An ideal material: Solving a mystery leads to the discovery of a true topological insulator

As insulators are cooled to absolute zero, their ability to insulate effectively becomes infinite. About 40 years ago, scientists observed that, under these conditions, some insulators atypically retain a tiny bit of conductivity. These materials, termed Kondo insulators, were not well-understood, until recently.

In Kondo insulators two ingredients combine to create what are called "heavy fermions." In materials such as SmB6, some of the electrons are effectively pinned, only having a spin degree of freedom. This is in contrast to the speedy conduction electrons, which can also move in the crystal, endowing it with metallic character. The energy-momentum relationship (band structure) is flat for the pinned electrons. The conduction electrons would normally have a quadratic ("U" shaped) energy-momentum relationship, but at low temperatures, they strongly interact with the effectively stationary electrons. The band structure reorganizes to take on more of the flattened character of the stationary electrons. This hybridization gives rise to electrons that act as if they are sluggish and is the origin of the term 'heavy fermions.' The transition from metal to insulator, where the electrons behave, in effect, as if they are 1000 times heavier, starts to occur as the system is cooled below 50 K (see illustration). But then something strange happens a few degrees above absolute zero.

Maxim Dzero is an expert in heavy fermion materials: "Decades ago, people went through the periodic table making all sorts of combinations of elements. With this material, the major mystery in 1970s was that it was an insulator that at low temperatures, but still retained some small residual conductivity."

The missing piece of the puzzle lay with theory that wouldn't been developed until recent years. Above 4 K, SmB6 appears to be an insulator; looking below 4 K, it is a metal with high resistivity. This seemed confusing until recently when condensed matter theorists who study topology claim that this is exactly what you should see in a topological insulator.

A perfect topological insulator would be insulating in the bulk, but, in 3-dimensions, allow current to pass over the surface. Predicting these materials is tricky and while scientists have some hints as to the ingredients, finding them is somewhat serendipitous. Even cold atoms interacting with lasers have been proposed as a candidate for realizing this kind of physics. In recent years, researchers have studied bismuth compounds as a topological material. Unfortunately, interactions and defects tend to destroy their bulk insulating behavior, making it difficult to study the existence of conducting surface states.

In 2010**, JQI and PFC-supported scientists at the CMTC made were able to show that the mystery surrounding Kondo insulators could be explained using topological theory. It turns out that the strong interactions create a situation where the surface conducting states are truly independent and isolated from the bulk. Recently, experimental groups have verified that SmB6 is indeed a true 3D topological insulator, and in fact, is the first compound to be classified as such.

An experiment at University of Michigan involves attaching 8 electrical contacts to a thin sample in a novel way so as to unambiguously distinguish between bulk and surface conduction. Independently, a group from the University of California at Irvine has made voltage measurements, probing the Hall effect. They observe that the Hall resistance is independent of sample thickness, which is consistent with SmB6 supporting surface conduction. If the bulk was conducting, then the resistance would increase as the sample thickness was decreased.

In a related, third experiment at the University of Maryland's Center for Nanophysics and Advanced Materials, researchers have reported careful measurements of the Kondo-insulating behavior of SmB6 at different temperatures, which supports the presence of underlying topological physics.

The surface conducting states of a topological insulator are expected to be quite impervious to disorder. Indeed, the experiments indicate this. Dzero explains, "The transport properties are quite good in spite of the crude things that are done to the sample. It is remarkable that the surface conductivity does not change."

Victor Galitski, in response to the experimental work that is posted currently on the open-access arXiv discusses the strength of the measurements, "There is one major qualitative prediction to distinguish the topological insulator: surface conduction. This is the first material in the world that does this. There is no other conceivable theory that will explain it besides topological insulators."

**Theory papers:

Theory of topological Kondo insulators, Maxim Dzero, Kai Sun, Piers Coleman, and Victor Galitski, Physical Review B (2012)

Topological Kondo Insulators, Maxim Dzero, Kai Sun, Piers Coleman, and Victor Galitski, Physical Review Letters, (2010)

*Experimental papers:

Discovery of the First Topological Kondo Insulator: Samarium Hexaboride, Steven Wolgast, Çağlıyan Kurdak, Kai Sun, J. W. Allen, Dae-Jeong Kim, Zachary Fisk, arXiv:1211.5104v2

Robust Surface Hall Effect and Nonlocal Transport in SmB6: Indication for an Ideal Topological Insulator, J. Botimer, D.J. Kim, S. Thomas, T. Grant, Z. Fisk and Jing Xia, arXiv:1211.6769

Hybridization, Correlation, and In-Gap States in the Kondo Insulator SmB6 Xiaohang Zhang, N. P. Butch, P. Syers, S. Ziemak, Richard L. Greene, and J. Paglione, arXiv:1211.5532