307 research outputs found
Spectral weight transfer in a disorder-broadened Landau level
In the absence of disorder, the degeneracy of a Landau level (LL) is
, where is the magnetic field, is the area of the sample
and is the magnetic flux quantum. With disorder, localized states
appear at the top and bottom of the broadened LL, while states in the center of
the LL (the critical region) remain delocalized. This well-known phenomenology
is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE)
[1]. One unnoticed issue is where the new states appear as the magnetic field
is increased. Here we demonstrate that they appear predominantly inside the
critical region. This leads to a certain ``spectral ordering'' of the localized
states that explains the stripes observed in measurements of the local inverse
compressibility [2-3], of two-terminal conductance [4], and of Hall and
longitudinal resistances [5] without invoking interactions as done in previous
work [6-8].Comment: 5 pages 3 figure
Experimental Measurement of the Berry Curvature from Anomalous Transport
Geometrical properties of energy bands underlie fascinating phenomena in a
wide-range of systems, including solid-state materials, ultracold gases and
photonics. Most famously, local geometrical characteristics like the Berry
curvature can be related to global topological invariants such as those
classifying quantum Hall states or topological insulators. Regardless of the
band topology, however, any non-zero Berry curvature can have important
consequences, such as in the semi-classical evolution of a wave packet. Here,
we experimentally demonstrate for the first time that wave packet dynamics can
be used to directly map out the Berry curvature. To this end, we use optical
pulses in two coupled fibre loops to study the discrete time-evolution of a
wave packet in a 1D geometrical "charge" pump, where the Berry curvature leads
to an anomalous displacement of the wave packet under pumping. This is both the
first direct observation of Berry curvature effects in an optical system, and,
more generally, the proof-of-principle demonstration that semi-classical
dynamics can serve as a high-resolution tool for mapping out geometrical
properties
Rectified voltage induced by a microwave field in a confined two-dimensional electron gas with a mesoscopic static vortex
We investigate the effect of a microwave field on a confined two dimensional
electron gas which contains an insulating region comparable to the Fermi
wavelength. The insulating region causes the electron wave function to vanish
in that region. We describe the insulating region as a static vortex. The
vortex carries a flux which is determined by vanishing of the charge density of
the electronic fluid due to the insulating region. The sign of the vorticity
for a hole is opposite to the vorticity for adding additional electrons. The
vorticity gives rise to non-commuting kinetic momenta. The two dimensional
electron gas is described as fluid with a density which obeys the Fermi-Dirac
statistics. The presence of the confinement potential gives rise to vanishing
kinetic momenta in the vicinity of the classical turning points. As a result,
the Cartesian coordinate do not commute and gives rise to a Hall current which
in the presence of a modified Fermi-Surface caused by the microwave field
results in a rectified voltage. Using a Bosonized formulation of the two
dimensional gas in the presence of insulating regions allows us to compute the
rectified current. The proposed theory may explain the experimental results
recently reported by J. Zhang et al.Comment: 14 pages, 2 figure
Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
The discovery of topological states of matter has profoundly augmented our
understanding of phase transitions in physical systems. Instead of local order
parameters, topological phases are described by global topological invariants
and are therefore robust against perturbations. A prominent example thereof is
the two-dimensional integer quantum Hall effect. It is characterized by the
first Chern number which manifests in the quantized Hall response induced by an
external electric field. Generalizing the quantum Hall effect to
four-dimensional systems leads to the appearance of a novel non-linear Hall
response that is quantized as well, but described by a 4D topological invariant
- the second Chern number. Here, we report on the first observation of a bulk
response with intrinsic 4D topology and the measurement of the associated
second Chern number. By implementing a 2D topological charge pump with
ultracold bosonic atoms in an angled optical superlattice, we realize a
dynamical version of the 4D integer quantum Hall effect. Using a small atom
cloud as a local probe, we fully characterize the non-linear response of the
system by in-situ imaging and site-resolved band mapping. Our findings pave the
way to experimentally probe higher-dimensional quantum Hall systems, where new
topological phases with exotic excitations are predicted
Fractional quantum Hall effect in the absence of Landau levels
It has been well-known that topological phenomena with fractional
excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982}
will emerge when electrons move in Landau levels. In this letter, we report the
discovery of the FQHE in the absence of Landau levels in an interacting fermion
model. The non-interacting part of our Hamiltonian is the recently proposed
topologically nontrivial flat band model on the checkerboard lattice
\cite{sun}. In the presence of nearest-neighboring repulsion (), we find
that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5
filling, however, a next-nearest-neighboring repulsion is needed for the
occurrence of the 1/5 FQHE when is not too strong. We demonstrate the
characteristic features of these novel states and determine the phase diagram
correspondingly.Comment: 6 pages and 4 figure
Global Minimum Depth In Edwards-Anderson Model
In the literature the most frequently cited data are quite contradictory, and
there is no consensus on the global minimum value of 2D Edwards-Anderson (2D
EA) Ising model. By means of computer simulations, with the help of exact
polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum
depth in 2D EA-type models. We found a dependence of the global minimum depth
on the dimension of the problem N and obtained its asymptotic value in the
limit . We believe these evaluations can be further used for
examining the behavior of 2D Bayesian models often used in machine learning and
image processing.Comment: 10 pages, 4 figures, 2 tables, submitted to conference on Engineering
Applications of Neural Networks (EANN 2019
Quantum Hall Effect in a Holographic Model
We consider a holographic description of a system of strongly coupled
fermions in 2+1 dimensions based on a D7-brane probe in the background of
D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We
study the system at finite temperature and charge density, and in the presence
of a background magnetic field. We show that Minkowski-like embeddings that
terminate above the horizon describe a family of quantum Hall states with
filling fractions that are parameterized by a single discrete parameter. The
quantization of the Hall conductivity is a direct consequence of the
topological quantization of the fluxes. When the magnetic field is varied
relative to the charge density away from these discrete filling fractions, the
embeddings deform continuously into black-hole-like embeddings that enter the
horizon and that describe metallic states. We also study the thermodynamics of
this system and show that there is a first order phase transition at a critical
temperature from the quantum Hall state to the metallic state.Comment: v2: 27 pages, 12 figures. There is a major revision in the
quantitative analysis. The qualitative results and conclusions are unchanged,
with one exception: we show that the quantum Hall state embeddings, which
exist for discrete values of the filling fraction, deform continuously into
metallic state embeddings away from these filling fraction
Statistical Signatures of Photon Localization
The realization that electron localization in disordered systems (Anderson
localization) is ultimately a wave phenomenon has led to the suggestion that
photons could be similarly localized by disorder. This conjecture attracted
wide interest because the differences between photons and electrons - in their
interactions, spin statistics, and methods of injection and detection - may
open a new realm of optical and microwave phenomena, and allow a detailed study
of the Anderson localization transition undisturbed by the Coulomb interaction.
To date, claims of three-dimensional photon localization have been based on
observations of the exponential decay of the electromagnetic wave as it
propagates through the disordered medium. But these reports have come under
close scrutiny because of the possibility that the decay observed may be due to
residual absorption, and because absorption itself may suppress localization.
Here we show that the extent of photon localization can be determined by a
different approach - measurement of the relative size of fluctuations of
certain transmission quantities. The variance of relative fluctuations
accurately reflects the extent of localization, even in the presence of
absorption. Using this approach, we demonstrate photon localization in both
weakly and strongly scattering quasi-one-dimensional dielectric samples and in
periodic metallic wire meshes containing metallic scatterers, while ruling it
out in three-dimensional mixtures of aluminum spheres.Comment: 5 pages, including 4 figure
The space group classification of topological band insulators
Topological band insulators (TBIs) are bulk insulating materials which
feature topologically protected metallic states on their boundary. The existing
classification departs from time-reversal symmetry, but the role of the crystal
lattice symmetries in the physics of these topological states remained elusive.
Here we provide the classification of TBIs protected not only by time-reversal,
but also by crystalline symmetries. We find three broad classes of topological
states: (a) Gamma-states robust against general time-reversal invariant
perturbations; (b) Translationally-active states protected from elastic
scattering, but susceptible to topological crystalline disorder; (c) Valley
topological insulators sensitive to the effects of non-topological and
crystalline disorder. These three classes give rise to 18 different
two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route
for the systematic search for new types of TBIs.Comment: Accepted in Nature Physic
Pair-breaking quantum phase transition in superconducting nanowires
A quantum phase transition (QPT) between distinct ground states of matter is
a wide-spread phenomenon in nature, yet there are only a few experimentally
accessible systems where the microscopic mechanism of the transition can be
tested and understood. These cases are unique and form the experimentally
established foundation for our understanding of quantum critical phenomena.
Here we report the discovery that a magnetic-field-driven QPT in
superconducting nanowires - a prototypical 1d-system - can be fully explained
by the critical theory of pair-breaking transitions characterized by a
correlation length exponent and dynamic critical exponent . We find that in the quantum critical regime, the electrical
conductivity is in agreement with a theoretically predicted scaling function
and, moreover, that the theory quantitatively describes the dependence of
conductivity on the critical temperature, field magnitude and orientation,
nanowire cross sectional area, and microscopic parameters of the nanowire
material. At the critical field, the conductivity follows a
dependence predicted by phenomenological scaling theories and more recently
obtained within a holographic framework. Our work uncovers the microscopic
processes governing the transition: The pair-breaking effect of the magnetic
field on interacting Cooper pairs overdamped by their coupling to electronic
degrees of freedom. It also reveals the universal character of continuous
quantum phase transitions.Comment: 22 pages, 5 figure
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