Random magnetic flux problem in a quantum wire

Mudry, Christopher; Brouwer, Piet W.; Furusaki, Akira

doi:10.1103/physrevb.59.13221

Cited by 47 publications

(93 citation statements)

References 98 publications

(101 reference statements)

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“…The sublattice symmetry is broken by the presence of on-site disorder, longrange hopping, 29 or (in some cases) by periodic boundary conditions. 30 Counterparts to this sublattice symmetry in other disordered systems or in quenched approximation to interacting problems are numerous. They occur in, e.g., the QCD Hamiltonian, 31,32 random XY spin chains, 33 diffusion in random environments, 34 supersymmetric quantum mechanics, 35 non-Hermitean quantum mechanics, 36 and two-dimensional disordered models in the continuum such as Dirac fermions with random vector potentials.…”

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confidence: 99%

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

2000

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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.

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

2000

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“…Mudry, Brouwer, and Furusaki [86,87] studied the transport properties of disordered wires with chiral symmetry (i.e. when the system consists of two or several sublattices, and only transitions between different sublattices are allowed).…”

Section: Fig 11 Shot Noise Measurements By Henny Et Almentioning

confidence: 99%

Shot noise in mesoscopic conductors

2000

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Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and BoltzmannLangevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

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“…A more detailed account of our implementation of the recursive Greenfunction method can be found in Refs. 53 Fig. 5.…”

Section: Bounded Wires: Nonzero Energymentioning

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Zero modes in the random hopping model

et al. 2002

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If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.

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Random magnetic flux problem in a quantum wire

Cited by 47 publications

References 98 publications

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

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

Shot noise in mesoscopic conductors

Zero modes in the random hopping model

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