817 research outputs found
Numerical verification of universality for the Anderson transition
We analyze the scaling behavior of the higher Lyapunov exponents at the
Anderson transition. We estimate the critical exponent and verify its
universality and that of the critical conductance distribution for box,
Gaussian and Lorentzian distributions of the random potential
Critical exponent for the quantum spin Hall transition in Z_2 network model
We have estimated the critical exponent describing the divergence of the
localization length at the metal-quantum spin Hall insulator transition. The
critical exponent for the metal-ordinary insulator transition in quantum spin
Hall systems is known to be consistent with that of topologically trivial
symplectic systems. However, the precise estimation of the critical exponent
for the metal-quantum spin Hall insulator transition proved to be problematic
because of the existence, in this case, of edge states in the localized phase.
We have overcome this difficulty by analyzing the second smallest positive
Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a
value for the critical exponent that is consistent with
that for topologically trivial symplectic systems.Comment: 5 pages, 4 figures, submitted to the proceedings of Localisation 201
Scaling of the conductance distribution near the Anderson transition
The single parameter scaling hypothesis is the foundation of our
understanding of the Anderson transition. However, the conductance of a
disordered system is a fluctuating quantity which does not obey a one parameter
scaling law. It is essential to investigate the scaling of the full conductance
distribution to establish the scaling hypothesis. We present a clear cut
numerical demonstration that the conductance distribution indeed obeys one
parameter scaling near the Anderson transition
Anderson transition in the three dimensional symplectic universality class
We study the Anderson transition in the SU(2) model and the Ando model. We
report a new precise estimate of the critical exponent for the symplectic
universality class of the Anderson transition. We also report numerical
estimation of the function.Comment: 4 pages, 5 figure
Topology dependent quantities at the Anderson transition
The boundary condition dependence of the critical behavior for the three
dimensional Anderson transition is investigated. A strong dependence of the
scaling function and the critical conductance distribution on the boundary
conditions is found, while the critical disorder and critical exponent are
found to be independent of the boundary conditions
Transport properties in network models with perfectly conducting channels
We study the transport properties of disordered electron systems that contain
perfectly conducting channels. Two quantum network models that belong to
different universality classes, unitary and symplectic, are simulated
numerically. The perfectly conducting channel in the unitary class can be
realized in zigzag graphene nano-ribbons and that in the symplectic class is
known to appear in metallic carbon nanotubes. The existence of a perfectly
conducting channel leads to novel conductance distribution functions and a
shortening of the conductance decay length.Comment: 4 pages, 6 figures, proceedings of LT2
Conductance distributions in disordered quantum spin-Hall systems
We study numerically the charge conductance distributions of disordered
quantum spin-Hall (QSH) systems using a quantum network model. We have found
that the conductance distribution at the metal-QSH insulator transition is
clearly different from that at the metal-ordinary insulator transition. Thus
the critical conductance distribution is sensitive not only to the boundary
condition but also to the presence of edge states in the adjacent insulating
phase. We have also calculated the point-contact conductance. Even when the
two-terminal conductance is approximately quantized, we find large fluctuations
in the point-contact conductance. Furthermore, we have found a semi-circular
relation between the average of the point-contact conductance and its
fluctuation.Comment: 9 pages, 17 figures, published versio
Chalker-Coddington model described by an S-matrix with odd dimensions
The Chalker-Coddington network model is often used to describe the transport
properties of quantum Hall systems. By adding an extra channel to this model,
we introduce an asymmetric model with profoundly different transport
properties. We present a numerical analysis of these transport properties and
consider the relevance for realistic systems.Comment: 7 pages, 4 figures. To appear in the EP2DS-17 proceeding
Universality of the critical conductance distribution in various dimensions
We study numerically the metal - insulator transition in the Anderson model
on various lattices with dimension (bifractals and Euclidian
lattices). The critical exponent and the critical conductance
distribution are calculated. We confirm that depends only on the {\it
spectral} dimension. The other parameters - critical disorder, critical
conductance distribution and conductance cummulants - depend also on lattice
topology. Thus only qualitative comparison with theoretical formulae for
dimension dependence of the cummulants is possible
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