The significance of the discovery of cuprate superconductivity

This is some draft text for Condensed Matter Physics: A Very Short Introduction. 

Feedback appreciated.

A big change in condensed matter physics occurred in the late 1980s due to an unexpected discovery that led to whole new areas of research. Why was this discovery so significant?

Superconductivity is amazing. At extremely low temperatures, many metals can conduct electricity without generating any heat. A ``holy grail’’ of physics is to discover a material that is a superconductor at room temperature. This could revolutionise the transmission of electricity. Until 1986, the highest temperature at which superconductivity was possible was about 23 K (-250 °C), in Nb₃Ge, a combination of the elements Niobium and Germanium. This requires cooling the material with liquid helium, which is expensive, and consequently limits commercial applications, such as MRI machines in hospitals.

In 1986, Alex Bednorz and Karl Muller, working at an IBM laboratory in Switzerland, investigated whether a chemical compound composed of the elements lanthanum, barium, copper, and oxygen (La, Ba, Cu, O) would be superconductor at a higher temperature. They were motivated by theoretical arguments that strong interactions between the electrons and the vibrations of the atoms could enhance the superconducting transition temperature, Tc. They found superconductivity below a Tc of 36 K, a new record. The material consisted of layers of copper and oxygen atoms and this lead to many other groups investigating similar classes of material. Within a year, materials were discovered with a Tc of 120 K (-150 °C). This was significant because superconductivity could be achieved by cooling with liquid nitrogen, which is about the same price as beer. Unfortunately, over the past thirty years, there has been little progress at increasing Tc to higher temperatures. Room temperature superconductivity remains a holy grail.

The discovery of Bednorz and Muller generated considerable excitement in the physics community, attracting many new researchers to superconductivity research. In March 1987 a special session was held during a regular meeting of the American Physical Society in New York City. A large ballroom was overflowing with more than one thousand physicists. I was one of thousands more outside watching on a TV monitor. Each speaker was only allowed three minutes to present their work and the session went long past midnight. This event was described on the front page of The New York Times as the ``Woodstock of Physics’’, in honour of the famous rock music festival held in New York state, and considered as emblematic of the 1960s.

Scientific history is full of serendipity. Some discoveries are accidental. It is now known that the reason that Bednorz and Muller chose to focus on this class of materials (strong interaction of electrons with atomic vibrations) was actually wrong. The high Tc does not arise from this interaction, but rather from a strong magnetic interaction between the electrons and from the two-dimensionality of the materials. The latter is a result of the layered crystal structure shown in Figure 5.2. Although the discovery was arguably somewhat serendipitous, its profound significance was shown in 1987, when Bednorz and Muller were awarded the Nobel Prize. In contrast, most scientists receive the prize decades after their ground-breaking discovery.

Figure 1. The repeat unit for the crystal structure of a superconducting copper oxide, BiSrCaCuO. A key ingredient is the layers of copper and oxygen atoms, which are isolated from each other by a large number of other atoms. The chemical complexity is reflected in the unit cell containing more than 50 atoms, including 5 different chemical elements.

From a fundamental physics point of view the superconductivity of these materials is not the only interesting and theoretically challenging property. The materials exhibit two new states of matter, known as the pseudogap state and the strange metal (see the phase diagram in Figure 5.3.). These conducting states have properties distinctly different from those found in common metals such as copper and gold.

Figure 2. Phase diagram of copper oxide superconductors. Temperature (T) versus doping. Doping describes the chemical composition of the material, particularly the density of charge carriers. The different states are antiferromagnet (AF), superconductor (SC), regular metal (FL), strange metal, and pseudogap.

Since 1986 more than ten thousand scientific papers have been published concerning possible theories to describe the different states in the phase diagram (Figure 5.3). Although some progress has been made, there is still no single accepted theory, and particularly no theory that has the simplicity and predictive power of the BCS theory of superconductivity in simple metals such as lead and tin. Developing a comprehensive theory remains one of the outstanding problems in Condensed Matter Physics.

Both experimental and theoretical studies suggest that all this rich new physics requires the low-dimensionality of these materials, i.e., they are almost living in Flatland.

But, why is low-dimensionality crucial? There is no simple explanation for this, but generally as the dimension of a system gets lower, the constituents fluctuate more (e.g. the atoms move around more), conventional orders become less stable, and new states of matter become possible.

Any comments?

Particularly how to make this more accessible and interesting to a general audience.