27 research outputs found
High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
We study theoretically the energy and spatially resolved local density of
states (LDoS) in graphene at high perpendicular magnetic field. For this
purpose, we extend from the Schr\"odinger to the Dirac case a
semicoherent-state Green's-function formalism, devised to obtain in a
quantitative way the lifting of the Landau-level degeneracy in the presence of
smooth confinement and smooth disordered potentials. Our general technique,
which rigorously describes quantum-mechanical motion in a magnetic field beyond
the semi-classical guiding center picture of vanishing magnetic length (both
for the ordinary two-dimensional electron gas and graphene), is connected to
the deformation (Weyl) quantization theory in phase space developed in
mathematical physics. For generic quadratic potentials of either scalar (i.e.,
electrostatic) or mass (i.e., associated with coupling to the substrate) types,
we exactly solve the regime of large magnetic field (yet at finite magnetic
length - formally, this amounts to considering an infinite Fermi velocity)
where Landau-level mixing becomes negligible. Hence, we obtain a closed-form
expression for the graphene Green's function in this regime, providing
analytically the discrete energy spectra for both cases of scalar and mass
parabolic confinement. Furthermore, the coherent-state representation is shown
to display a hierarchy of local energy scales ordered by powers of the magnetic
length and successive spatial derivatives of the local potential, which allows
one to devise controlled approximation schemes at finite temperature for
arbitrary and possibly disordered potential landscapes. As an application, we
derive general analytical non-perturbative expressions for the LDoS, which may
serve as a good starting point for interpreting experimental studies.Comment: 27 pages, 2 figures ; v2: typos corrected, corresponds to published
versio
Quantum transport properties of two-dimensional electron gases under high magnetic fields
We study quantum transport properties of two-dimensional electron gases under
high perpendicular magnetic fields. For this purpose, we reformulate the
high-field expansion, usually done in the operatorial language of the
guiding-center coordinates, in terms of vortex states within the framework of
real-time Green functions. These vortex states arise naturally from the
consideration that the Landau levels quantization can follow directly from the
existence of a topological winding number. The microscopic computation of the
current can then be performed within the Keldysh formalism in a systematic way
at finite magnetic fields (i.e. beyond the semi-classical limit ). The formalism allows us to define a general vortex current density as
long as the gradient expansion theory is applicable. As a result, the total
current is expressed in terms of edge contributions only. We obtain the first
and third lowest order contributions to the current due to Landau-levels mixing
processes, and derive in a transparent way the quantization of the Hall
conductance. Finally, we point out qualitatively the importance of
inhomogeneities of the vortex density to capture the dissipative longitudinal
transport.Comment: 21 pages, 5 figures ; main change: the discussion about the
longitudinal transport (Part A of Section VI) is rewritten and enhance
Transmission coefficient through a saddle-point electrostatic potential for graphene in the quantum Hall regime
From the scattering of semicoherent-state wavepackets at high magnetic field,
we derive analytically the transmission coefficient of electrons in graphene in
the quantum Hall regime through a smooth constriction described by a quadratic
saddle-point electrostatic potential. We find anomalous half-quantized
conductance steps that are rounded by a backscattering amplitude related to the
curvature of the potential. Furthermore, the conductance in graphene breaks
particle-hole symmetry in cases where the saddle-point potential is itself
asymmetric in space. These results have implications both for the
interpretation of split-gate transport experiments, and for the derivation of
quantum percolation models for graphene.Comment: 4 pages, 2 figures Minor modifications as publishe
Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
We develop in detail a new formalism [as a sequel to the work of T. Champel
and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for
treating quantum problems involving slowly-varying potentials at high magnetic
fields in two-dimensional electron gases. For an arbitrary smooth potential we
show that electronic Green's function is fully determined by closed recursive
expressions that take the form of a high magnetic field expansion in powers of
the magnetic length l_B. For illustration we determine entirely Green's
function at order l_B^3, which is then used to obtain quantum expressions for
the local charge and current electronic densities at equilibrium. Such results
are valid at high but finite magnetic fields and for arbitrary temperatures, as
they take into account Landau level mixing processes and wave function
broadening. We also check the accuracy of our general functionals against the
exact solution of a one-dimensional parabolic confining potential,
demonstrating the controlled character of the theory to get equilibrium
properties. Finally, we show that transport in high magnetic fields can be
described hydrodynamically by a local equilibrium regime and that dissipation
mechanisms and quantum tunneling processes are intrinsically included at the
microscopic level in our high magnetic field theory. We calculate microscopic
expressions for the local conductivity tensor, which possesses both transverse
