https://doi.org/10.1140/epjb/e2003-00048-0
Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I
CEA/DSM, Service de Physique de l'État Condensé,
Centre d'Études de Saclay, 91191, Gif-sur-Yvette Cedex, France
Corresponding author: a jpichard@cea.fr
Received:
21
June
2002
Published online:
14
February
2003
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 square
lattice with periodic boundary conditions and nearest neighbor hopping
t. This paper is restricted to the magic number of particles N=4
for which a square Wigner molecule is formed when U increases and
to the size L=6 suitable for exact numerical diagonalizations. When
the Coulomb energy to kinetic energy ratio
reaches a value
, there is a level crossing between
ground states of different momenta. Above
, the mesoscopic
crystallization proceeds through an intermediate regime (
) where unpaired fermions with a reduced Fermi energy
co-exist with a strongly paired, nearly solid assembly. We suggest that
this is the mesoscopic trace of the supersolid proposed by Andreev and
Lifshitz. When a random substrate is included, the level crossing at
is avoided and gives rise to a lower threshold
where two usual approximations break down: the Wigner surmise for the
distribution of the first energy excitation and the Hartree-Fock
approximation for the ground state.
PACS: 71.10.-w – Theories and models of many-electron systems / 73.21.La – Quantum dots / 73.20.Qt – Electron solids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003