Spin Texture and Circular Dichroism in Photoelectron Spectroscopy from the Topological Insulator\({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}\): First-Principles Photoemission Calculations

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.

A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry based classification of condensed matter. Exotic spin transport phenomena such as the dissipationless quantum spin Hall effect have been speculated to originate from a novel topological order whose identification requires a spin sensitive measurement, which does not exist to this date in any system (neither in Hg(Cd)Te quantum wells nor in the topological insulator BiSb). Using Mott polarimetry, we probe the spin degrees of freedom of these quantum spin Hall states and demonstrate that topological quantum numbers are uniquely determined from spin texture imaging measurements. Applying this method to the Bi{1-x}Sb{x} series, we identify the origin of its novel order and unusual chiral properties. These results taken together constitute the first observation of surface electrons collectively carrying a geometrical quantum (Berry's) phase and definite chirality (mirror Chern number, n_M =-1), which are the key electronic properties for realizing topological computing bits with intrinsic spin Hall-like topological phenomena. Our spin-resolved results not only provides the first clear proof of a topological insulating state in nature but also demonstrate the utility of spin-resolved ARPES technique in measuring the quantum spin Hall phases of matter.