Session D2: Correlated System including Topological Insulators: Materials, Measurements, and Majorana Modes

Tunable topological insulators with a single spin-polarized surface Dirac cone

The topological insulator is a fundamentally new time-reversal-invariant topologically ordered phase of matter, which exhibits exotic quantum-Hall-like behavior even in the absence of an applied magnetic field. These materials are characterized by a spin-orbit coupling induced bulk energy gap and an odd number of spin-polarized Dirac cones localized on their surfaces. In this talk, I will review the first experimental realization of the topological insulator in Bi$_{1-x}$Sb$_{x }$[1,2], and then report our recent experimental discovery and findings of a new generation of topological insulators with order-of-magnitude larger bulk band gaps and a single spin-helical surface Dirac cone [3,4]. I will also discuss a novel `effective gating' technique that can be used to optimize the insulating properties of the bulk, and to tune the Dirac carrier density on the surfaces of these new topological insulators [5]. These experiments pave the way for future transport based studies of topological insulator devices, and offer the potential for a graphene-like revolution to take place for topological insulators. [1] ``A topological Dirac insulator in a quantum spin Hall phase'', D. Hsieh et al., Nature 452, 970 (2008). [2] ``Observation of unconventional quantum spin textures in topological insulators'', D. Hsieh et al., Science 323, 919 (2009). [3] ``Observation of a large-gap topological-insulator class with a single Dirac cone on the surface'', Y. Xia et al., Nature Phys. 5, 398 (2009). [4] ``Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$'', D. Hsieh et al., Phys. Rev. Lett., 103, 146401 (2009). [5] ``A tunable topological insulator in the spin helical Dirac transport regime'', D. Hsieh et al., Nature 460, 1101 (2009).   

Quantum oscillations in a topological insulator Bi-Sb

It has been elucidated by photoemission that Bi$_{1-x}$Sb$_x$ alloy in the insulating doping range (0.07 $\le x \le$ 0.22) is a topological insulator, where an insulating bulk supports an intrinsically metallic surface. However, the relevance of the metallic surface state in the transport properties of Bi$_{1-x}$Sb$_x$ has been unclear. In high-quality Bi$_{0.91}$Sb$_{0.09}$ crystals, we observe strong quantum oscillations bearing a clear 2D character, which gives compelling evidence that a 2D electron system is responsible for the metallic transport observed in nominally-insulating Bi$_{0.91}$Sb$_{0.09} $ [A. A. Taskin and Y. Ando, Phys. Rev. B {\bf 80}, 085303 (2009)]. A puzzling aspect of our finding is that the amplitude of the 2D quantum oscillations is orders of magnitude larger than what is naively expected for the surface electrons, possibly pointing to a novel physics of helical Dirac fermions. For a higher doping of $x$ = 0.17, we obtain an even more puzzling result that the quantum oscillations present a very unusual angular dependence that defies any conventional interpretations in terms of Fermi surfaces. We are trying to understand it by invoking novel conduction channels in topological insulators. Work in collaboration with A. A. Taskin.   

Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors

A time reversal invariant (TRI) topological superconductor has a full pairing gap in the bulk and topologically protected gapless states on the surface or at the edge. In this paper, we show that in the weak pairing limit, the topological quantum number of a TRI superconductor can be completely determined by the Fermi surface properties, and is independent of the electronic structure away from the Fermi surface. In three dimensions (3D), the integer topological quantum number in a TRI superconductor is determined by the sign of the pairing order parameter and the first Chern number of the Berry phase gauge field on the Fermi surfaces. In two (2D) and one (1D) dimension, the $Z_2$ topological quantum number of a TRI superconductor is determined simply by the sign of the pairing order parameter on the Fermi surfaces. We also obtain a generic and explicit expression of the $Z_2$ topological invariant in 1D and 2D.   

Dislocations as ideal metallic quantum wires in topological insulators

Topological insulators are novel states of matter that have been realized in the recently discovered systems such as Bi$_{0.9}$Sb$_{0.1}$. What happens if a topological defect is present in such a material? In this talk I will show that strikingly, dislocation lines in a topological insulator can be metallic - i.e. associated with one dimensional fermionic excitations. The condition for the appearance of these modes is derived, and only found to depend on the ``weak'' topological indices. In contrast to electrons in a regular quantum wire, these modes are topologically protected, and not scattered by disorder. Our results provide a novel route to creating a potentially ideal quantum wire in a bulk solid. Since dislocations are ubiquitous in real materials, they could dominate spin and charge transport in topological insulators. Experimental signatures of such dislocation hosted 1D metals are discussed. The existence of these metallic modes has important consequences for the classification of topological band structures in the presence of lattice order. We also report new results for lattice topological superconductors in three dimensions, where both the two and one dimensional indices appear. (Ref: Ying Ran, Yi Zhang and Ashvin Vishwanath, Nature Physics 5, 298, 2009)