448 research outputs found
Anomalous Enhancement of the Boltzmann Conductivity in Disordered Zigzag Graphene Nanoribbons
We study the conductivity of disordered zigzag graphene nanoribbons in the
incoherent regime by using the Boltzmann equation approach. The band structure
of zigzag nanoribbons contains two energy valleys, and each valley has an
excess one-way channel. The crucial point is that the numbers of conducting
channels for two propagating directions are imbalanced in each valley due to
the presence of an excess one-way channel. It was pointed out that as a
consequence of this imbalance, a perfectly conducting channel is stabilized in
the coherent regime if intervalley scattering is absent. We show that even in
the incoherent regime, the conductivity is anomalously enhanced if intervalley
scattering is very weak. Particularly, in the limit of no intervalley
scattering, the dimensionless conductance approaches to unity with increasing
ribbon length as if there exists a perfectly conducting channel. We also show
that anomalous valley polarization of electron density appears in the presence
of an electric field.Comment: 10 pages, 3 figure
Conductance Fluctuations in Disordered Wires with Perfectly Conducting Channels
We study conductance fluctuations in disordered quantum wires with unitary
symmetry focusing on the case in which the number of conducting channels in one
propagating direction is not equal to that in the opposite direction. We
consider disordered wires with left-moving channels and right-moving
channels. In this case, left-moving channels become perfectly conducting,
and the dimensionless conductance for the left-moving channels behaves as
in the long-wire limit. We obtain the variance of in the
diffusive regime by using the Dorokhov-Mello-Pereyra-Kumar equation for
transmission eigenvalues. It is shown that the universality of conductance
fluctuations breaks down for unless is very large.Comment: 6 pages, 2 figure
Nonuniversal Shot Noise in Disordered Quantum Wires with Channel-Number Imbalance
The number of conducting channels for one propagating direction is equal to
that for the other direction in ordinary quantum wires. However, they can be
imbalanced in graphene nanoribbons with zigzag edges. Employing the model
system in which a degree of channel-number imbalance can be controlled, we
calculate the shot-noise power at zero frequency by using the
Boltzmann-Langevin approach. The shot-noise power in an ordinary diffusive
conductor is one-third of the Poisson value. We show that with increasing the
degree of channel-number imbalance, the universal one-third suppression breaks
down and a highly nonuniversal behavior of shot noise appears.Comment: 10 pages, 3 figure
Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels
We study the conductance of disordered wires with unitary symmetry focusing
on the case in which perfectly conducting channels are present due to the
channel-number imbalance between two-propagating directions. Using the exact
solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission
eigenvalues, we obtain the average and second moment of the conductance in the
long-wire regime. For comparison, we employ the three-edge Chalker-Coddington
model as the simplest example of channel-number-imbalanced systems with , and obtain the average and second moment of the conductance by using a
supersymmetry approach. We show that the result for the Chalker-Coddington
model is identical to that obtained from the DMPK equation.Comment: 20 pages, 1 figur
Conductance of Disordered Wires with Symplectic Symmetry: Comparison between Odd- and Even-Channel Cases
The conductance of disordered wires with symplectic symmetry is studied by
numerical simulations on the basis of a tight-binding model on a square lattice
consisting of M lattice sites in the transverse direction. If the potential
range of scatterers is much larger than the lattice constant, the number N of
conducting channels becomes odd (even) when M is odd (even). The average
dimensionless conductance g is calculated as a function of system length L. It
is shown that when N is odd, the conductance behaves as g --> 1 with increasing
L. This indicates the absence of Anderson localization. In the even-channel
case, the ordinary localization behavior arises and g decays exponentially with
increasing L. It is also shown that the decay of g is much faster in the
odd-channel case than in the even-channel case. These numerical results are in
qualitative agreement with existing analytic theories.Comment: 4 page
Conductance Distribution in Disordered Quantum Wires with a Perfectly Conducting Channel
We study the conductance of phase-coherent disordered quantum wires focusing
on the case in which the number of conducting channels is imbalanced between
two propagating directions. If the number of channels in one direction is by
one greater than that in the opposite direction, one perfectly conducting
channel without backscattering is stabilized regardless of wire length.
Consequently, the dimensionless conductance does not vanish but converges to
unity in the long-wire limit, indicating the absence of Anderson localization.
To observe the influence of a perfectly conducting channel, we numerically
obtain the distribution of conductance in both cases with and without a
perfectly conducting channel. We show that the characteristic form of the
distribution is notably modified in the presence of a perfectly conducting
channel.Comment: 7 pages, 16 figure
Weak topological insulator with protected gapless helical states
A workable model for describing dislocation lines introduced into a
three-dimensional topological insulator is proposed. We show how fragile
surface Dirac cones of a weak topological insulator evolve into protected
gapless helical modes confined to the vicinity of dislocation line. It is
demonstrated that surface Dirac cones of a topological insulator (either strong
or weak) acquire a finite-size energy gap, when the surface is deformed into a
cylinder penetrating the otherwise surface-less system. We show that when a
dislocation with a non-trivial Burgers vector is introduced, the finite-size
energy gap play the role of stabilizing the one-dimensional gapless states.Comment: 8 pages, 17 figure
Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry
The conductance of disordered wires with symplectic symmetry is studied by a
random-matrix approach. It has been believed that Anderson localization
inevitably arises in ordinary disordered wires. A counterexample is recently
found in the systems with symplectic symmetry, where one perfectly conducting
channel is present even in the long-wire limit when the number of conducting
channels is odd. This indicates that the odd-channel case is essentially
different from the ordinary even-channel case. To study such differences, we
derive the DMPK equation for transmission eigenvalues for both the even- and
odd- channel cases. The behavior of dimensionless conductance is investigated
on the basis of the resulting equation. In the short-wire regime, we find that
the weak-antilocalization correction to the conductance in the odd-channel case
is equivalent to that in the even-channel case. We also find that the variance
does not depend on whether the number of channels is even or odd. In the
long-wire regime, it is shown that the dimensionless conductance in the
even-channel case decays exponentially as --> 0 with increasing system
length, while --> 1 in the odd-channel case. We evaluate the decay
length for the even- and odd-channel cases and find a clear even-odd
difference. These results indicate that the perfectly conducting channel
induces clear even-odd differences in the long-wire regime.Comment: 28pages, 5figures, Accepted for publication in J. Phys. Soc. Jp
Spin Berry phase in the Fermi arc states
Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its
band dispersion exhibits multiple subbands of partially flat dispersion,
originating from the Fermi arc states. Remarkably, the lowest energy flat
subbands bear a finite size energy gap, implying that electrons in the Fermi
arc surface states are susceptible of the spin Berry phase. This is shown to be
a consequence of spin-to-surface locking in the surface electronic states. We
verify this behavior and the existence of spin Berry phase in the low-energy
effective theory of Fermi arc surface states on a cylindrical nanowire by
deriving the latter from a bulk Weyl Hamiltonian. We point out that in any
surface state exhibiting a spin Berry phase pi, a zero-energy bound state is
formed along a magnetic flux tube of strength, hc/(2e). This effect is
highlighted in a surfaceless bulk system pierced by a dislocation line, which
shows a 1D chiral mode along the dislocation line.Comment: 9 pages, 9 figure
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