A new experimental approach for the exploration of topological quantum phenomena : Topological Insulators and Superconductors

The three-dimensional topological insulator (originally called topological insulators) is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of quantum-Hall-like states. Their topological order can be realized at room temperatures without magnetic fields and they can be turned into magnets and exotic superconductors leading to world-wide interest and activity in topological insulators. One of the major challenges in going from quantum Hall-like 2D states to 3D topological insulators is to develop new experimental approaches/methods to precisely probe this novel form of topological-order since the standard tools and settings that work for IQH-state also work for QSH states. The method to probe 2D topological-order is exclusively with charge transport, which either measures quantized transverse conductance plateaus in IQH systems or longitudinal conductance in quantum spin Hall (QSH) systems. In a 3D topological insulator, the boundary itself supports a two dimensional electron gas (2DEG) and transport is not (Z$_2$) topologically quantized. In this paper, we review the birth of momentum- and spin-resolved spectroscopy as a new experimental approach and as a directly boundary sensitive method to study and prove topological-order in three-dimensions via the direct measurements of the topological invariants {$ u_o$} that are associated with the Z$_2$ topology of the spin-orbit band structure and opposite parity band

Observation of topological order in a Superconducting doped topological insulator (based on the Bi2Se3 class)

Topological insulators embody a new state of matter characterized entirely by the topological invariants of the bulk electronic structure rather than any form of spontaneously broken symmetry. Unlike the 2D quantum Hall or quantum spin-Hall-like systems, the three dimensional (3D) topological insulators can host magnetism and superconductivity which has generated widespread research activity in condensed-matter and materials-physics communities. Thus there is an explosion of interest in understanding the rich interplay between topological and the broken-symmetry states (such as superconductivity), greatly spurred by proposals that superconductivity introduced into certain band structures will host exotic quasiparticles which are of interest in quantum information science. The observations of superconductivity in doped Bi_2Se_3 (Cu$_x$Bi$_2$Se$_3$) and doped Bi_2Te_3 (Pd$_x$-Bi$_2$Te$_3$ T$_c$ $sim$ 5K) have raised many intriguing questions about the spin-orbit physics of these ternary complexes while any rigorous theory of superconductivity remains elusive. Here we present key measurements of electron dynamics in systematically tunable normal state of Cu$_x$Bi$_2$Se$_3$ (x=0 to 12%) gaining insights into its spin-orbit behavior and the topological nature of the surface where superconductivity takes place at low temperatures. Our data reveal that superconductivity occurs (in sample compositions) with electrons in a bulk relativistic kinematic regime and we identify that an unconventional doping mechanism causes the topological surface character of the undoped compound to be preserved at the Fermi level of the superconducting compound, where Cooper pairing occurs at low temperatures. These experimental observations provide important clues for developing a theory of topological-superconductivity in 3D topological insulators.