191 research outputs found
From quantum disorder to quantum chaos
We study the statistics of wave functions in a ballistic chaotic system. The
statistical ensemble is generated by adding weak smooth random potential, which
allows us to apply the ballistic -model approach. We analyze conditions
of applicability of the -model, emphasizing the role played by the
single-particle mean free path and the Lyapunov exponent due to the random
potential. In particular, we present a resolution of the puzzle of repetitions
of periodic orbits counted differently by the -model and by the trace
formula.Comment: 15 pages, no figures. Contribution to a special issue of J. Low Temp.
Phys. dedicated to Peter Woelfle's 60th birthda
Interaction-induced magnetoresistance in a two-dimensional electron gas
We study the interaction-induced quantum correction
\delta\sigma_{\alpha\beta} to the conductivity tensor of electrons in two
dimensions for arbitrary T\tau (where T is the temperature and \tau the
transport scattering time), magnetic field, and type of disorder. A general
theory is developed, allowing us to express \delta\sigma_{\alpha\beta} in terms
of classical propagators (``ballistic diffusons''). The formalism is used to
calculate the interaction contribution to the longitudinal and the Hall
resistivities in a transverse magnetic field in the whole range of temperature
from the diffusive (T\tau 1) regime, both in
smooth disorder and in the presence of short-range scatterers. Further, we
apply the formalism to anisotropic systems and demonstrate that the interaction
induces novel quantum oscillations in the resistivity of lateral superlattices.Comment: 35 pages, 14 figure
Low-temperature spin Coulomb drag in a two-dimensional electron gas
The phenomenon of low-temperature spin Coulomb drag in a two-dimensional
electron gas is investigated. The spin transresistivity coefficient is
essentially enhanced in the diffusive regime, as compared to conventional
predictions. The origin of this enhancement is the quantum coherence of spin-up
and spin-down electrons propagating in the same random impurity potential and
coupled via the Coulomb interaction. A comprehensive analysis of spin and
interlayer Coulomb drag effects is presented.Comment: 5 pages, 4 figure
Anomalous Hooke's law in disordered graphene
The discovery of graphene, a single monolayer of graphite, has closed the
discussion on stability of 2D crystals. Although thermal fluctuations of such
crystals tend to destroy the long-range order in the system, the crystal can be
stabilized by strong anharmonicity effects. This competition is the central
issue of the crumpling transition, i.e., a transition between flat and crumpled
phases. We show that anharmonicity-controlled fluctuations of a graphene
membrane around equilibrium flat phase lead to unusual elastic properties. In
particular, we demonstrate that stretching of a flake of graphene is a
nonlinear function of the applied tension at small tension:
and
for clean and strongly disordered graphene, respectively. Conventional linear
Hooke's law, is realized at sufficiently large tensions:
where depends both on temperature and on the
disorder strength.Comment: 10 pages, 3 figure
Mesoscopic fluctuations of the local density of states in interacting electron systems
We review our recent theoretical results for mesoscopic fluctuations of the
local density of states in the presence of electron-electron interaction. We
focus on the two specific cases: (i) a vicinity of interacting critical point
corresponding to Anderson-Mott transition, and (ii) a vicinity of
non-interacting critical point in the presence of a weak electron-electron
attraction. In both cases strong mesoscopic fluctuations of the local density
of states exist.Comment: A brief review based on arXiv:1305.2888, arXiv:1307.5811,
arXiv:1412.3306, arXiv:1603.0301
Multifractality at Anderson transitions with Coulomb interaction
We explore mesoscopic fluctuations and correlations of the local density of
states (LDOS) near localization transition in a disordered interacting
electronic system. It is shown that the LDOS multifractality survives in the
presence of Coulomb interaction. We calculate the spectrum of multifractal
dimensions in spatial dimensions and show that it differs from
that in the absence of interaction. The multifractal character of fluctuations
and correlations of the LDOS can be studied experimentally by scanning
tunneling microscopy of two-dimensional and three-dimensional disordered
structures.Comment: 16 pages, 2 figure
Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
We develop a theory of the local density of states (LDOS) of disordered
superconductors, employing the non-linear sigma-model formalism and the
renormalization-group framework. The theory takes into account the interplay of
disorder and interaction couplings in all channels, treating the systems with
short-range and Coulomb interactions on equal footing. We explore 2D systems
