30 research outputs found
Effect of spin on electron motion in a random magnetic field
We consider properties of a two-dimensional electron system in a random
magnetic field. It is assumed that the magnetic field not only influences
orbital electron motion but also acts on the electron spin. For calculations,
we suggest a new trick replacing the initial Hamiltonian by a Dirac
Hamiltonian. This allows us to do easily a perturbation theory and derive a
supermatrix sigma model, which takes a form of the conventional sigma model
with the unitary symmetry. Using this sigma model we calculate several
correlation functions including a spin-spin correlation function. As compared
to the model without spin, we get different expressions for the single-particle
lifetime and the transport time. The diffusion constant turns out to be 2 times
smaller than the one for spinless particles.Comment: 7 pages, revtex, result of the spin correlation function corrected,
Appendix adde
Comment on "Antilocalization in a 2D Electron Gas in a Random Magnetic Field"
In a recent Letter, Taras-Semchuk and Efetov reconsider the problem of
electron localization in a random magnetic field in two dimensions. They claim
that due to the long-range nature of the vector potential correlations an
additional term appears in the effective field theory (-model) of the
problem, leading to delocalization at the one-loop level. This calls into
question the results of earlier analytical studies, where the random magnetic
field problem was mapped onto the conventional unitary-class -model,
implying that the leading quantum correction is of two-loop order and of a
localizing nature. We show in this Comment, however, that the new term in fact
does not exist and was erroneously obtained by Taras-Semchuk and Efetov because
of an inconsistent treatment violating gauge invariance.Comment: 1 page, 2 figure
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
Det-Det Correlations for Quantum Maps: Dual Pair and Saddle-Point Analyses
An attempt is made to clarify the ballistic non-linear sigma model formalism
recently proposed for quantum chaotic systems, by the spectral determinant
Z(s)=Det(1-sU) of a quantized map U element of U(N). More precisely, we study
the correlator omega_U(s)= (averaging t over the unit circle).
Identifying the group U(N) as one member of a dual pair acting in the spinor
representation of Spin(4N), omega_U(s) is expanded in terms of irreducible
characters of U(N). In close analogy with the ballistic non-linear sigma model,
a coherent-state integral representation of omega_U(s) is developed. We show
that the leading-order saddle-point approximation reproduces omega_U(s)
exactly, up to a constant factor; this miracle can be explained by interpreting
omega_U(s) as a character of U(2N), for which the saddle-point expansion yields
the Weyl character formula. Unfortunately, this decomposition behaves
non-smoothly in the semiclassical limit, and to make further progress some
averaging over U needs to be introduced. Several averaging schemes are
investigated. In general, a direct application of the saddle-point
approximation to these schemes is demonstrated to give incorrect results; this
is not the case for a `semiclassical averaging scheme', for which all loop
corrections vanish identically. As a side product of the dual pair
decomposition, we compute a crossover between the Poisson and CUE ensembles for
omega_U(s)
Ballistic electron motion in a random magnetic field
Using a new scheme of the derivation of the non-linear -model we
consider the electron motion in a random magnetic field (RMF) in two
dimensions. The derivation is based on writing quasiclassical equations and
representing their solutions in terms of a functional integral over
supermatrices with the constraint . Contrary to the standard scheme,
neither singling out slow modes nor saddle-point approximation are used. The
-model obtained is applicable at the length scale down to the electron
wavelength. We show that this model differs from the model with a random
potential (RP).However, after averaging over fluctuations in the Lyapunov
region the standard -model is obtained leading to the conventional
localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is
remove
Ehrenfest time dependent suppression of weak localization
The Ehrenfest time dependence of the suppression of the weak localization
correction to the conductance of a {\em clean} chaotic cavity is calculated.
Unlike in earlier work, no impurity scattering is invoked to imitate
diffraction effects. The calculation extends the semiclassical theory of K.
Richter and M. Sieber [Phys. Rev. Lett. {\bf 89}, 206801 (2002)] to include the
effect of a finite Ehrenfest time.Comment: 3 Pages, 1 Figure, RevTe
Universal spectral statistics of Andreev billiards: semiclassical approach
The classification of universality classes of random-matrix theory has
recently been extended beyond the Wigner-Dyson ensembles. Several of the novel
ensembles can be discussed naturally in the context of superconducting-normal
hybrid systems. In this paper, we give a semiclassical interpretation of their
spectral form factors for both quantum graphs and Andreev billiards.Comment: final improved version (to be published in Physical Review E), 6
pages, revtex
Field Theory of Mesoscopic Fluctuations in Superconductor/Normal-Metal Systems
Thermodynamic and transport properties of normal disordered conductors are
strongly influenced by the proximity of a superconductor. A cooperation between
mesoscopic coherence and Andreev scattering of particles from the
superconductor generates new types of interference phenomena. We introduce a
field theoretic approach capable of exploring both averaged properties and
mesoscopic fluctuations of superconductor/normal-metal systems.
As an example the method is applied to the study of the level statistics of a
SNS-junction.Comment: 4 pages, REVTEX, two eps-figures included; submitted to JETP letter
Weak Localization and Integer Quantum Hall Effect in a Periodic Potential
We consider magnetotransport in a disordered two-dimensional electron gas in
the presence of a periodic modulation in one direction. Existing quasiclassical
and quantum approaches to this problem account for Weiss oscillations in the
resistivity tensor at moderate magnetic fields, as well as a strong
modulation-induced modification of the Shubnikov-de Haas oscillations at higher
magnetic fields. They do not account, however, for the operation at even higher
magnetic fields of the integer quantum Hall effect, for which quantum
interference processes are responsible. We then introduce a field-theory
approach, based on a nonlinear sigma model, which encompasses naturally both
the quasiclassical and quantum-mechanical approaches, as well as providing a
consistent means of extending them to include quantum interference corrections.
A perturbative renormalization-group analysis of the field theory shows how
weak localization corrections to the conductivity tensor may be described by a
modification of the usual one-parameter scaling, such as to accommodate the
anisotropy of the bare conductivity tensor. We also show how the two-parameter
scaling, conjectured as a model for the quantum Hall effect in unmodulated
systems, may be generalized similarly for the modulated system. Within this
model we illustrate the operation of the quantum Hall effect in modulated
systems for parameters that are realistic for current experiments.Comment: 15 pages, 4 figures, ReVTeX; revised version with condensed
introduction; two figures taken out; reference adde