointing out this error. Below, I have drafted a corrected paragraph

"In a fluid (gas or liquid) one way to distort a cubic volume of the fluid is to compress the cube into a shape (a rectangular prism) where the lengths of the sides are not identical, but the angles between the sides of the shape are still 90 degrees. Sound waves in air consist of this type of compression: oscillations in the density and pressure of the air occur in the same direction that the sound wave travels. 

      In an isotropic solid there is a second type of distortion: the shape of the cube is changed to that of a rhombohedron, the angles are no longer 90 degrees, but the lengths of the sides remain the same. Associated with these two types of distortions, there are two distinct ways in which sound can travel through a solid. A second type of sound wave corresponds to the second type of distortion, and is called a shear wave. The two types of sound travel at different speeds. An earthquake produces both types of waves: pressure waves and shear waves, the latter travelling slower. Observing and comparing the two types of waves plays an important role in seismology and in the detection of earthquakes."

There are some subtle issues here that go beyond what is appropriate in a VSI. Damped shear waves can exist in a liquid for wavevectors larger than some critical value. I will discuss the issues in a separate blogpost.

Please do write other errors in the comments below. This will help with future revisions.

Condensed Matter Physics: A Very Short Introduction (hard copies) now available on Amazon USA

My book has finally been released by Amazon in the USA. I don't like Amazon but it is cheap and you can avoid shipping charges.

In Australia Amazon has listed under "Engineering and Transportation" and is currently out of stock. 

A few things condensed matter physics has taught me about science (and life)

We all have a worldview, some way that we look at life and what we observe. There are certain assumptions we tend to operate from, often implicitly. Arguably, our worldview is shaped by our experiences: family, friendships, education, jobs, community organisations, and our cultural context (political, economic, and social).

A significant part of my life experience has been working in universities as a condensed matter physicist and being part of a broader scientific community. Writing a Condensed Matter Physics: A Very Short Introduction crystallised some of my thoughts about what CMP might mean in broader contexts. I am more aware of how my experience in CMP has had a significant influence on the way I view not just the scientific enterprise, but also broader philosophical and social issues. Here are a few concrete examples.

Complex systems. The objects studied in condensed matter physics have many interacting components (atoms). Further, there is an incredible diversity of systems (materials and phenomena) that are studied. Many different properties and parameters are needed to characterise a system and its possible states. There are many different ways of investigating each system. Similarly, almost everything else of interest in science and life is a complex system.

Emergence. This is central to CMP. The whole is greater than the sum of the parts. The whole is qualitatively different from the parts. Related features include robustness, universality, surprises, and the difficulty of making predictions. An emergent perspective can provide insights into other complex systems: from biology to psychology to politics.

Differentiation and integration. A key aspect of describing and understanding a complex system is conceptually breaking it into smaller parts (differentiation), determining how those parts interact with one another, and determining how those interacting parts combine to produce properties of the whole system (integration).

Diversity: The value of multiple perspectives and methods. Due to the complexity of condensed matter systems, multiple methods are needed to characterise their different properties. Due to emergence, there are various scales and hierarchies present. Investigating and describing the system at these different scales provides different perspectives on the system. What does the scientist do with all these different perspectives? Interpretation and synthesis are needed. That is not an easy or clearcut enterprise.

 Navigating the middle ground. The most interesting CMP occurs in an intermediate interaction regime that is challenging theoretically. Insight can be gained by considering two extremes that are more amenable to analysis: weak interaction and strong interaction. I had fun using conservative-liberal political tensions as a metaphor for divisions in the strongly correlated electron community.

The Art of Interpretation. Everything requires interpretation: a phone text message, a newspaper article, a novel, a political event, data from a science experiment, and any scientific theory. With interpretation, we assign meaning and significance to something. How we do this is complex and draws on our worldview, both explicitly and implicitly. Regardless of our best intentions, interpretation always has subjective elements.

Synthesis. Given the diversity of data, perspectives, and interpretation, it is a challenge to synthesise them into some coherent and meaningful whole. All the pieces are rarely consistent with one another. Some will be ignored, some discarded, some considered peripheral, and others central. This synthesis is also an act of interpretation.

All models are wrong but some are useful. One way to understand complex systems is in terms of "simple" models that aim to capture the essential features of certain phenomena. In CMP significant progress (and many Nobel Prizes) has resulted from the proposal and study of such models. There is a zoo of them. Many are named after their main inventor or proponent: Ising, Anderson, Hubbard, Heisenberg, Landau, BCS,... All theories in CMP are also models since they involve some level of approximation, at least in their implementation. These models are all wrong, in the sense that they fail to describe all features and phenomena of the system. But, the best models are useful. Their simplicity makes them amenable to understanding, mathematical analysis, or computer simulation. Furthermore, the models can give insight into the essential physics underlying phenomena, predict trends, or be used to analyse experimental data. 

The autonomy of academic disciplines. Reality is stratified. At each level of the hierarchy, one has unique phenomena, methods, concepts, and theories. Most of these are independent of the details of what happens at lower levels of the hierarchy. Given the richness at each level, I do not preference one discipline as more fundamental or important than the others.

Pragmatic limits to knowledge. We know so much.  We know so little. On the one hand, it is amazing to me how successful CMP has been. We have achieved an excellent understanding, at least qualitatively of many emergent phenomena in systems that are chemically and structurally complex (e.g., liquid crystals and superconductivity in crystals involving many chemical elements). On the other hand, there are systems such as glasses and cuprate superconductors that have been incredibly resistant to understanding. Good research is very hard, even for the brilliant. Gains are often incremental and small. This experience leads me to have sober expectations about what is possible, particularly as one moves from CMP to more complex systems such as human societies, national economies, and brains.

Science is a human endeavour. Humans can be clever, creative, insightful, rational, objective, cooperative, fiercely independent and capable of great things. The achievements of science are a great testimony to the human spirit. Humans can also be stubborn, egotistical, greedy, petty, irrational, ruthlessly competitive, and prone to fads, mistakes and social pressures. Science always happens in a context: social, political, cultural, and economic. Context does not determine scientific outcomes but due to human nature, it can corrupt how science is done.

The humanity of scientists leads to a lack of objectivity captured in Walter Kauzmann's maxim: people will tend to believe what they want to believe rather than what the evidence before them suggests that they should believe. My decades of experience working as a scientist leads me to scepticism about extravagant claims that some scientists make, particularly hype about the potential significance (scientific, technological, or philosophical) of their latest discovery or their field of research. Too often such claims do not stand the test of time.

Humility. This brings together practically everything above. The world is complex, people are complex, and human-world interactions are complex. It is easy to be wrong. We often have a pretty limited perspective of what is going on.