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 the 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 one parameter finite-size 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 β and follows the Wigner surmise irrespective of whether states are metallic or critical.
Highlights
In order to corroborate our finding on the existence of extended states at weak magnetic field, we directly evaluate the localization length ξ(E, B) of the 2D system employing the transfer matrix technique[18,19]
Starting from the 2DSU model Hamiltonian (1), we focus on the localization issue at the weak field regime, starting at B = 0 where it is known to display metal-insulator transition (MIT) for system with the symplectic symmetry
Based on analyses of level statistics (Fig. 1) and localization length (Fig. 2), it has been demonstrated that a band of metallic states persists for finite magnetic field 0 < B < Bc 1/50
Summary
Our analysis of nearest level spacing distribution suggests that states in the same energy range (as for B = 0) are still extended at finite magnetic field even though this 2D system belongs to the unitary class.
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