Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening

Abstract The relationship between electron momentum densities (EMDs) and a band gap is clarified in momentum space. The interference between wavefunctions via reciprocal lattice vectors, making a band gap in momentum space, causes the scattering of electrons from the first Brillouin zone to the othe...

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Autores principales:	N. Hiraoka, T. Nomura
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/2f54f25d9db54030a229dc959c6567f9
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spelling	oai:doaj.org-article:2f54f25d9db54030a229dc959c6567f92021-12-02T15:05:41ZElectron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening10.1038/s41598-017-00628-42045-2322https://doaj.org/article/2f54f25d9db54030a229dc959c6567f92017-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-00628-4https://doaj.org/toc/2045-2322Abstract The relationship between electron momentum densities (EMDs) and a band gap is clarified in momentum space. The interference between wavefunctions via reciprocal lattice vectors, making a band gap in momentum space, causes the scattering of electrons from the first Brillouin zone to the other zones, so-called Umklapp scattering. This leads to the broadening of EMDs. A sharp drop of the EMD in the limit of a zero gap becomes broadened as the gap opens. The broadening is given by a simple quantity, E g /v F , where E g is the gap magnitude and v F the Fermi velocity. As the ideal case to see such an effect, we investigate the EMDs in graphene and graphite. They are basically semimetals, and their EMDs have a hexagonal shape enclosed in the first Brillouin zone. Since the gap is zero at Dirac points, a sharp drop exists at the corners (K/K’ points) while the broadening becomes significant away from K/K’s, showing the smoothest fall at the centers of the edges (M’s). In fact, this unique topology mimics a general variation of the EMDs across the metal-insulator transition in condensed matters. Such an anisotropic broadening effect is indeed observed by momentum-density-based experiments e.g. x-ray Compton scattering.N. HiraokaT. NomuraNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-7 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q N. Hiraoka T. Nomura Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
description	Abstract The relationship between electron momentum densities (EMDs) and a band gap is clarified in momentum space. The interference between wavefunctions via reciprocal lattice vectors, making a band gap in momentum space, causes the scattering of electrons from the first Brillouin zone to the other zones, so-called Umklapp scattering. This leads to the broadening of EMDs. A sharp drop of the EMD in the limit of a zero gap becomes broadened as the gap opens. The broadening is given by a simple quantity, E g /v F , where E g is the gap magnitude and v F the Fermi velocity. As the ideal case to see such an effect, we investigate the EMDs in graphene and graphite. They are basically semimetals, and their EMDs have a hexagonal shape enclosed in the first Brillouin zone. Since the gap is zero at Dirac points, a sharp drop exists at the corners (K/K’ points) while the broadening becomes significant away from K/K’s, showing the smoothest fall at the centers of the edges (M’s). In fact, this unique topology mimics a general variation of the EMDs across the metal-insulator transition in condensed matters. Such an anisotropic broadening effect is indeed observed by momentum-density-based experiments e.g. x-ray Compton scattering.
format	article
author	N. Hiraoka T. Nomura
author_facet	N. Hiraoka T. Nomura
author_sort	N. Hiraoka
title	Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
title_short	Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
title_full	Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
title_fullStr	Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
title_full_unstemmed	Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening
title_sort	electron momentum densities near dirac cones: anisotropic umklapp scattering and momentum broadening
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/2f54f25d9db54030a229dc959c6567f9
work_keys_str_mv	AT nhiraoka electronmomentumdensitiesneardiracconesanisotropicumklappscatteringandmomentumbroadening AT tnomura electronmomentumdensitiesneardiracconesanisotropicumklappscatteringandmomentumbroadening
_version_	1718388756264779776

Electron momentum densities near Dirac cones: Anisotropic Umklapp scattering and momentum broadening

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