Absence of Localization in Disordered Two Dimensional Electron Gas at Weak Magnetic Field and Strong Spin-Orbit Coupling

TL;DR

This study demonstrates that in a disordered two-dimensional electron gas with strong spin-orbit coupling, metallic phases persist at weak magnetic fields, challenging the traditional localization paradigm and revealing a crossover to critical states.

Contribution

It provides numerical evidence that metallic phases survive at weak magnetic fields in 2D systems with strong spin-orbit coupling, contrary to existing localization theories.

Findings

Metallic phase persists at weak magnetic fields.

Crossover from metallic to critical phase occurs with increasing energy.

Level statistics depend only on symmetry parameter β, following Wigner surmise.

Abstract

The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong magnetic fields this paradigm fails (recall quantum Hall effect), it is believed to hold at weak magnetic fields. Here we explore the nature of quantum states at weak magnetic field and strongly fluctuating spin-orbit coupling, employing highly accurate numerical procedure based on level spacing distribution and transfer matrix technique combined with finite-size one-parameter scaling hypothesis. Remarkably, the metallic phase, (known to exist at zero magnetic field), persists also at finite (albeit weak) magnetic fields, and eventually crosses over into a critical phase, which has already been confirmed at high magnetic fields. A schematic phase diagram drawn in the energy-magnetic field plane elucidates the occurrence of localized, metallic and critical phases. In addition, it is shown that nearest-level statistics is determined solely by the symmetry parameter $\beta$ and follows the Wigner surmise irrespective of whether states are metallic or critical.