On the other hand, for strong interactions the charges form a kind of Wigner crystal, pinned by the disorder, the Coulomb energy being dominant over kinetic energy and disorder.
Transport measurements following the pioneering works of Kravchenko and coworkers [2] and made with electron and hole gases give evidence of a metal-insulator transition in two dimension. The transition is obtained by changing the carrier density.
Studying spinless fermions in two-dimensional disordered clusters, we have collected numerical results suggesting the existence of a new quantum phase, which is neither a Fermi glass nor a Wigner crystal, for intermediate Coulomb energy to kinetic energy ratios [3].
Spin-polarized
ground state for interacting electrons in two dimensions
Ferromagnetic instabilities
result from the interplay between the electronic Coulomb interaction
and the Pauli principle: the minimum spin state minimizes the kinetic
energy while the maximum spin reduces the effect of the Coulomb
repulsion (a familiar example of this is Hund's rule for atoms). This
leads to the Stoner instability, which gives a spontaneous
magnetization when the typical interaction exchange energy between two
particles close to the Fermi level is of the order of the single
particle level spacing.
We have studied numerically [4] the ground state magnetization for clusters of interacting electrons in two dimensions in the regime when the single particle wave functions are localized by disorder. We have found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.
We have studied numerically [4] the ground state magnetization for clusters of interacting electrons in two dimensions in the regime when the single particle wave functions are localized by disorder. We have found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.
Probability distribution of the
ground state spin S in the localized single-particle phase and increase
of the ground-state polarization with the number of particles N (at a
constant density).
Superconductor
to insulator transition in three dimensions
We have studied numerically [5]
the interplay of disorder and attractive interactions for
spin-1/2 fermions in the three-dimensional Hubbard model. The results
obtained by projector quantum Monte Carlo simulations show that at
moderate disorder, increasing the attractive interaction leads to a
transition from delocalized superconducting states to the insulating
phase of localized pairs. This transition takes place well within the
metallic phase of the single-particle Anderson model.
Distribution of the charge
density difference for an added pair, projected on the (x,y) plane for
a lattice of size L=6, N=108 particles. with W/t=2 (left) and
W/t=7 (right); U=0 (top) and U/t=-4 (bottom). The interaction-induced
localization in clear, for strong enough interactions, in the
bottom-right picture.
References
[1] E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[2] E. Abrahams, S.V. Kravchenko, and M.P. Sarachik, Rev. Mod. Phys. 73, 251 (2001).
[3] G. Benenti, X. Waintal and J.--L. Pichard, New quantum phase between the Fermi glass and the Wigner crystal in two dimensions, Phys. Rev. Lett. 83, 1826 (1999).
[4] G. Benenti, G. Caldara and D.L. Shepelyansky, Spin polarized ground state for interacting electrons in two dimensions, Phys. Rev. Lett. 86, 5333 (2001).
[5] B. Srinivasan, G. Benenti, and D.L. Shepelyansky, Transition to an insulating phase induced by attractive interactions in the disordered three-dimensional Hubbard model, Phys. Rev. B 66, 172506 (2002).