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arXiv · 1910.10179

Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry

Noah F. Q. Yuan·Liang Fu
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Abstract

A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits non-analyticity such as divergence. Critical points can be first classified as ordinary and high-order ones, and the ordinary critical points have been studied thoroughly by L\'eon van Hove. In this work, we describe and classify high-order critical points based on topology, scaling and symmetry, which are beyond L\'eon van Hove's framework. We show that high-order critical points can have power-law divergent DOS with particle-hole asymmetry, and can be realized at generic or symmetric momenta by tuning a few parameters such as twist angle, strain, pressure and/or external fields.

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Noah F. Q. Yuan, Liang Fu. 2019-10-22. Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry. https://doi.org/10.1103/physrevb.101.125120

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