Topological Defects and Entanglement in Topological Insulators

Ashvin Vishwanath, University of California, Berkeley

The talk will discuss the following two topics.

Topological defects, such as domain walls and vortices, have long fascinated physicists. We show that dislocation lines are associated with one dimensional fermionic excitations in a‘topological insulator’, a novel band insulator believed to be realized in the bulk materials such as Bi_0.9Sb_0.1. In contrast to fermionic excitations in a regular quantum wire, these modes are topologically protected like the helical edge states of the quantum spin-Hall insulator, and not scattered by disorder. Since dislocations are ubiquitous in real materials, these excitations could dominate spin and charge transport in topological insulators. Our results provide a novel route to creating a potentially ideal quantum wire in a bulk solid.

How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases, like topological insulators, that share the same symmetry but differ at the level of topology. The entanglement spectrum has been proposed as a ground state property that captures characteristic edge excitations. Here we study the entanglement spectrum of topological insulators. We first show that insulators with topological surface states will necessarily also have protected modes in the entanglement spectrum. However, surprisingly, the converse is not true. Protected entanglement modes can also appear for insulators without physical surface states, in which case they capture a more elusive topological property. This is illustrated by considering insulators with only inversion symmetry. Inversion is shown to act in an unusual way on the entanglement spectrum, that leads to this protection. A connection is made to the quantized magneto-electric polarizability, which is forced by inversion symmetry to be quantized.