69 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
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
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
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
Antilocalization in a 2D Electron Gas in a Random Magnetic Field
We construct a supersymmetric field theory for the problem of a
two-dimensional electron gas in a random, static magnetic field. We find a new
term in the free energy, additional to those present in the conventional
unitary sigma-model, whose presence relies on the long-range nature of the
disorder correlations. Under a perturbative renormalization group analysis of
the free energy, the new term contributes to the scaling function at one-loop
order and leads to antilocalization.Comment: 4 pages, RevTe
Energy-level correlations in chiral symmetric disordered systems: Corrections to the universal results
We investigate the deviation of the level-correlation functions from the
universal form for the chiral symmetric classes. Using the supersymmetric
nonlinear sigma model we formulate the perturbation theory. The large energy
behavior is compared with the result of the diagrammatic perturbation theory.
We have the diffuson and cooperon contributions even in the average density of
states. For the unitary and orthogonal classes we get the small energy behavior
that suggests a weakening of the level repulsion. For the symplectic case we
get a result with opposite tendency.Comment: 7 pages, revtex, 2 eps figures, references added, some minor change
Hidden degree of freedom and critical states in a two-dimensional electron gas in the presence of a random magnetic field
We establish the existence of a hidden degree of freedom and the critical
states of a spinless electron system in a spatially-correlated random magnetic
field with vanishing mean. Whereas the critical states are carried by the
zero-field contours of the field landscape, the hidden degree of freedom is
recognized as being associated with the formation of vortices in these special
contours. It is argued that, as opposed to the coherent backscattering
mechanism of weak localization, a new type of scattering processes in the
contours controls the underlying physics of localization in the random magnetic
field system. In addition, we investigate the role of vortices in governing the
metal-insulator transition and propose a renormalization-group diagram for the
system under study.Comment: 17 pages, 16 figures; Figs. 1, 7, 9, and 10 have been reduced in
quality for e-submissio
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
Quantum interference and the formation of the proximity effect in chaotic normal-metal/superconducting structures
We discuss a number of basic physical mechanisms relevant to the formation of
the proximity effect in superconductor/normal metal (SN) systems. Specifically,
we review why the proximity effect sharply discriminates between systems with
integrable and chaotic dynamics, respectively, and how this feature can be
incorporated into theories of SN systems. Turning to less well investigated
terrain, we discuss the impact of quantum diffractive scattering on the
structure of the density of states in the normal region. We consider ballistic
systems weakly disordered by pointlike impurities as a test case and
demonstrate that diffractive processes akin to normal metal weak localization
lead to the formation of a hard spectral gap -- a hallmark of SN systems with
chaotic dynamics. Turning to the more difficult case of clean systems with
chaotic boundary scattering, we argue that semiclassical approaches, based on
classifications in terms of classical trajectories, cannot explain the gap
phenomenon. Employing an alternative formalism based on elements of
quasiclassics and the ballistic -model, we demonstrate that the inverse
of the so-called Ehrenfest time is the relevant energy scale in this context.
We discuss some fundamental difficulties related to the formulation of low
energy theories of mesoscopic chaotic systems in general and how they prevent
us from analysing the gap structure in a rigorous manner. Given these
difficulties, we argue that the proximity effect represents a basic and
challenging test phenomenon for theories of quantum chaotic systems.Comment: 21 pages (two-column), 6 figures; references adde
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