1,347 research outputs found
Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder
We review recent work on the random hopping problem in a
quasi-one-dimensional geometry of N coupled chains (quantum wire with
off-diagonal disorder). Both density of states and conductance show a
remarkable dependence on the parity of N. The theory is compared to numerical
simulations.Comment: 8 pages, to appear in Physica E (special issue on Dynamics of Complex
Systems); 6 figure
Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view
It is shown that, in the scaling regime, transport properties of quantum
wires with off-diagonal disorder are described by a family of scaling equations
that depend on two parameters: the mean free path and an additional continuous
parameter. The existing scaling equation for quantum wires with off-diagonal
disorder [Brouwer et al., Phys. Rev. Lett. 81, 862 (1998)] is a special point
in this family. Both parameters depend on the details of the microscopic model.
Since there are two parameters involved, instead of only one, localization in a
wire with off-diagonal disorder is not universal. We take a geometric point of
view and show that this nonuniversality follows from the fact that the group of
transfer matrices is not semi-simple. Our results are illustrated with
numerical simulations for a tight-binding model with random hopping amplitudes.Comment: 12 pages, RevTeX; 3 figures included with eps
Electron fractionalization in two-dimensional graphenelike structures
Electron fractionalization is intimately related to topology. In
one-dimensional systems, fractionally charged states exist at domain walls
between degenerate vacua. In two-dimensional systems, fractionalization exists
in quantum Hall fluids, where time-reversal symmetry is broken by a large
external magnetic field. Recently, there has been a tremendous effort in the
search for examples of fractionalization in two-dimensional systems with
time-reversal symmetry. In this letter, we show that fractionally charged
topological excitations exist on graphenelike structures, where quasiparticles
are described by two flavors of Dirac fermions and time-reversal symmetry is
respected. The topological zero-modes are mathematically similar to fractional
vortices in p-wave superconductors. They correspond to a twist in the phase in
the mass of the Dirac fermions, akin to cosmic strings in particle physics.Comment: 4 pages, 2 figure
Spin-directed network model for the surface states of weak three-dimensional topological insulators
A two-dimensional spin-directed network model is
constructed that describes the combined effects of dimerization and disorder
for the surface states of a weak three-dimensional
topological insulator. The network model consists of helical edge states of
two-dimensional layers of topological insulators which
are coupled by time-reversal symmetric interlayer tunneling. It is argued that,
without dimerization of interlayer couplings, the network model has no
insulating phase for any disorder strength. However, a sufficiently strong
dimerization induces a transition from a metallic phase to an insulating phase.
The critical exponent for the diverging localization length at
metal-insulator transition points is obtained by finite-size scaling analysis
of numerical data from simulations of this network model. It is shown that the
phase transition belongs to the two-dimensional symplectic universality class
of Anderson transition.Comment: 36 pages and 27 figures, plus Supplemental Materia
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