and longitudinal components, providing a microscopic basis for the
understanding of dissipative features in quantum Hall systems.Comment: small typos corrected; published versio
Local density of states in disordered two-dimensional electron gases at high magnetic field
Motivated by high-accuracy scanning tunneling spectroscopy measurements on
disordered two-dimensional electron gases in strong magnetic field, we present
an exact solution for the local density of states (LDoS) of electrons moving in
an arbitrary potential smooth on the scale of the magnetic length, that can be
locally described up to its second derivatives. We use a technique based on
coherent state Green's functions, allowing us to treat on an equal footing
confining and open quantum systems. The energy-dependence of the LDoS is found
to be universal in terms of local geometric properties, such as drift velocity
and potential curvature. We also show that thermal effects are quite important
close to saddle points, leading to an overbroadening of the tunneling
trajectories.Comment: 4 pages, 3 figures ; typos corrected + one reference update
Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling
We theoretically investigate the spectral properties and the spatial
dependence of the local density of states (LDoS) in disordered two-dimensional
electron gases (2DEG) in the quantum Hall regime, taking into account the
combined presence of electrostatic disorder, random Rashba spin-orbit in-
teraction, and finite Zeeman coupling. To this purpose, we extend a
coherent-state Green's function formalism previously proposed for spinless 2DEG
in the presence of smooth arbitrary disorder, that here incorporates the
nontrivial coupling between the orbital and spin degrees of freedom into the
electronic drift states. The formalism allows us to obtain analytical and
controlled nonperturbative expressions of the energy spectrum in arbitrary
locally flat disorder potentials with both random electric fields and Rashba
coupling. As an illustration of this theory, we derive analytical microscopic
expressions for the LDoS in different temperature regimes which can be used as
a starting point to interpret scanning tunneling spectroscopy data at high
magnetic fields. In this context, we study the spatial dependence and linewidth
of the LDoS peaks and explain an experimentally-noticed correlation between the
spatial dispersion of the spin-orbit splitting and the local extrema of the
potential landscape.Comment: 18 pages, 5 figures; typos corrected and Sec. IV A rewritten;
published versio
0-pi Transitions in a Superconductor/Chiral Ferromagnet/Superconductor Junction induced by a Homogeneous Cycloidal Spiral
We study the pi phase in a superconductor-ferromagnet-superconductor
Josephson junction, with a ferromagnet showing a cycloidal spiral spin
modulation with in-plane propagation vector. Our results reveal a high
sensitivity of the junction to the spiral order and indicate the presence of
0-pi quantum phase transitions as function of the spiral wave vector. We find
that the chiral magnetic order introduces chiral superconducting triplet pairs
that strongly influence the physics in such Josephson junctions, with potential
applications in nanoelectronics and spintronics.Comment: 4 pages, 4 figures; the derivation part has been reorganized + added
note and new references, published versio
Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states
We have developed a Green's function formalism based on the use of an
overcomplete semicoherent basis of vortex states, specially devoted to the
study of the Hamiltonian quantum dynamics of electrons at high magnetic fields
and in an arbitrary potential landscape smooth on the scale of the magnetic
length. This formalism is used here to derive the exact Green's function for an
arbitrary quadratic potential in the special limit where Landau level mixing
becomes negligible. This solution remarkably embraces under a unified form the
cases of confining and unconfining quadratic potentials. This property results
from the fact that the overcomplete vortex representation provides a more
general type of spectral decomposition of the Hamiltonian operator than usually
considered. Whereas confining potentials are naturally characterized by
quantization effects, lifetime effects emerge instead in the case of
saddle-point potentials. Our derivation proves that the appearance of lifetimes
has for origin the instability of the dynamics due to quantum tunneling at
saddle points of the potential landscape. In fact, the overcompleteness of the
vortex representation reveals an intrinsic microscopic irreversibility of the
states synonymous with a spontaneous breaking of the time symmetry exhibited by
the Hamiltonian dynamics.Comment: 19 pages, 4 figures ; a few typos corrected + some passages in Sec. V
rewritte
Diagrammatic Approach for the High-Temperature Regime of Quantum Hall Transitions
We use a general diagrammatic formalism based on a local conductivity
approach to compute electronic transport in continuous media with long-range
disorder, in the absence of quantum interference effects. The method allows us
then to investigate the interplay of dissipative processes and random drifting
of electronic trajectories in the high-temperature regime of quantum Hall
transitions. We obtain that the longitudinal conductance \sigma_{xx} scales
with an exponent {\kappa}=0.767\pm0.002 in agreement with the value
{\kappa}=10/13 conjectured from analogies to classical percolation. We also
derive a microscopic expression for the temperature-dependent peak value of
\sigma_{xx}, useful to extract {\kappa} from experiments.Comment: 4+epsilon pages, 5 figures, attached with Supplementary Material. A
discussion and a plot of the temperature-dependent longitudinal conductance
was added in the final versio