Eigenvalue estimates for bilayer graphene
© 2019, Springer Nature Switzerland AG. Recently, Ferrulli–Laptev–Safronov (2016) obtained eigenvalue estimates for an operator associated with bilayer graphene in terms of L q norms of the (possibly non-self-adjoint) potential. They proved that for 1 < q< 4 / 3 all nonembedded eigenvalues lie...
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ftloughboroughun:oai:figshare.com:article/13227638 2023-05-15T17:07:17+02:00 Eigenvalue estimates for bilayer graphene Jean-Claude Cuenin 2019-02-09T00:00:00Z https://figshare.com/articles/journal_contribution/Eigenvalue_estimates_for_bilayer_graphene/13227638 unknown 2134/13227638.v1 https://figshare.com/articles/journal_contribution/Eigenvalue_estimates_for_bilayer_graphene/13227638 CC BY-NC-ND 4.0 CC-BY-NC-ND Uncategorized Bilayer graphene Trigonal warping Eigenvalue estimates Complex potentials Embedded eigenvalues Science & Technology Physical Sciences Physics Multidisciplinary Particles & Fields Mathematical SCHRODINGER-OPERATORS BOUNDS INEQUALITIES DIRAC Mathematical Physics Atomic Molecular Nuclear Particle and Plasma Physics Text Journal contribution 2019 ftloughboroughun 2022-01-01T19:16:42Z © 2019, Springer Nature Switzerland AG. Recently, Ferrulli–Laptev–Safronov (2016) obtained eigenvalue estimates for an operator associated with bilayer graphene in terms of L q norms of the (possibly non-self-adjoint) potential. They proved that for 1 < q< 4 / 3 all nonembedded eigenvalues lie near the edges of the spectrum of the free operator. In this note, we prove this for the larger range 1 ≤ q≤ 3 / 2. The latter is optimal if embedded eigenvalues are also considered. We prove similar estimates for a modified bilayer operator with so-called trigonal warping term. Here, the range for q is smaller since the Fermi surface has less curvature. The main tool is new uniform resolvent estimates that may be of independent interest and is collected in an appendix (in greater generality than needed). Other Non-Article Part of Journal/Newspaper laptev Loughborough University: Figshare |
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Loughborough University: Figshare |
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ftloughboroughun |
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unknown |
topic |
Uncategorized Bilayer graphene Trigonal warping Eigenvalue estimates Complex potentials Embedded eigenvalues Science & Technology Physical Sciences Physics Multidisciplinary Particles & Fields Mathematical SCHRODINGER-OPERATORS BOUNDS INEQUALITIES DIRAC Mathematical Physics Atomic Molecular Nuclear Particle and Plasma Physics |
spellingShingle |
Uncategorized Bilayer graphene Trigonal warping Eigenvalue estimates Complex potentials Embedded eigenvalues Science & Technology Physical Sciences Physics Multidisciplinary Particles & Fields Mathematical SCHRODINGER-OPERATORS BOUNDS INEQUALITIES DIRAC Mathematical Physics Atomic Molecular Nuclear Particle and Plasma Physics Jean-Claude Cuenin Eigenvalue estimates for bilayer graphene |
topic_facet |
Uncategorized Bilayer graphene Trigonal warping Eigenvalue estimates Complex potentials Embedded eigenvalues Science & Technology Physical Sciences Physics Multidisciplinary Particles & Fields Mathematical SCHRODINGER-OPERATORS BOUNDS INEQUALITIES DIRAC Mathematical Physics Atomic Molecular Nuclear Particle and Plasma Physics |
description |
© 2019, Springer Nature Switzerland AG. Recently, Ferrulli–Laptev–Safronov (2016) obtained eigenvalue estimates for an operator associated with bilayer graphene in terms of L q norms of the (possibly non-self-adjoint) potential. They proved that for 1 < q< 4 / 3 all nonembedded eigenvalues lie near the edges of the spectrum of the free operator. In this note, we prove this for the larger range 1 ≤ q≤ 3 / 2. The latter is optimal if embedded eigenvalues are also considered. We prove similar estimates for a modified bilayer operator with so-called trigonal warping term. Here, the range for q is smaller since the Fermi surface has less curvature. The main tool is new uniform resolvent estimates that may be of independent interest and is collected in an appendix (in greater generality than needed). |
format |
Other Non-Article Part of Journal/Newspaper |
author |
Jean-Claude Cuenin |
author_facet |
Jean-Claude Cuenin |
author_sort |
Jean-Claude Cuenin |
title |
Eigenvalue estimates for bilayer graphene |
title_short |
Eigenvalue estimates for bilayer graphene |
title_full |
Eigenvalue estimates for bilayer graphene |
title_fullStr |
Eigenvalue estimates for bilayer graphene |
title_full_unstemmed |
Eigenvalue estimates for bilayer graphene |
title_sort |
eigenvalue estimates for bilayer graphene |
publishDate |
2019 |
url |
https://figshare.com/articles/journal_contribution/Eigenvalue_estimates_for_bilayer_graphene/13227638 |
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laptev |
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laptev |
op_relation |
2134/13227638.v1 https://figshare.com/articles/journal_contribution/Eigenvalue_estimates_for_bilayer_graphene/13227638 |
op_rights |
CC BY-NC-ND 4.0 |
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CC-BY-NC-ND |
_version_ |
1766062652783591424 |