A hex on protection

Credit: © 2010 APS

Three-dimensional topological insulators are bulk insulators with charged surface states that are distinct from the bulk. The surface states are gapless (metallic) with linear excitation energy that in three dimensions traces out a cone, as does the Dirac energy spectrum for massless fermions. Robust against perturbations and scattering, such surface states are 'topologically protected' — the surface contains an odd number of 'Dirac cones' as a result of the topological index (Chern number) that characterizes the electronic band structure. Besides being mathematical curiosities, these states are also under consideration for fault-tolerant quantum computation and low-power spintronic devices.

In 2008, Bi₂Te₃ was predicted to be the simplest three-dimensional topological insulator (Q. Xiao-Liang et al. Phys. Rev. B 78, 195424; 2008). Soon thereafter, angle-resolved photoemission spectroscopy experiments on Sn-doped Bi₂Te₃ — doping shifts the bulk states away from the Fermi energy, leaving only the surface states accessible to the charge carriers — confirmed the presence of a single Dirac cone at the centre of the unit cell in momentum space (Y. L. Chen et al. Science 325, 178–181; 2009). The Fermi surface associated with the surface states changes volume with doping concentration and varies from a hexagram at zero doping to a hexagon. Using scanning tunnelling microscopy (STM), Zhanybek Alpichshev and co-workers have now imaged the surface of Bi₂Te₃ and studied the protected nature of the surface states (Z. Alpichshev et al. Phys. Rev. Lett. 104, 016401; 2010).

Constant-energy contours of the surface-state bands of pure Bi₂Te₃ are pictured, showing the change from the Dirac point at −330 meV (hexagon; upper left) to 0 meV (hexagram; lower right), where red denotes the occupied states. From about −100 meV, the surface becomes warped. Oscillations resulting from defect-induced interference patterns of electron waves detected by STM abruptly cease below −100 meV: backscattering is suppressed.

So far, these angle-resolved photoemission spectroscopy and STM data are consistent with protected surface states. But the oscillations in STM spectra show a linear energy dependence where Alpichshev et al. believe the Fermi surface changes from convex hexagon to concave hexagram. The presence of hexagonal warping may indicate extra scattering channels along 'nesting wave vectors' that connect parts of the Fermi surface together (L. Fu Phys. Rev. Lett. 103, 266801; 2009). Thus surface-band deformations could lead to competing ground states that would otherwise have been forbidden.