that would be Anderson insulators in the absence of interaction and 2D or 3D
systems that undergo Anderson transition in the absence of interaction. We
evaluate both the average tunneling density of states and its mesoscopic
fluctuations which are related to the LDOS multifractality in normal disordered
systems. The obtained average LDOS shows a pronounced depletion around the
Fermi energy, both in the metallic phase (i.e., above the superconducting
critical temperature ) and in the insulating phase near the
superconductor-insulator transition (SIT). The fluctuations of the LDOS are
found to be particularly strong for the case of short-range interactions --
especially, in the regime when is enhanced by Anderson localization. On
the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS
fluctuations. However, also in a model with Coulomb interaction, the
fluctuations become strong when the systems approaches the SIT
Superconductor-insulator transitions: Phase diagram and magnetoresistance
Influence of disorder-induced Anderson localization and of electron-electron
interaction on superconductivity in two-dimensional systems is explored. We
determine the superconducting transition temperature , the temperature
dependence of the resistivity, the phase diagram, as well as the
magnetoresistance. The analysis is based on the renormalization group (RG) for
a nonlinear sigma model. Derived RG equations are valid to the lowest order in
disorder but for arbitrary electron-electron interaction strength in
particle-hole and Cooper channels. Systems with preserved and broken
spin-rotational symmetry are considered, both with short-range and with
long-range (Coulomb) interaction. In the cases of short-range interaction, we
identify parameter regions where the superconductivity is enhanced by
localization effects. Our RG analysis indicates that the
superconductor-insulator transition is controlled by a fixed point with a
resistivity of the order of the quantum resistance . When
a transverse magnetic field is applied, we find a strong nonmonotonous
magnetoresistance for temperatures below .Comment: 34 pages, 20 figure
Weak antilocalization in two-dimensional systems with large Rashba splitting
We develop the theory of quantum transport and magnetoconductivity for
two-dimensional electrons with an arbitrary large (even exceeding the Fermi
energy), linear-in-momentum Rashba or Dresselhaus spin-orbit splitting. For
short-range disorder potential, we derive the analytical expression for the
quantum conductivity correction, which accounts for interference processes with
an arbitrary number of scattering events and is valid beyond the diffusion
approximation. We demonstrate that the zero-field conductivity correction is
given by the sum of the universal logarithmic "diffusive" term and a
"ballistic" term. The latter is temperature independent and encodes information
about spectrum properties. This information can be extracted experimentally by
measuring the conductivity correction at different temperatures and electron
concentrations. We calculate the quantum correction in the whole range of
classically weak magnetic fields and find that the magnetoconductivity is
negative both in the diffusive and in the ballistic regimes, for an arbitrary
relation between the Fermi energy and the spin-orbit splitting. We also
demonstrate that the magnetoconductivity changes with the Fermi energy when the
Fermi level is above the "Dirac point" and does not depend on the Fermi energy
when it goes below this point.Comment: 12 pages, 5 figures and Online Supplemental Material (15 pages, 7
figures
Transversal magnetoresistance and Shubnikov-de Haas oscillations in Weyl semimetals
We explore theoretically the magnetoresistance of Weyl semimetals in
transversal magnetic fields away from charge neutrality. The analysis within
the self-consistent Born approximation is done for the two different models of
disorder: (i) short-range impurties and (ii) charged (Coulomb) impurities. For
these models of disorder, we calculate the conductivity away from charge
neutrality point as well as the Hall conductivity, and analyze the transversal
magnetoresistance (TMR) and Shubnikov-de Haas oscillations for both types of
disorder. We further consider a model with Weyl nodes shifted in energy with
respect to each other (as found in various materials) with the chemical
potential corresponding to the total charge neutrality. In the experimentally
most relevant case of Coulomb impurities, we find in this model a large TMR in
a broad range of quantizing magnetic fields. More specifically, in the
ultra-quantum limit, where only the zeroth Landau level is effective, the TMR
is linear in magnetic field. In the regime of moderate (but still quantizing)
magnetic fields, where the higher Landau levels are relevant, the rapidly
growing TMR is supplemented by strong Shubnikov-de Haas oscillations,
consistent with experimental observations
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