New Quantum Phase between the Fermi Glass and the Wigner Crystal in Two Dimensions

Abstract

For intermediate Coulomb energy to Fermi energy ratios r s , spinless fermions in a random potential form a new quantum phase which is neither a Fermi glass, nor a Wigner crystal. Studying small clusters, we show that this phase gives rise to an ordered flow of enhanced persistent currents for disorder strength and ratios r s , where a metallic phase has been recently observed in two dimensions. PACS numbers: 71.30. + h, 72.15.Rn An important parameter for a system of charged particles is the Coulomb energy to Fermi energy ratio r s . In a disordered two-dimensional system, the ground state is obvious in two limits. For large r s , the charges form a kind of pinned Wigner crystal, the Coulomb repulsion being dominant over the kinetic energy and the disorder. For small r s , the interaction becomes negligible and the ground state is a Fermi glass with localized one electron states. There is no theory for intermediate r s , while many transport measurements following the pioneering works of Kravchenko et al.[1] and made with electron and hole gases give evidence of an intermediate metallic phase in two dimensions, observed [2], for instance, when 6 , r s , 9 for a hole gas in GaAs heterostructures. A simple model of spinless fermions with Coulomb repulsion in small disordered 2D clusters exhibits a new ground state characterized by an ordered flow of enhanced persistent currents for those values of r s . In a given cluster, as we turn on the interaction, the Fermi ground state can be followed from r s 0 up to a first level crossing. A second crossing occurs at a larger threshold after which the ground state can be followed to the limit r s !`. There is then an intermediate state between the two crossings. In small clusters, the location of the crossings depends on the considered potentials, but a study over the statistical ensemble of the currents supported by the ground state gives us two welldefined values r F s and r W s : Mapping the system on a torus threaded by an Aharonov-Bohm flux, we denote, respectively, I l and I t the total longitudinal (direction enclosing the flux) and transverse parts of the driven current. One finds for their typical amplitudes jI t j ഠ exp2͑r s ͞r F s ͒ and I l ഠ exp2͑r s ͞r W s ͒ with r F s , r W s . Below r F s , the flux gives rise to a glass of local currents and the sign of I l can be diamagnetic or paramagnetic, depending on the random potentials. Above r F s , the transverse current is suppressed while an ordered flow of longitudinal currents persists up to r W s , where charge crystallization occurs. The sign of I l can be paramagnetic or diamagnetic, depending on the filling factor (as for the Wigner crystal), but does not depend on the random potentials (in contrast to the Fermi glass). One finds r F s and r W s in agreement with the values delimiting the new metallic phase when 0.3 , k F l , 3, k F and l denoting the Fermi wave vector and the elastic mean free path, respectively. For k F l $ 1, I l is strongly increased between r F s and r W s . This suggests that the...

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

“…Even if our model is much simpler than the realistic problem of interest, it contains non-trivial features that may be useful to understand the transition, like the concept of charge reorganization discussed above. The intermediate regime that we find between the limits of weak and strong interactions can be considered as a precursor of the correlated phase found in numerical studies [13] of two dimensional disordered clusters (with long-range Coulomb interaction) when the Wigner molecule is about to be formed. Consistently with our results, the use of the Kubo-Greenwood formula and an exact diagonalization in a truncated basis of Hartree-Fock states [65] yields an average conductance which is slightly increased by a small repulsive interaction for spinless electrons in strongly disordered 2D systems.…”

“…In the next subsection we give the estimation of the typical interaction strength needed to establish the Mott phase. Recent works [13,51,52] on 2D disordered clusters with Coulomb interaction also shows that one goes from the Fermi glass towards the pinned Wigner crystal through an intermediate regime (located between two different Coulomb-to-Fermi energy-ratios r f s and r w s ). The difference with our problem is that, in the 2D case, a topological change can be observed in the pattern of the driven currents, which cannot exist in the 1D case.…”

“…[12]. The metallic behavior is observed in a parameter region of the system which is believed to be limited by its crystallization threshold [13,14]. Finally, the conventional view of an infinite zero-temperature quasiparticle lifetime at the Fermi energy has been questioned by the interpretation of measurements yielding a saturation of the electronic decoherence rate with decreasing temperature [15].…”

A model for addition spectra in quantum dots

“…The weakness of the model is that it is no more than a simple interpolation between the two limits. Such an interpolation is, clearly, a big leap -especially, since some new quantum phases might exist between the two limits (Chakravarty et al, 1999, Benenti et al, 1999. The model, however, is not intended to describe subtle correlations in the ground state of N interacting particles.…”

“…Experiments , Patel et al, 1998, Simmel et al, 1999 , however, show an approximately Gaussian distribution for ∆ 2 , with a width considerably larger than the average single-particle level spacing ∆ and with no sign of a bimodal structure. The disagreement between experiment and the charging model led to a number of theoretical studies of P (∆ 2 ), based on exact diagonalization of the microscopic Hamiltonian , Berkovits, 1998 as well as on various approximations such as RPA (Blanter et al, 1997, Berkovits andAltshuler, 1997), the extreme classical limit (Koulakov et al, 1997) and the self-consistent Hartree-Fock scheme (Walker et al, 1999, Cohen et al, 1999, Levit and Orgad, 1999, or the somewhat related configuration interaction method (Benenti et al, 2000). In this paper we propose, and study, a simple model for the addition spectrum and the peak spacing of a weakly disordered (or chaotic) quantum dot.…”