703 research outputs found
Berry phase and quantized Hall effect in three-dimension
We consider Bloch electrons in the electromagnetic field and argue the
relation between the Berry phase and the quantized Hall conductivity in
three-dimension. The Berry phase we consider here is induced by the adiabatic
change of the time-dependent vector potential. The relation has been shown in
two-dimensional systems, and we generalize the relation in three-dimensional
systems.Comment: corrected some typos. Accepted for publication in J. Phys. Soc. Jp
Localization problem of the quasiperiodic system with the spin orbit interaction
We study one dimensional quasiperiodic system obtained from the tight-binding
model on the square lattice in a uniform magnetic field with the spin orbit
interaction. The phase diagram with respect to the Harper coupling and the
Rashba coupling are proposed from a number of numerical studies including a
multifractal analysis. There are four phases, I, II, III, and IV in this order
from weak to strong Harper coupling. In the weak coupling phase I all the wave
functions are extended, in the intermediate coupling phases II and III mobility
edges exist, and accordingly both localized and extended wave functions exist,
and in the strong Harper coupling phase IV all the wave functions are
localized. Phase I and Phase IV are related by the duality, and phases II and
III are related by the duality, as well. A localized wave function is related
to an extended wave function by the duality, and vice versa. The boundary
between phases II and III is the self-dual line on which all the wave functions
are critical. In the present model the duality does not lead to pure spectra in
contrast to the case of Harper equation.Comment: 10 pages, 11 figure
Superconductivity and Abelian Chiral Anomalies
Motivated by the geometric character of spin Hall conductance, the
topological invariants of generic superconductivity are discussed based on the
Bogoliuvov-de Gennes equation on lattices.
They are given by the Chern numbers of degenerate condensate bands for
unitary order, which are realizations of Abelian chiral anomalies for
non-Abelian connections. The three types of Chern numbers for the and
-directions are given by covering degrees of some doubled surfaces around
the Dirac monopoles. For nonunitary states, several topological invariants are
defined by analyzing the so-called -helicity. Topological origins of the
nodal structures of superconducting gaps are also discussed.Comment: An example with a figure and discussions are supplemente
Critical Level Statistics of the Fibonacci Model
We numerically analyze spectral properties of the Fibonacci model which is a
one-dimensional quasiperiodic system. We find that the energy levels of this
model have the distribution of the band widths obeys and , the gap
distribution () .
We also compare the results with those of multi-scale Cantor sets. We find
qualitative differences between the spectra of the Fibonacci model and the
multi-scale Cantor sets.Comment: 7 page
Topological aspects of quantum spin Hall effect in graphene: Z topological order and spin Chern number
For generic time-reversal invariant systems with spin-orbit couplings, we
clarify a close relationship between the Z topological order and the spin
Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively,
in the quantum spin Hall effect. It turns out that a global gauge
transformation connects different spin Chern numbers (even integers) modulo 4,
which implies that the spin Chern number and the Z topological order yield
the same classification. We present a method of computing spin Chern numbers
and demonstrate it in single and double plane of graphene.Comment: 5 pages, 3 figure
Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation
The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains
with precious mean quasiperiodic exchange modulation is studied by the density
matrix renormalization group method. It is found that the energy gap of the
chain with length N scales as with nonuniversal exponent
if the Ising component of the exhange coupling is antiferromagnetic.
This behavior is expected to be the characteristic feature of the quantum spin
chains with relevant aperiodicity. This is in contrast to the XY chain for
which the precious mean exchange modulation is marginal and the gap scales as
. On the contrary, it is also verified that the energy gap scales as
if the Ising component of the exhange coupling is ferromagnetic. Our
results are not only consistent with the recent bosonization analysis of Vidal,
Mouhanna and Giamarchi but also clarify the nature of the strong coupling
regime which is inaccesssible by the bosonization approach.Comment: 8 pages, 15 figures, 1 table; Proceedings of the workshop 'Frontiers
in Magnetism', Kyoto, Oct. 199
Time-Reversal Symmetry in Non-Hermitian Systems
For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy
when the system has a half-odd-integer spin and the time reversal operator
obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we
point out that for non-hermitian systems, there exists a degeneracy similar to
Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from
the mathematical structure of split-quaternion, instead of quaternion from
which the Kramers degeneracy follows in the usual hermitian cases. Furthermore,
we also show that particle/hole symmetry gives rise to a pair of states with
opposite energies on the basis of the split quaternion in a class of
non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN
Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2
Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde
Phase transition between d-wave and anisotropic s-wave gaps in high temperature oxides superconductors
We study models for superconductivity with two interactions: due to
antiferromagnetic(AF) fluctuations and due to phonons, in a weak coupling
approach to the high temperature superconductivity. The nature of the two
interactions are considerably different; is positive and sharply peaked
at (,) while is negative and peaked at () due to
weak phonon screening. We numerically find (a) weak BCS attraction is enough to
have high critical temperature if a van Hove anomaly is at work, (b) (AF)
is important to give d-wave superconductivity, (c) the gap order parameter
is constant(s-wave) at extremely overdope region and it
changes to anisotropic s-wave as doping is reduced, (d) there exists a first
order phase transition between d-wave and anisotropic s-wave gaps. These
results are qualitatively in agreement with preceding works; they should be
modified in the strongly underdope region by the presence of antiferromagnetic
fluctuations and ensuing AF pseudogap.Comment: 4 pages in RevTex (double column), 4 figure
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