Expt 8) Metal-insulator transitions

Prior to 1939, the Bloch-Wilson rule for predicting whether a given material would be an insulator or a metal reigned supreme. However, all was not well as early as 1937. De Boer and Verwey, in a famous paper, pointed out that 3d electron systems like NiO are orders of magnitude less conductive (about a factor of 10¹⁰ less!) than expected by the simple Wilson counting rule. In a short monograph, Peierls and Mott shared some of their ideas on the paper by de Boer and Verwey, which is a very interesting read because of the authors’ qualitative reasoning. The Mott/Peierls discussion is very representative of how physics is actually done. Most notably, they speculated on the role of the electron-electron Coulomb interaction despite others raising the possibility that the potential barriers between electrons were larger for some reason in 3d compounds. Only years later were the rather vague Mott/Peierls ideas made more quantitative.

Among the “anomalous” insulators discovered by de Boer and Verwey, Fe₃O₄ was unusual; it remained metallic despite belonging to the class of atypical 3d insulators. From the Bloch-Wilson perspective, though, Fe₃O₄ was a “normal” metal. Just two years later, in 1939, this sense of normalcy was shattered. Verwey demonstrated that Fe₃O₄ undergoes a transition from a high temperature metal to a low temperature insulator at 120K. The transition is evidenced in the resistivity plot below. It should be noted that magnetic and structural discontinuities are also observed at the same temperature. This work opened up the study of metal-insulator transitions as well as materials we refer to today as strongly correlated electron systems. It could no longer be that the barriers between the electrons were anomalously high in these 3d insulators — a new physical concept was needed. These kinds of problems remain largely unsolved today, though much progress has been made. It is from these kinds of correlated insulators that many years later, we would eventually get cuprate superconductivity. The metal-insulator problem would re-emerge with renewed ferocity.

Log() vs 1/T in Fe₃O₄ with different phase fractions of Fe₂O₃. When the concentration of Fe₂O₃ is high, the resistivity no longer exhibits a discontinuity. Image taken from here.

Expt 7) Resistance minimum and Kondo effect

In 1934, de Haas, de Boer and van den Berg showed that the low temperature resistance of “not very pure” gold exhibited a rather peculiar feature. There existed a minimum in the resistance as temperature was reduced. Below are two figures showing the resistance of as a function of temperature in the range from 1-5 K and from 4-12 K:

In normal metals, like gold, it was thought that as temperature decreased, one would always observe a decrease in resistance due to reduced phonon scattering and then a plateau at low temperatures due to the presence of impurities. It was thus surprising that in gold, and subsequently many other metals, the resistance possessed a minimum and then started to increase at lower temperatures. Understanding of this phenomenon, now known as the Kondo effect, took the combined effort of many physicists.

About 30 years after the initial discovery, material purity could be controlled to systematically investigate the effect of magnetic impurities on the resistance minimum. Clogston, Matthias and colleagues in 1961 showed that 1% of iron dissolved in a Nb-Mo alloy exhibited a Curie-Weiss susceptibility at low temperatures, which provided strong evidence of local moments. Then, in 1964, Sarachik and colleagues demonstrated that this 1% dissolution of Fe in Nb-Mo alloys systematically led to a resistance minimum. Below is the famous plot from Sarachik’s paper showing the resistance minimum as the Nb-Mo ratio was varied. When the susceptibility showed local moment formation, a minimum in the resistance developed:

A theoretical breakthrough was made in 1964 when J. Kondo used perturbation theory to analyze the s-d model developed by P.W. Anderson to show that a resistance minimum can arise due to the scattering of conduction electrons from magnetic impurities. However, only with the advent of the renormalization group was the problem fully solved by Wilson in 1975, as Kondo’s solution gave an unphysical logarithmic divergence in the resistance at low temperatures. It took more than 40 years to solve this seemingly innocent problem, which still continues to be of interest today in the context of heavy fermion superconductors and quantum dots.

Expt 6) Superfluidity in 4He

In 1938, Pyotr Kapitza and, independently, John F. Allen and Don Misener demonstrated that on cooling below the “lambda temperature”, the viscosity of liquid ⁴He suddenly reduced by orders of magnitude. Kaptiza coined the name “superfluidity” in his famous paper, where he also presciently compared superfluidity to superconductivity.

He used a rather ingenious experimental setup where the liquid flowed between two disks spaced about half a micron apart. By showing that the liquid helium in the superfluid phase flowed easily, while that in the normal phase did not, he estimated that the viscosity drops by about a factor of 1500. Strikingly, there is no data in the paper, but only a diagram of the apparatus he used to measure the viscosity (and to ensure that the flow of the liquid was laminar). Allen and Misener also published similar results, but their upper bound for the viscosity was orders of magnitude higher than Kapitza’s. They used flow through narrow capillaries to estimate the viscosity. While these results were quite definitive, it is worth remembering that experiments prior to these two had already shown a quite large drop in the viscosity on entering the superfluid state but with less spectacular results, presumably due to more turbulent flow. In these experiments, the researchers tried their best to ensure that the flow was largely laminar.

Below is a video showing a few of the dramatic effects in superfluid ⁴He.

Expt 5) Meissner-Oschsenfeld effect and, separately, persistent currents

There are actually two separate experiments that are worth highlighting here, as they both pertain to superconductivity.

Meissner-Oschenfeld effect is discovered in 1933
Prior to 1933, it was possible to interpret superconductivity as “perfect conductivity”. However, that all changed with Meissner and Ochsenfeld’s experiment. Not only was magnetic field screened in the superconducting state of lead and tin, but it was expelled when cooling below the superconducting transition temperature. Superconductors exhibit ideal diamagnetism independent of whether they are zero-field cooled or field-cooled (assuming the magnitude of the magnetic field is insufficient to destroy the superconductivity or induce vortices). Meisser and Ochsenfeld’s experiment demonstrated that superconductivity was not just associated with reduced scattering, but was a new bona-fide thermodynamic state. In contrast to persistent currents, perfect diamagnetism is an equilibrium effect and cannot be logically deduced from “infinite conductivity”. It is a separate physical phenomenon. Because it is an equilibrium effect, its observation is generally required for a compound to be classified as a superconductor.

Here is a translation of the original paper, which was written in German.

Persistent currents and Garrett Flim’s risky trip in 1932
Rather than making a great discovery, it is the showmanship of this experiment that really, for me, puts it on this list. Persistent currents in superconducting rings had already been observed in Kammerlingh Onnes’ laboratory by 1914. Persistent current, in contrast to the Meissner-Oschsenfeld effect, is a metastable non-equilibrium phenomenon.

Gerrit Flim worked in Kammerlingh Onnes’ laboratory, and continued doing so after Kammerlingh Onnes’ death in 1926. By 1932, technology had advanced to the point where liquid helium dewars had become portable. Thus, Flim set up a 200A current (!!) in a superconducting lead ring while in his Leiden laboratory and made the trip to the Royal Institution in London to show a stunned audience that the current was still flowing upon arrival. He did so by demonstrating that a compass needle deflected due to the persistent current in the ring. (If the temperature of the superconductor had accidentally exceeded the critical temperature during his trip, the current would have quickly dissipated, possibly resulting in major injuries!) More of the history of this story is here, from where the figure below is reproduced.