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

Benalcazar, Wladimir Alejandro

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https://hdl.handle.net/2142/101538 Copy

Description

Title

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

Author(s)

Benalcazar, Wladimir Alejandro

Issue Date

2018-07-06

Director of Research (if dissertation) or Advisor (if thesis)

Hughes, Taylor

Doctoral Committee Chair(s)

Vishveshwara, Smitha

Committee Member(s)

• Gadway, Bryce
• Lorenz, Virginia

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2018-08

Type of Resource

text

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

Copyright and License Information

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

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