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 10.7: Talk

Monday, March 16, 2020, 16:45–17:00, HSZ 201

Lévy flights and Hydrodynamic Superdiffusion on the Dirac Cone of Graphene — •Egor Kiselev¹ and Jörg Schmalian^1,2 — ¹Institut für Theorie der Kondensierten Materie, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany — ²Institut für Festkörperphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany

We show that the hydrodynamic collision processes of graphene electrons at the neutrality point can be described in terms of a Fokker-Planck equation with a fractional derivative, corresponding to a Lévy flight in momentum space. Thus, electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to superdiffusive dynamics of collective excitations. We discuss the relevance of our results to experiments with injected electron beams, and show how the superdiffusive behavior makes it possible to obtain analytical results for transport coefficients relevant to the hydrodynamics of graphene electrons.