20 research outputs found
Critical Quantum Chaos in 2D Disordered Systems with Spin-Orbit Coupling
We examine the validity of the recently proposed semi-Poisson level spacing
distribution function P(S), which characterizes `critical quantum chaos', in 2D
disordered systems with spin-orbit coupling. At the Anderson transition we show
that the semi-Poisson P(S) can describe closely the critical distribution
obtained with averaged boundary conditions, over Dirichlet in one direction
with periodic in the other and Dirichlet in both directions. We also obtain a
sub-Poisson linear number variance ,
with asymptotic value . The obtained critical statistics,
intermediate between Wigner and Poisson, is relevant for disordered systems and
chaotic models.Comment: 4 pages with 5 figure
Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice I
In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid
phase taking place at zero temperature between the quantum liquid and the
solid. In this and a succeeding paper, we re-visit this issue for a few
polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion
on a two dimensional L * L square lattice with periodic boundary conditions and
nearest neighbor hopping.Comment: 12 pages, 17 postscript figures, final version, added reference
Mesoscopic Wigner crystallization in two dimensional lattice models
The quantum-classical crossover from the Fermi liquid towards the Wigner
solid is numerically revisited, considering small square lattice models where
electrons interact via a Coulomb potential. The studies of models without
disorder and spin and including disorder and spin show that the electron solid
is formed in two stages, giving rise to an intriguing solid-liquid regime at
intermediate couplingsComment: To appear in the proceedings of the XXXVIth Rencontres de Moriond
edited by T. Martin and G. Montambau
From the Fermi Liquid Towards the Wigner Solid in Two Dimensions
The quantum-classical crossover from the Fermi liquid towards the Wigner
solid is numerically revisited, considering small square lattice models where
electrons interact via a Coulomb U/r potential. We review a series of exact
numerical results obtained in the presence of weak site disorder for fully
polarized electrons (spinless fermions) and when the spin degrees of freedom
are included. A novel intermediate regime between the Fermi system of weakly
interacting localized particles and the correlated Wigner solid is obtained. A
detailed analysis of the non disordered case shows that the intermediate ground
state is a solid entangled with an excited liquid. For electrons in two
dimensions, this raises the question of the existence of an unnoticed
intermediate liquid-solid phase. Using the Coulomb energy to kinetic energy
ratio r_s ~ U ~ n_s^{-1/2}, we discuss certain analogies between the numerical
results obtained as a function of U for a few particles and the low temperature
behaviors obtained as a function of the carrier density n_s in two dimensional
electron gases. Notably, the new ``exotic state of matter'' numerically
observed at low energies in small clusters occurs at the same intermediate
ratios r_s than the unexpected low temperature metallic behavior characterizing
dilute electron gases. The finite size effects in the limit of strong disorder
are eventually studied in the last section, providing two numerical evidences
that the weak coupling Fermi limit is delimited by a second order quantum phase
transition when one increases U.Comment: 45 pages, review article to appear in ``Exotic states in Quantum
Nanostructures'' ed. S. Sarkar, Kluwer, Dordrech
Ground state of a partially melted Wigner molecule
We consider three spinless fermions free to move on 2d square lattice with
periodic boundary conditions and interacting via a U/r Coulomb repulsion. When
the Coulomb energy to kinetic energy ratio r_s is large, a rigid Wigner
molecule is formed. As r_s decreases, we show that melting proceeds via an
intermediate regime where a floppy two particle molecule coexists with a
partially delocalized particle. A simple ansatz is given to describe the ground
state of this mesoscopic solid-liquid regime.Comment: to appear in Europhysics Letter
Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder
Using the persistent current I induced by an Aharonov-Bohm flux in square
lattices with random potentials, we study the interplay between electronic
correlations and disorder upon the ground state (GS) of a few polarized
electrons (spinless fermions) with Coulomb repulsion. K being the total
momentum, we show that I is proportional to K in the continuum limit. We use
this relation to distinguish between the continuum regimes, where the lattice
GS behaves as in the continuum limit and I is independent of the interaction
strength U when K is conserved, and the lattice regimes where I decays as U
increases. Changing the disorder strength W and U, we obtain many regimes which
we study using the map of local currents carried by three spinless fermions
Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents
For an interacting system of N electrons, we study the conditions under which
a lattice model of size L with nearest neighbor hopping t and U/r Coulomb
repulsion has the same ground state as a continuum model. For a fixed value of
N, one gets identical results when the inter-electron spacing to the Bohr
radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an
enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three
criteria giving similar r_s^* are proposed and checked using square lattices.Comment: 7 pages, 5 postscript figure
Role of a parallel magnetic field in two dimensional disordered clusters containing a few correlated electrons
An ensemble of 2d disordered clusters with a few electrons is studied as a
function of the Coulomb energy to kinetic energy ratio r_s. Between the Fermi
system (small r_s) and the Wigner molecule (large r_s), an interaction induced
delocalization of the ground state takes place which is suppressed when the
spins are aligned by a parallel magnetic field. Our results confirm the
existence of an intermediate regime where the Wigner antiferromagnetism
defavors the Stoner ferromagnetism and where the enhancement of the Lande g
factor observed in dilute electron systems is reproduced.Comment: 4 pages, 3 figure