582,801 research outputs found
Delocalization and Diffusion Profile for Random Band Matrices
We consider Hermitian and symmetric random band matrices in dimensions. The matrix entries , indexed by x,y \in
(\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy}
= \E |h_{xy}|^2. We assume that is negligible if exceeds the
band width . In one dimension we prove that the eigenvectors of are
delocalized if . We also show that the magnitude of the matrix
entries \abs{G_{xy}}^2 of the resolvent is self-averaging
and we compute \E \abs{G_{xy}}^2. We show that, as and , the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator
whose diffusion constant we compute. Similar results are obtained in higher
dimensions
Anomalous Nernst and Hall effects in magnetized platinum and palladium
We study the anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) in
proximity-induced ferromagnetic palladium and platinum which is widely used in
spintronics, within the Berry phase formalism based on the relativistic band
structure calculations. We find that both the anomalous Hall ()
and Nernst () conductivities can be related to the spin Hall
conductivity () and band exchange-splitting () by
relations and
,
respectively. In particular, these relations would predict that the
in the magnetized Pt (Pd) would be positive (negative) since
the is positive (negative). Furthermore, both
and are approximately proportional to the
induced spin magnetic moment () because the is a linear
function of . Using the reported in the magnetized Pt and Pd, we
predict that the intrinsic anomalous Nernst conductivity (ANC) in the magnetic
platinum and palladium would be gigantic, being up to ten times larger than,
e.g., iron, while the intrinsic anomalous Hall conductivity (AHC) would also be
significant.Comment: Accepted for publication in the Physical Review
Sandwich semigroups in locally small categories II: Transformations
Fix sets and , and write for the set of all
partial functions . Fix a partial function , and define the
operation on by for
. The sandwich semigroup
is denoted . We apply general results from Part I to
thoroughly describe the structural and combinatorial properties of
, as well as its regular and idempotent-generated
subsemigroups, Reg and .
After describing regularity, stability and Green's relations and preorders, we
exhibit Reg as a pullback product of certain regular
subsemigroups of the (non-sandwich) partial transformation semigroups
and , and as a kind of "inflation" of
, where is the image of the sandwich element . We also
calculate the rank (minimal size of a generating set) and, where appropriate,
the idempotent rank (minimal size of an idempotent generating set) of
, Reg and . The same program is also carried out for sandwich
semigroups of totally defined functions and for injective partial functions.
Several corollaries are obtained for various (non-sandwich) semigroups of
(partial) transformations with restricted image, domain and/or kernel.Comment: 35 pages, 11 figures, 1 table. V2: updated according to referee
report, expanded abstract, to appear in Algebra Universali
Invaded cluster simulations of the XY model in two and three dimensions
The invaded cluster algorithm is used to study the XY model in two and three
dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model,
in the same universality class as the 3D XY model, is also studied. The static
critical properties of the model and the dynamical properties of the algorithm
are reported. The results are K_c=0.45412(2) for the 3D XY model and
eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results
are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show
any critical slowing for the magnetization or critical temperature estimator
for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v
Thermal Hall conductivity of marginal Fermi liquids subject to out-of plane impurities in high- cuprates
The effect of out-of-plane impurities on the thermal Hall conductivity
of in-plane marginal-Fermi-liquid (MFL) quasiparticles in
high- cuprates is examined by following the work on electrical Hall
conductivity by Varma and Abraham [Phys. Rev. Lett. 86, 4652
(2001)]. It is shown that the effective Lorentz force exerted by these
impurities is a weak function of energies of the MFL quasiparticles, resulting
in nearly the same temperature dependence of and ,
indicative of obedience of the Wiedemann-Franz law. The inconsistency of the
theoretical result with the experimental one is speculated to be the
consequence of the different amounts of out-of-plane impurities in the two
YBaCuO samples used for the and measurements.Comment: 5 pages, 2 eps figures; final versio
Thermally Activated Deviations from Quantum Hall Plateaus
The Hall conductivity of a two-dimensional electron system
is quantized in units of when the Fermi level is located in the
mobility gap between two Landau levels. We consider the deviation of
from a quantized value caused by the thermal activation of
electrons to the extended states for the case of a long range random potential.
This deviation is of the form . The prefactor
is equal to at temperatures above a characteristic
temperature . With the temperature decreasing below , decays according to a power law: . Similar results are valid for a fractional Hall
plateau near filling factor if is replaced by the fractional charge
.Comment: 4 pages in PostScript (figures included
Transverse "resistance overshoot" in a Si/SiGe two-dimensional electron gas in the quantum Hall effect regime
We investigate the peculiarities of the "overshoot" phenomena in the
transverse Hall resistance R_{xy} in Si/SiGe. Near the low magnetic field end
of the quantum Hall effect plateaus, when the filling factor \nu approaches an
integer i, R_{xy} overshoots the normal plateau value h/ie^2. However, if
magnetic field B increases further, R_{xy} decreases to its normal value. It is
shown that in the investigated sample n-Si/Si_{0.7}Ge_{0.3}, overshoots exist
for almost all \nu. Existence of overshoot in R_{xy} observed in different
materials and for different \nu, where splitting of the adjacent Landau bands
has different character, hints at the common origin of this effect. Comparison
of the experimental curves R_{xy}(\nu) for \nu = 3 and \nu = 5 with and without
overshoot showed that this effect exist in the whole interval between plateaus,
not only in the region where R_{xy} exceeds the normal plateau value.Comment: 3 pages, 5 EPS figure
Quantum Hall effects of graphene with multi orbitals: Topological numbers, Boltzmann conductance and Semi-classical quantization
Hall conductance as the Chern numbers of the Berry connection
in the magnetic Brillouin zone is calculated for a realistic multi band
tight-band model of graphene with non-orthogonal basis. It is confirmed that
the envelope of coincides with a semi-classical result when
magnetic field is sufficiently small.
The Hall resistivity from the weak-field Boltzmann theory also
explains the overall behaviour of the if the Fermi surface is
composed of a single energy band. The plateaux of are explained
from semi-classical quantization and necessary modification is proposed for the
Dirac fermion regimes.Comment: 5pages, 3figure
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