Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Graphene (jointly with DY, MA, HL, DS, O) (joint session TT/DY/HL)

DY 10.9: Talk

Monday, March 16, 2020, 17:15–17:30, HSZ 201

Localization at the Van Hove singularity — •Peter Silvestrov¹ and Jakub Tworzydlo² — ¹Institute for Mathematical Physics, TU Braunschweig, 38106 Braunschweig, Germany — ²Institute of Theoretical Physics, Warsaw University, Hoża 69, 00–681 Warsaw, Poland

Van Hove singularities are found in the electron spectrum of many 2-dimensional materials of current interest, including graphene systems (twisted bilayer and monolayer on a substrate), transitional dichalcogenides, and 2-dimensional superconductors. They appear due to saddle points in the energy bands at certain momenta. Even though the effective kinetic energy corresponding to such saddle point is unbounded from both above and below, we show that exponentially localized electronic states generically appear here in the presence of a smooth potential U(x,y) with sufficiently diverse landscape. We also consider high order Van Hove singularities, where we predict a discrete spectrum of non-exponentially localized states.