647 research outputs found
Localization and interactions in topological and non-topological bands in two dimensions
A two-dimensional electron gas in a high magnetic field displays
macroscopically degenerate Landau levels, which can be split into Hofstadter
subbands by means of a weak periodic potential. By carefully engineering such a
potential, one can precisely tune the number, bandwidths, bandgaps and Chern
character of these subbands. This allows a detailed study of the interplay of
disorder, interaction and topology in two dimensional systems. We first explore
the physics of disorder and single-particle localization in subbands derived
from the lowest Landau level, that nevertheless may have a topological nature
different from that of the entire lowest Landau level. By projecting the
Hamiltonian onto subbands of interest, we systematically explore the
localization properties of single-particle eigenstates in the presence of
quenched disorder. We then introduce electron-electron interactions and
investigate the fate of many-body localization in subbands of varying
topological character
Many-body localization in Landau level subbands
We explore the problem of localization in topological and non-topological
nearly-flat subbands derived from the lowest Landau level, in the presence of
quenched disorder and short-range interactions. We consider two models: a
suitably engineered periodic potential, and randomly distributed point-like
impurities. We perform numerical exact diagonalization on a torus geometry and
use the mean level spacing ratio as a diagnostic of
ergodicity. For topological subbands, we find there is no ergodicity breaking
in both the one and two dimensional thermodynamic limits. For non-topological
subbands, in constrast, we find evidence of an ergodicity breaking transition
at finite disorder strength in the one-dimensional thermodynamic limit.
Intriguingly, indications of similar behavior in the two-dimensional
thermodynamic limit are found, as well. This constitutes a novel,
setting for the study of the many-body localization
transition in one and two dimensions
Composite fermions in bands with N-fold rotational symmetry
We study the effect of band anisotropy with discrete rotational symmetry
(where ) in the quantum Hall regime of two-dimensional electron
systems. We focus on the composite Fermi liquid (CFL) at half filling of the
lowest Landau level. We find that the magnitude of anisotropy transferred to
the composite fermions decreases very rapidly with . We demonstrate this by
performing density matrix normalization group calculations on the CFL, and
comparing the anisotropy of the composite fermion Fermi contour with that of
the (non-interacting) electron Fermi contour at zero magnetic field. We also
show that the effective interaction between the electrons after projecting into
a single Landau level is much less anisotropic than the band, a fact which does
not depend on filling and thus has implications for other quantum Hall states
as well. Our results confirm experimental observations on anisotropic bands
with warped Fermi contours, where the only detectable effect on the composite
Fermi contour is an elliptical distortion ().Comment: 6 pages + bibliography, 5 figure
Connection between Fermi contours of zero-field electrons and composite fermions in two-dimensional systems
We investigate the relation between the Fermi sea (FS) of zero-field carriers
in two-dimensional systems and the FS of the corresponding composite fermions
which emerge in a high magnetic field at filling , as the
kinetic energy dispersion is varied. We study cases both with and without
rotational symmetry, and find that there is generally no straightforward
relation between the geometric shapes and topologies of the two FSs. In
particular, we show analytically that the composite Fermi liquid (CFL) is
completely insensitive to a wide range of changes to the zero-field dispersion
which preserve rotational symmetry, including ones that break the zero-field FS
into multiple disconnected pieces. In the absence of rotational symmetry, we
show that the notion of `valley pseudospin' in many-valley systems is
generically not transferred to the CFL, in agreement with experimental
observations. We also discuss how a rotationally symmetric band structure can
induce a reordering of the Landau levels, opening interesting possibilities of
observing higher-Landau-level physics in the high-field regime.Comment: 7 pages + references, 7 figures. Added many-body DMRG calculatio
Geometry of flux attachment in anisotropic fractional quantum Hall states
Fractional quantum Hall (FQH) states are known to possess an internal metric
degree of freedom that allows them to minimize their energy when contrasting
geometries are present in the problem (e.g., electron band mass and dielectric
tensor). We investigate the internal metric of several incompressible FQH
states by probing its response to band mass anisotropy using infinite DMRG
simulations on a cylinder geometry. We test and apply a method to extract the
internal metric of a FQH state from its guiding center structure factor. We
find that the response to band mass anisotropy is approximately the same for
states in the same Jain sequence, but changes substantially between different
sequences. We provide a theoretical explanation of the observed behavior of
primary states at filling in terms of a minimal microscopic model
of flux attachment.Comment: 12 pages including references, 14 figure
Global Tracking Passivity--based PI Control of Bilinear Systems and its Application to the Boost and Modular Multilevel Converters
This paper deals with the problem of trajectory tracking of a class of
bilinear systems with time--varying measurable disturbance. A set of matrices
{A,B_i} has been identified, via a linear matrix inequality, for which it is
possible to ensure global tracking of (admissible, differentiable) trajectories
with a simple linear time--varying PI controller. Instrumental to establish the
result is the construction of an output signal with respect to which the
incremental model is passive. The result is applied to the boost and the
modular multilevel converter for which experimental results are given.Comment: 9 pages, 10 figure
Fermi surfaces of composite fermions
The fractional quantum Hall (FQH) effect was discovered in two-dimensional
electron systems subject to a large perpendicular magnetic field nearly four
decades ago. It helped launch the field of topological phases, and in addition,
because of the quenching of the kinetic energy, gave new meaning to the phrase
"correlated matter". Most FQH phases are gapped like insulators and
superconductors; however, a small subset with even denominator fractional
fillings nu of the Landau level, typified by nu = 1/2, are found to be gapless,
with a Fermi surface akin to metals. We discuss our results, obtained
numerically using the infinite Density Matrix Renormalization Group (iDMRG)
scheme, on the effect of non-isotropic distortions with discrete N-fold
rotational symmetry of the Fermi surface at zero magnetic field on the Fermi
surface of the correlated nu = 1/2 state. We find that while the response for N
= 2 (elliptical) distortions is significant (and in agreement with experimental
observations with no adjustable parameters), it decreases very rapidly as N is
increased. Other anomalies, like resilience to breaking the Fermi surface into
disjoint pieces, are also found. This highlights the difference between Fermi
surfaces formed from the kinetic energy, and those formed of purely potential
energy terms in the Hamiltonian.Comment: Review of arXiv:1701.07832, arXiv:1704.06265 and arXiv:1706.09470
with some new results. Conference proceedings for "Quantum Fluids and Solids
2019", Edmonton, AB, August 201
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