Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only

Abstract

The conductance of a quantum wire with off-diagonal disorder that preserves a sublattice symmetry (the random hopping problem with chiral symmetry) is considered. Transport at the band center is anomalous relative to the standard problem of Anderson localization both in the diffusive and localized regimes. In the diffusive regime, there is no weak-localization correction to the conductance and universal conductance fluctuations are twice as large as in the standard cases. Exponential localization occurs only for an even number of transmission channels in which case the localization length does not depend on whether time-reversal and spin rotation symmetry are present or not. For an odd number of channels the conductance decays algebraically. Upon moving away from the band center transport characteristics undergo a crossover to those of the standard universality classes of Anderson localization. This crossover is calculated in the diffusive regime. Numerical simulations agree qualitatively with the theory.

Zero modes in the random hopping model

“…For wires without point contacts at the left and right ends, this crossover was studied by three of the authors in Ref. 54. There, we found that the crossover to the standard orthogonal class happens for ϳ c , where…”

“…11͑b͒ is best fitted by the conductance distribution of a thick quantum wire with an odd number N of channels derived in Ref. 54. He thus concludes that the critical zero mode in the two-dimensional geometry of Fig.…”

“…Such an enhanced localization length is characteristic of the crossover between the chiral and standard classes for a quantum wire without boundaries. 54 For Nϭ6 ͑even N) and energies ϭ10 Ϫ9 , 10 Ϫ6 , ͗ln g͘ in Figs. 8͑a͒-8͑c͒ decreases linearly with length, but with different slopes for small and large L. These slopes correspond to exponential localization controlled by a boundary-condition-dependent zero mode and to exponential localization in the chiral orthogonal class ͑or, strictly speaking, the crossover between the chiral and standard orthogonal classes͒ in an infinite wire, respectively.…”

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

“…Typically, in lower dimensions (1D,2D) eigenvectors close to the origin are more delocalized than those at the bulk. The reasons for such anomalous behavior have been traced back [28] to the absence of weak-localization corrections in the chiral case. By contrast in three dimensions, it has been claimed [26] that eigenstates close to the origin are more localized than those in the bulk for a broad range of disorder strengths.…”

Finite-size effects and localization properties of disordered quantum wires with chiral symmetry

“…Among these works, models with pure off-diagonal disorder have been studied in connection to peculiar properties that seem to differentiate them from models with pure diagonal disorder only [1,2,3,4,5]. Unusual phenomena like anomalies in the density of states (DOS) and in the localization properties of quantum wires have been reported for a random hopping model of disorder in the vicinity of energy E = 0.…”