The random magnetic flux problem in a quantum wire

Abstract

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\epsilon =0$ plays a special role. Away from $\epsilon =0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\epsilon =0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.

16 pages, RevTeX; 9 figures included; to appear in Physical Review B

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• Delocalization Transition via Supersymmetry in one Dimension
• Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field
• Anderson localization due to random magnetic field in two dimensions
• The two-dimensional Anderson model of localization with random hopping
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
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• Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view
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• Disordered two-dimensional electron systems with chiral symmetry
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Conductance scaling at the band center of wide wires with pure non--diagonal disorder
• Two-level correlation function of critical random-matrix ensembles
• Unusual electronic properties of clean and disordered zigzag graphene nanoribbons
• Critical conductance of the chiral 2d random flux model
• Disordered Graphene Ribbons as Topological Multicritical Systems
• Two parameter scaling in the crossover from symmetry class BDI to AI
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