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Chandrasekaran_Shtyk_Betouras_Chamon_PRR_2020.pdf (2.49 MB)

Catastrophe theory classification of Fermi surface topological transitions in two dimensions

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journal contribution
posted on 2021-01-05, 11:46 authored by Anirudh Chandrasekaran, Alex Shtyk, Joseph BetourasJoseph Betouras, Claudio Chamon
We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure, strain, bias voltage, etc), the theory guarantees that the singularity belongs to to one of seventeen standard types. We show that at each of these singularities the density of states diverges as a power law, with a universal exponent characteristic of the particular catastrophe, and we provide its universal ratio of amplitudes of the prefactors of energies above and below the singularity. We further show that crystal symmetry restricts which types of catastrophes can occur at the points of high symmetry in the Brillouin zone. For each of the seventeen wallpaper groups in two-dimensions, we list which catastrophes are possible at each high symmetry point.

Funding

DOE Grant No. DEFG02-06ER46316

Controlling unconventional properties of correlated materials by Fermi surface topological transitions and deformations.

Engineering and Physical Sciences Research Council

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History

School

  • Science

Department

  • Physics

Published in

Physical Review Research

Volume

2

Issue

1

Publisher

American Physical Society (APS)

Version

  • VoR (Version of Record)

Publisher statement

This is an Open Access Article. It is published by American Physical Society (APS) under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

2020-02-24

Publication date

2020-03-23

Copyright date

2020

eISSN

2643-1564

Language

  • en

Depositor

Dr Joseph Betouras. Deposit date: 2 January 2021

Article number

013355

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