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Title:Electric multipole moments and higher-order topological phases in crystalline insulators and superconductors
Author(s):Benalcazar, Wladimir Alejandro
Director of Research:Hughes, Taylor
Doctoral Committee Chair(s):Vishveshwara, Smitha
Doctoral Committee Member(s):Gadway, Bryce; Lorenz, Virginia
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):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
Abstract: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.
Issue Date:2018-07-06
Rights Information:copyright 2018 by Wladimir A. Benalcazar. All rights reserved.
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08

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