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Topological invariants of eigenvalue intersections and decrease of Wannier functions Panati, Gianluca
Description
We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a topological invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n in Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. The set of the canonical models is proved to be universal, in a suitable sense. With the help of this universality theorem, we show that the single band Wannier function w satisfies w(x) ≍ |x|−3/2. In particular, the expectation value of the modulus of the position operator is infinite.
Item Metadata
Title |
Topological invariants of eigenvalue intersections and decrease of Wannier functions
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2013-05-01
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Description |
We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a topological invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n in Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. The set of the canonical models is proved to be universal, in a suitable sense. With the help of this universality theorem, we show that the single band Wannier function w satisfies w(x) ≍ |x|−3/2. In particular, the expectation value of the modulus of the position operator is infinite.
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Extent |
29 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Sapienza Universita di Roma
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Series | |
Date Available |
2014-08-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivs 2.5 Canada
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DOI |
10.14288/1.0043396
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivs 2.5 Canada