Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors

This dissertation discusses extensions of the theory of polarization in crystalline insulators. The notion that electronic wave functions of energy bands in crystalline insulators have Berry phases associated with the positions of electronic charge is at the basis of our understanding of topological band theory. We show, by using the Berry phase formulation and generalizations of it, as well as by exact diagonalization of tight-binding models, that crystalline insulators can generate charge and polarization patterns compatible with the notion of quadrupole and octupole electric moments. In the presence of certain symmetries, these moments are quantized, and their boundary signatures fractionalized. These higher multipole moments then correspond to new symmetry-protected topological phases (SPTs). A salient signature of these SPTs is the existence of zero-dimensional, corner-localized mid-gap energy states. We then study topological crystalline superconductors, in which these zero-dimensional mid-gap states amount to the existence of Majorana bound states (MBS). We thoroughly classify these systems when rotational group symmetries are enforced, and investigate the existence of zero-dimensional MBS trapped at topological defects in these crystals. The finding of these higher multipole moments or generalizations of them to other platforms constitute a new paradigm for the realization of symmetry protected topological phases.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Benalcazar, Wladimir Alejandro

Contributors dc:contributor

• Hughes, Taylor
• Vishveshwara, Smitha
• Gadway, Bryce
• Lorenz, Virginia

• condensed matter physics, topological phases of matter, higher-order topological phases, topological insulators, topological superconductors, topological photonics, polarization, dipole moment, quadrupole moment, Majorana bound states

Statement dc:rights

• copyright 2018 by Wladimir A. Benalcazar. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101538

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101538