Topological semimetals and nodal superconductors

Chang, Po-Yao

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https://hdl.handle.net/2142/87989 Copy

Description

Title

Topological semimetals and nodal superconductors

Author(s)

Chang, Po-Yao

Issue Date

2015-07-06

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

Ryu, Shinsei

Doctoral Committee Chair(s)

Hughes, Taylor L.

Committee Member(s)

• Mason, Nadya
• Cooper, S. Lance

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Topology
• Topological semimetals
• Nodal superconductors
• Entanglement spectrum
• Topological insulators
• Non-centrosymmetric superconductors
• K-theory
• Classificaltions

Abstract

Besides topological band insulators, which have a full bulk gap, there are also gapless phases of matter that belong to the broad class of topological materials, such as topological semimetals and nodal superconductors. We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.

Graduation Semester

2015-8

Type of Resource

text

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http://hdl.handle.net/2142/87989

Copyright and License Information

Copyright 2015 Po-Yao Chang

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