Catastrophe theory classification of Fermi surface topological transitions in two dimensions
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 si...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.013355 |
| _version_ | 1797211481198034944 |
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| author | Anirudh Chandrasekaran Alex Shtyk Joseph J. Betouras Claudio Chamon |
| author_facet | Anirudh Chandrasekaran Alex Shtyk Joseph J. Betouras Claudio Chamon |
| author_sort | Anirudh Chandrasekaran |
| collection | DOAJ |
| description | 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 one of seventeen standard types known as catastrophes. 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 for 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. |
| first_indexed | 2024-04-24T10:27:10Z |
| format | Article |
| id | doaj.art-8778e6aedaf04e4fbac907159a67ca30 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:27:10Z |
| publishDate | 2020-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-8778e6aedaf04e4fbac907159a67ca302024-04-12T16:51:54ZengAmerican Physical SocietyPhysical Review Research2643-15642020-03-012101335510.1103/PhysRevResearch.2.013355Catastrophe theory classification of Fermi surface topological transitions in two dimensionsAnirudh ChandrasekaranAlex ShtykJoseph J. BetourasClaudio ChamonWe 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 one of seventeen standard types known as catastrophes. 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 for 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.http://doi.org/10.1103/PhysRevResearch.2.013355 |
| spellingShingle | Anirudh Chandrasekaran Alex Shtyk Joseph J. Betouras Claudio Chamon Catastrophe theory classification of Fermi surface topological transitions in two dimensions Physical Review Research |
| title | Catastrophe theory classification of Fermi surface topological transitions in two dimensions |
| title_full | Catastrophe theory classification of Fermi surface topological transitions in two dimensions |
| title_fullStr | Catastrophe theory classification of Fermi surface topological transitions in two dimensions |
| title_full_unstemmed | Catastrophe theory classification of Fermi surface topological transitions in two dimensions |
| title_short | Catastrophe theory classification of Fermi surface topological transitions in two dimensions |
| title_sort | catastrophe theory classification of fermi surface topological transitions in two dimensions |
| url | http://doi.org/10.1103/PhysRevResearch.2.013355 |
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