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: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Nature Portfolio
2017
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/2f54f25d9db54030a229dc959c6567f9 |
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| Sumario: | 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. |
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