Condensed matter physics is not just defined by the objects it studies: condensed states of matter. Rather, the field is also defined by a particular approach. The focus is on finding unifying concepts and organizing principles to address fundamental questions concerning a wide range of phenomena in materials that are chemically and structurally diverse. This approach means looking at the different scales (length, time, and energy) associated with phenomena. In particular, CMP often looks at scales intermediate between the macroscopic and atomic scales. I argued before, that in this sense Kamerlingh Onnes was the first condensed matter experimentalist. In a similar sense, Lev Landau (1908 - 1968) is arguably the first condensed matter theorist, with three papers that he published in 1937, marking the beginning of theoretical CMP.
Landau lived in the Soviet Union and his 1937 papers were almost his last because in 1938 he was arrested for comparing Stalinism to Nazism. The Institute Director, Pyotr Kapitsa, personally wrote to Stalin to no avail. After a year Kapitsa wrote to Molotov (of cocktail fame!), then the nominal head of government, arguing that Landau was indispensable to ``clear up one of the most puzzling areas in modern physics." In the year following his release Landau developed a theory to explain many of the experiment results on superfluid helium that Kapitsa had obtained. (A nice thank you present!) Landau made notable contributions in all areas of theoretical physics, not just condensed matter. Wikipedia lists more than twenty separate entries describing results, equations, or phenomenon that bear Landau's name. With his former student, Evgeny Lifshitz, Landau co-authored a classic nine-volume series, Course in Theoretical Physics, that is still a standard reference today. Landau also founded a School of Theoretical Physics that produced a plethora of distinguished theoretical physicists. Tragically, Landau’s scientific career ended after a terrible car accident when he was fifty-two years old. He died six years later from injuries associated with the accident. In 1962, Landau was awarded the Nobel Prize in Physics for his work on the theory of superfluidity.
Landau and Kapitsa in 1948.
Landau’s first 1937 paper was concerned with developing the simplest possible theory that could describe the properties of a material near a critical point in the phase diagram, such as associated with a liquid-gas transition or a ferromagnet. A key assumption was that most of the microscopic details, such as the chemical composition of the material, don’t matter much. Landau introduced an order parameter to quantify the amount of ordering present and the symmetry of the ordering. The order parameter varies with temperature and other external parameters such as pressure or magnetic field. It is only non-zero in the ordered state. Landau wrote down the simplest form for the (free) energy of the system as a function of the order parameter. It turns out that symmetry significantly constrains the possible forms for this function. Furthermore, the form is qualitatively different for temperatures above and below the critical temperature. From this simple theory, Landau obtained results for how the order parameter varies with temperature and how there should be a jump (discontinuity) in the specific heat at the critical temperature. What was particularly important was the idea of universality: that most of the microscopic details did not matter and that a wide range of materials and states of matter should have similar properties. Furthermore, the ideas in this paper were foundational for the important ideas about the critical point.
A significant achievement of Landau’s approach to phase transitions was that in 1950, together with Vitaly Ginsburg (1916 - 2009), Landau proposed a theory that could describe many of the properties of superconductors, including how they behaved in the presence of a magnetic field and in thin films. For this work, Ginsburg shared the Nobel Prize in Physics in 2003. Although the Ginzburg-Landau theory could explain a wide range of superconducting phenomena, it left many questions unanswered, including the actual nature and origin of the ordering associated with the superconducting state.
The Ginzburg-Landau theory suggested that the relevant symmetry was a particular symmetry associated with electromagnetism: gauge symmetry. This is a rather abstract concept, but one can give a simple example that may help. With regard to electricity we are familiar with voltage: for example, a 9-volt battery, or a 240-volt appliance. The voltage refers to the electric potential energy; the larger the voltage the stronger the electrical driving force. Voltages are all relative, i.e., they are defined relative to some reference. What is physical is differences in voltage. This is similar to how gravitational potential energy (or elevation) is always defined relative to some reference height, e.g. the floor of the room, sea level, the center of the earth. There is also a gauge symmetry associated with magnetic fields and quantum theory but these are both more complicated and abstract. Later I will discuss experimental manifestations of this breaking of gauge symmetry.
[I am mindful that there are many subtleties about what the ordering and the broken symmetry actually are. For example, this is a breaking of a global gauge symmetry not a local one (which is not allowed by Elitzur's theorem). However, such subtleties are beyond a general audience].
Do you agree that in the sense I discuss Landau was the first condensed matter theorist?
Perhaps it should be van der Waals?
Any corrections?
Any suggestions on how to make this more accessible to a general audience?
Ross, I enjoyed reading this. As an outsider to CMP I might even be in your target audience!
ReplyDeleteOne writing approach to consider would be sprinkle the (fascinating) biographical details about Landau through the technical part of the text. This is a trick that Bill Bryson uses in his highly effective writing about technical topics.
I couldn't quite follow the paragraph about gauge symmetry - perhaps I am reading it too early in the morning?
I would perhaps consider Bloch as the first condensed matter theorist. The band theory of solids is arguably the most important concept in condensed matter theory. Landau had overall a higher impact than Bloch though.
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