Superdiffusion in random two dimensional system with ubiquitous long-range hopping

by Prof. Alexander L. Burin

Tulane University, New Orleans

at Condensed Matter Seminar

Mon, 27 Jun 2022, 11:30
Sacta-Rashi Building for Physics (54), room 207

Abstract

Although it is recognized that Anderson localization always takes place for a dimension d less or
equal d = 2, while it is not possible for hopping V (r) decreasing with the distance slower or as r−d,
the localization problem in the crossover regime for the dimension d = 2 and hopping V (r) / r−2
is not resolved yet. Following earlier suggestions we show that for the hopping determined by twodimensional
anisotropic dipole-dipole or RKKY interactions there exist two distinguishable phases
at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive
transport, while the second phase is characterized by diffusive transport and delocalized eigenstates
with fractal dimension less than 2. The crossover between phases is resolved analytically using the
extension of scaling theory of localization and verified using an exact numerical diagonalization.

Created on 24-06-2022 by Meidan, Dganit (dganit)
Updaded on 24-06-2022 by Meidan, Dganit (dganit)