Abstract:

It has recently been proposed that band insulators with strong spin-orbit coupling can support a new phase of quantum matter called a 'topological insulator'. This exotic phase of matter is a subject of intense research because it is predicted to give rise to dissipationless spin currents, axion electrodynamic phenomena and non-Abelian quasi-particles. However, it is experimentally challenging to identify a topological insulator because unlike ordinary phases of matter such as magnets, liquid crystals or superconductors, topological insulators are not described by a local order parameter associated with a spontaneously broken symmetry but rather by a quantum entanglement of its wavefunction, dubbed 'topological order'. Because conventional experimental probes are designed to be sensitive to local order parameters, methods of measuring topological order are relatively unknown.

Topologically ordered phases of matter are extremely rare, the most well known example being the quantum Hall phase, which is realized in a cold two-dimensional electron system subject to a large external magnetic field. Its topological order is identified by measuring a quantized magneto-transport, which is carried by robust conducting states localized along the one-dimensional edges of the sample. In topological insulators, intrinsic spin-orbit coupling simulates the effect of a spin-dependent external magnetic field, leading to quantum Hall-like physics without any external magnetic field. However, unlike quantum Hall phases, topological insulators exhibit no quantized transport response, therefore its topological order cannot be detected by means of a transport measurement.

In this thesis, we show that topological insulators exhibit robust conducting states that are localized on the two-dimensional surfaces of the sample. These surface states have an unusual spin-polarized band structure that cannot be realized on the surfaces of ordinary insulators, nor in purely two-dimensional electron systems. By measuring the spin-polarized band dispersion of surface states using a combination of synchrotron based spin- and angle-resolved photoemission spectroscopy (ARPES), we show that their topological order can be detected. In Chapter 1, we describe the relationship between the topological orders found in quantum Hall systems and in topological insulators. In Chapter 2, we provide a description of the experimental technique of spin-resolved ARPES and a general procedure for mapping spin-polarized surface state band structures. In Chapter 3, we apply this method to study the Bi1- x Sbx alloy series and demonstrate that a topological insulator is realized in a specific composition range. The work presented in this thesis constitutes the first experimental evidence of a topological insulator in nature.