Two-dimensional disordered electron systems: a network model approach

Peter Freche; Martin Janssen; Rainer Merkt

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arXiv · cond-mat/9710297

Two-dimensional disordered electron systems: a network model approach

Peter Freche·Martin Janssen·Rainer Merkt

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Abstract

We demonstrate that network models for wave mechanical systems with quenched disorder cover the physics of mesoscopic electrons. The models are constructed as a network of random scattering matrices connecting incoming to outgoing wave amplitudes. The corresponding wave dynamics is given by a discrete unitary time evolution operator. We report on three different universality classes: two-dimensional, spinless, non-chiral electrons with (O2NC) and without time reversal symmetry (U2NC), and two-dimensional, non-chiral electrons with time reversal symmetric spin-scattering (S2NC). We determine the phase diagram in the parameter space of scattering strengths. The O/U2NC models show strong localization. We find symmetry factors in localization lengths as well as multifractal exponents in agreement with theoretical predictions. The S2NC model displays a localization-delocalization transition. We determine the critical exponent of the localization length and the multifractal scaling exponent of the order parameter to be $ν\approx 2.4$ and $α_0\approx 2.18$, respectively.

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Peter Freche, Martin Janssen, Rainer Merkt. 1997-10-28. Two-dimensional disordered electron systems: a network model approach. https://arxiv.org/abs/cond-mat/9710297

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