Crystalline topological phases: Bulk-boundary correspondence, geometric response, entanglement, and non-Hermitian skin effect

Zhu, Penghao

Permalink

https://hdl.handle.net/2142/121922 Copy

Description

Title

Crystalline topological phases: Bulk-boundary correspondence, geometric response, entanglement, and non-Hermitian skin effect

Author(s)

Zhu, Penghao

Issue Date

2023-07-28

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

Hughes, Taylor L

Doctoral Committee Chair(s)

Bradlyn, Barry

Committee Member(s)

• Madhavan, Vidya
• Gadway, Bryce

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Topological crystalline phases

Abstract

This thesis focuses on theoretical investigations of topological crystalline phases in both Hermitian and non-Hermitian systems. The first part of this thesis studies the geometric response and entanglement structure of rotation symmetric topological phases. We compute the fractional charges trapped at disclinations of rotation symmetric topological insulators from the Wannier representations in real space, and use band representation theory to construct topological indices of the fractional disclination charge. We find the disclination charge is fractionalized in units of e/n for Cn-rotation symmetric topological crystalline insulators; and for spin-1/2 topological crystalline insulators, with additional time reversal symmetry, the disclination charge is fractionalized in units of 2e/n. We also construct the relationship between the configuration of Wannier orbitals and the number of protected in-gap states in the entanglement spectrum for different symmetric cuts in real space, with which we express the fractional corner charge in terms of the number of protected in-gap states of the entanglement spectrum. The second part investigates delicate topological phases, which are novel phases beyond any previously known classification. We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite – assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. We show that the geometric component of this subextensive moment is related to the surface quantum anomalous Hall conductivity and gapless chiral hinge modes, which is exemplified by the Hopf insulator. We also introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator and serves as the first example of Class-AII delicate topological insulator. Besides novel bulk-boundary correspondence, we furthermore demonstrate that the phase of the reflection amplitude can probe the delicate topology by capturing a characteristic feature of a delicate TI. In the last part of this thesis, we explore geometric responses and non-Hermitian skin effect of semi-metallic and metallic systems. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle which is an integer multiple of 2π, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines and thus non-Hermitian skin effects. We also demonstrate that rank-2 chirality imbalances can be established in a non-Hermitian lattice system leading to momentum-resolved chiral dynamics, and a rank-2 NHSE where there are both edge- and corner-localized skin modes. We then experimentally test this phenomenology in a 2-dimensional topolectric circuit that implements a NH Hamiltonian with a long-lived rank-2 chiral mode. Finally, we study spin rank-2 chiral modes that correspond to spin-momentum locking terms with conserved, commuting pseudospins built from a combination of spin and orbitals. The 2D spin rank-2 chrail mode has linear dispersion and anomalous charge and pseudospin currents, which can be realized as a surface mode of a 3D Weyl semimetal. Crucially, there is a mixed quadrupole moment in the 3D Weyl semimetal that captures a mixed pseudospin-charge bulk response cancelling the anomaly of surface modes. This work opens an important new direction in the quasi-topological semimetal responses characterized by mixed multipole moments of the nodal Fermi surfaces.

Graduation Semester

2023-12

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Penghao Zhu

Owning Collections