4,145 research outputs found
Fixed-N Superconductivity: The Crossover from the Bulk to the Few-Electron Limit
We present a truly canonical theory of superconductivity in ultrasmall
metallic grains by variationally optimizing fixed-N projected BCS
wave-functions, which yields the first full description of the entire crossover
from the bulk BCS regime (mean level spacing bulk gap )
to the ``fluctuation-dominated'' few-electron regime (). A
wave-function analysis shows in detail how the BCS limit is recovered for , and how for pairing correlations become
delocalized in energy space. An earlier grand-canonical prediction for an
observable parity effect in the spectral gaps is found to survive the fixed-N
projection.Comment: 4 pages, 3 figures, RevTeX, V2: minor charges to mach final printed
versio
Distribution of level curvatures for the Anderson model at the localization-delocalization transition
We compute the distribution function of single-level curvatures, , for
a tight binding model with site disorder, on a cubic lattice. In metals
is very close to the predictions of the random-matrix theory (RMT). In
insulators has a logarithmically-normal form. At the Anderson
localization-delocalization transition fits very well the proposed novel
distribution with , which
approaches the RMT result for large and is non-analytical at small . We
ascribe such a non-analiticity to the spatial multifractality of the critical
wave functions.Comment: 4 ReVTeX pages and 4(.epsi)figures included in one uuencoded packag
Universality of Decoherence
We consider environment induced decoherence of quantum superpositions to
mixtures in the limit in which that process is much faster than any competing
one generated by the Hamiltonian of the isolated system. While
the golden rule then does not apply we can discard . By allowing
for simultaneous couplings to different reservoirs, we reveal decoherence as a
universal short-time phenomenon independent of the character of the system as
well as the bath and of the basis the superimposed states are taken from. We
discuss consequences for the classical behavior of the macroworld and quantum
measurement: For the decoherence of superpositions of macroscopically distinct
states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure
Superconductivity in Ultrasmall Metallic Grains
We develop a theory of superconductivity in ultrasmall (nm-scale) metallic
grains having a discrete electronic eigenspectrum with a mean level spacing of
order of the bulk gap. The theory is based on calculating the eigenspectrum
using a generalized BCS variational approach, whose applicability has been
extensively demonstrated in studies of pairing correlations in nuclear physics.
We discuss how conventional mean field theory breaks down with decreasing
sample size, how the so-called blocking effect weakens pairing correlations in
states with non-zero total spin, and how this affects the discrete
eigenspectrum's behavior in a magnetic field, which favors non-zero total spin.
In ultrasmall grains, spin magnetism dominates orbital magnetism, just as in
thin films in a parallel field; but whereas in the latter the magnetic-field
induced transition to a normal state is known to be first-order, we show that
in ultrasmall grains it is softened by finite size effects. Our calculations
qualitatively reproduce the magnetic-field dependent tunneling spectra for
individual aluminum grains measured recently by Ralph, Black and Tinkham. We
argue that previously-discussed parity effects for the odd-even ground state
energy difference are presently not observable for experimental reasons, and
propose an analogous parity effect for the pair-breaking energy that should be
observable provided that the grain size can be controlled sufficiently well.
Finally, experimental evidence is pointed out that the dominant role played by
time-reversed pairs of states, well-established in bulk and in dirty
superconductors, persists also in ultrasmall grains.Comment: 21 pages RevTeX, 12 EPS figures included, uses epsf.st
Thermodynamic properties of a small superconducting grain
The reduced BCS Hamiltonian for a metallic grain with a finite number of
electrons is considered. The crossover between the ultrasmall regime, in which
the level spacing, , is larger than the bulk superconducting gap, ,
and the small regime, where , is investigated analytically
and numerically. The condensation energy, spin magnetization and tunneling peak
spectrum are calculated analytically in the ultrasmall regime, using an
approximation controlled by as small parameter, where is the
number of interacting electron pairs. The condensation energy in this regime is
perturbative in the coupling constant , and is proportional to . We find that also in a large regime with
, in which pairing correlations are already rather well developed,
the perturbative part of the condensation energy is larger than the singular,
BCS, part. The condition for the condensation energy to be well approximated by
the BCS result is found to be roughly . We show how
the condensation energy can, in principle, be extracted from a measurement of
the spin magnetization curve, and find a re-entrant susceptibility at zero
temperature as a function of magnetic field, which can serve as a sensitive
probe for the existence of superconducting correlations in ultrasmall grains.
Numerical results are presented which suggest that in the large limit the
1/N correction to the BCS result for the condensation energy is larger than
.Comment: 17 pages, 7 figures, Submitted to Phys. Rev.
On the critical level-curvature distribution
The parametric motion of energy levels for non-interacting electrons at the
Anderson localization critical point is studied by computing the energy
level-curvatures for a quasiperiodic ring with twisted boundary conditions. We
find a critical distribution which has the universal random matrix theory form
for large level-curvatures corresponding to
quantum diffusion, although overall it is close to approximate log-normal
statistics corresponding to localization. The obtained hybrid distribution
resembles the critical distribution of the disordered Anderson model and makes
a connection to recent experimental data.Comment: 4 pages, 3 figure
Temperature-induced pair correlations in clusters and nuclei
The pair correlations in mesoscopic systems such as -size superconducting
clusters and nuclei are studied at finite temperature for the canonical
ensemble of fermions in model spaces with a fixed particle number: i) a
degenerate spherical shell (strong coupling limit), ii) an equidistantly spaced
deformed shell (weak coupling limit). It is shown that after the destruction of
the pair correlations at T=0 by a strong magnetic field or rapid rotation,
heating can bring them back. This phenomenon is a consequence of the fixed
number of fermions in the canonical ensemble
Re-entrant spin susceptibility of a superconducting grain
We study the spin susceptibility chi of a small, isolated superconducting
grain. Due to the interplay between parity effects and pairing correlations,
the dependence of chi on temperature T is qualitatively different from the
standard BCS result valid in the bulk limit. If the number of electrons on the
grain is odd, chi shows a re-entrant behavior as a function of temperature.
This behavior persists even in the case of ultrasmall grains where the mean
level spacing is much larger than the BCS gap. If the number of electrons is
even, chi(T) is exponentially small at low temperatures.Comment: 9 pages, 3 figures. To be published in PR
A small superconducting grain in the canonical ensemble
By means of the Lanczos method we analyze superconducting correlations in
ultrasmall grains at fixed particle number. We compute the ground state
properties and the excitation gap of the pairing Hamiltonian as a function of
the level spacing . Both quantities turn out to be parity dependent and
universal functions of the ratio ( is the BCS gap). We
then characterize superconductivity in the canonical ensemble from the scaling
behavior of correlation functions in energy space.Comment: 11 pages Revtex, 5 figures .ep
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