6,281 research outputs found
Effect of Hilbert space truncation on Anderson localization
The 1-D Anderson model possesses a completely localized spectrum of
eigenstates for all values of the disorder. We consider the effect of
projecting the Hamiltonian to a truncated Hilbert space, destroying time
reversal symmetry. We analyze the ensuing eigenstates using different measures
such as inverse participation ratio and sample-averaged moments of the position
operator. In addition, we examine amplitude fluctuations in detail to detect
the possibility of multifractal behavior (characteristic of mobility edges)
that may arise as a result of the truncation procedure.Comment: 20 pages, 23 figure
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
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
Beyond universal behavior in the one-dimensional chain with random nearest neighbor hopping
We study the one-dimensional nearest neighbor tight binding model of
electrons with independently distributed random hopping and no on-site
potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to
sub-lattice symmetry, for each realization). For non-singular distributions of
the hopping, it is known that the model exhibits a universal, singular behavior
of the density of states and of the localization
length , near the band center . (This singular
behavior is also applicable to random XY and Heisenberg spin chains; it was
first obtained by Dyson for a specific random harmonic oscillator chain).
Simultaneously, the state at shows a universal, sub-exponential decay
at large distances . In this study, we consider
singular, but normalizable, distributions of hopping, whose behavior at small
is of the form , characterized by a
single, continuously tunable parameter . We find, using a
combination of analytic and numerical methods, that while the universal result
applies for , it no longer holds in the interval . In particular, we find that the form of the density of states singularity
is enhanced (relative to the Dyson result) in a continuous manner depending on
the non-universal parameter ; simultaneously, the localization length
shows a less divergent form at low energies, and ceases to diverge below
. For , the fall-off of the state at large
distances also deviates from the universal result, and is of the form , which decays faster than an exponential for
.Comment: 14 pages, 7 figure
Structural, optical and nanomechanical properties of (1 1 1) oriented nanocrystalline ZnTe thin films
Structural, optical and nanomechanical properties of nanocrystalline Zinc Telluride (ZnTe) films
of thickness upto 10 microns deposited at room temperature on borosilicate glass substrates are reported.
X-ray diffraction patterns reveal that the films were preferentially oriented along the (1 1 1) direction.
The maximum refractive index of the films was 2.74 at a wavelength of 2000 nm. The optical band gap
showed strong thickness dependence. The average film hardness and Young’s modulus obtained from loaddisplacement
curves and analyzed by Oliver-Pharr method were 4 and 70 GPa respectively. Hardness of
(1 1 1) oriented ZnTe thin films exhibited almost 5 times higher value than bulk. The studies show clearly
that the hardness increases with decreasing indentation size, for indents between 30 and 300 nm in depth
indicating the existence of indentation size effect. The coefficient of friction for these films as obtained from
the nanoscratch test was ∼0.4.Financial support
in the form of fellowships to MSRNK and SK from the
ACRHEM project of DRDO is acknowledged
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