Berlin 2018 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 66: Poster: Stat. Phys. (Gen., Critical Phen., Biol.)
DY 66.17: Poster
Donnerstag, 15. März 2018, 15:30–18:00, Poster A
Integer quantum Hall transitions on tight-binding lattices — •Martin Puschmann1,2, Philipp Cain1, Michael Schreiber1, and Thomas Vojta2 — 1Institute of Physics, Chemnitz University of Technology, Chemnitz, Germany — 2Department of Physics, Missouri University of Science and Technology, Rolla, MO, United States
We investigate the integer quantum Hall transition in the lowest Landau band of two-dimensional tight-binding lattices for non-interacting electrons affected by a perpendicular magnetic field. Specifically, we consider both simple square lattices, where Landau levels are broadened by random potentials, and random Voronoi-Delaunay lattices in which (topological) disorder is introduced by bonds between randomly positioned sites. Based on a recursive Green function approach, we calculate the smallest positive Lyapunov exponent describing the long-range behavior of the wave function intensities along a quasi-one-dimensional lattice stripe. In both systems, we observe that the critical exponent of the localization length takes a value of ν≈2.60. Our critical estimates, thus, coincide with those based on the semi-classical Chalker-Coddington (CC) network model, see e.g. [1]. They do not agree with the reduced critical exponent, ν≈2.37, found by Gruzberg et al. in a recently proposed geometrically disordered CC model [2].
[1] K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304 (2009)
[2] I. A. Gruzberg et al., Phys. Rev. B 95, 125414 (2017)