Visualizing Quantum States of Matter
Topological Insulators
Energy-band structure and spin orientation for normal and topological surface states. (a) In a normal metal, electrons occupy energy (E) levels up to a maximum level, the Fermi level, and for a given momentum k = (kx,ky) they have two possible spin orientations (spin-up and spin-down). (b) In a topological surface state, the energy levels form two bands that meet at their tips, and for a given k there is only one spin orientation. (Link to M. Franz News and Views in Nature)
Energy-band structure and spin orientation for normal and topological surface states. (a) In a normal metal, electrons occupy energy (E) levels up to a maximum level, the Fermi level, and for a given momentum k = (kx,ky) they have two possible spin orientations (spin-up and spin-down). (b) In a topological surface state, the energy levels form two bands that meet at their tips, and for a given k there is only one spin orientation (more info).

Overview

Soon after the discovery of quantum mechanics, solid-state physics provided the fundamental understanding of why some solids are insulating (like diamond) and others are highly conducting (like graphite), even though they are comprised of the same element. Now, 70 years later, the concept of insulators and metals is being revised again. In the last few years, through a set of theoretical and experimental developments, physicists have come to realize that insulators can actually be divided into two categories. The first is the “ordinary” insulator ,such as diamond, in which electrons fully occupy energy bands (which derive their character from atomic orbitals). The next available electronic states are rather far away in energy. This energy gap is what renders diamond and silicon insulating. The second group are the topological insulators, in which the energy gap between the occupied and empty states is fundamentally modified due to the spin-orbit interaction. The interaction between electrons’ spin and orbital angular momentum has its roots in the physics of relativity, where the electric and magnetic field can be interchanged depending on the vantage point of an observer. This interaction plays a role in materials composed of heavy elements such as Bi or Sb. In topological insulators, the spin-orbit interaction is so strong that the insulating energy gap is inverted — the states that should have been at high energy above the gap appear below the gap. This twist in the order of electronic states, like the twist in the Mobius band, cannot be “unwound” (this accounts for the topological nature of the new class of insulators). As a result, we have highly conducting metallic states on the surface — a feature not seen in ordinary insulators. Moreover, these surface states have been theoretically predicted and experimentally demonstrated to have electrical properties that are fundamentally different from other two-dimensional conducting states discovered to date. They are immune to scattering from ordinary defects and can carry electrical currents even in the presence of large energy barriers that stop other electronic states. Underlying the novel properties of these topological surfaces states are their unusual spin texture (with the so-called π Berry phase) and their light-like (Dirac) energy-momentum relation. The prediction and confirmation of these novel electronic states have led to an explosion of activity in this area of physics.

Recent Progress

Our group has carried out some of first STM experiments on topological insulators and their novel surface states. We have demonstrated that these states are immune to the backscattering that strongly suppresses electrical transport for normal electronic states such as those of simple metals (as in a Cu wire) [1]. We have also shown that these states transmit through crystalline barriers that stop other surface states [2]. These results establish some of the most exotic properties of these novel states predicted to date.