Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I

Abstract

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 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 rs = U L/(2t √ πN ) reaches a value r F s ≈ 10, there is a level crossing between ground states of different momenta. Above r F s , the mesoscopic crystallization proceeds through an intermediate regime (r F s < rs < r W s ≈ 28) 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 r F s is avoided and gives rise to a lower threshold r F s (W ) < r F s 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

Local transport in a disorder-stabilized correlated insulating phase

“…We show that our observations can be explained in the theoretical framework of defect motion in a quantum solid that was originally developed by Andreev and Lifshitz in context of solid He 3 , 15 and later adapted for a WS ground state. 16,17 In our case, transport in both quantum and classical regime can be understood in terms of tunnelling of localized defects in an interaction-induced pinned electron solid phase as n s is reduced below the melting point n * s . The defects, which act as quasiparticles at low T , can arise from regular interstitials, vacancies, dislocation loops etc., as well as from zero-point vibration of individual lattice sites.…”

Low-Temperature Collapse of Electron Localization in Two Dimensions

“…A possible description may be based on the behavior of defects in an interaction-induced, disorder stabilized pinned electron quantum solid (QS): The existence of delocalized zero-point defects (defectons) in a crystal with strong zero-point fluctuations was first proposed for solid helium [24] and has been adapted for 2DES [8,25,26]. Moderate disorder has been predicted to facilitate the formation of a Wigner crystal for r s close to the values in our 2DES (r s 4-6) [27], a range where defecton formation is likely [17].…”

“…The scaling theory of localization prohibits extended electronic states in two dimensions (2D) at absolute zero in the presence of disorder [2]. While there has been extensive theoretical work on the possibility of a delocalization caused by electron-electron interactions, e.g., [3][4][5][6][7][8][9], conclusive experimental evidence of such an effect has not been observed. On the contrary, the insulating phase in 2D at low temperatures has proven robust, in particular, in the case of strong localization, where the resistivity h=e 2 .…”

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

“…The weak coupling Fermi limit and the strong coupling correlated lattice limit of the three particle system are described in Sec. 4 and Sec. 5.…”

“…In a first paper [4], the supersolid phase conjectured [1] by Andreev and Lifshitz was introduced, together with a related variational approach using a fixed number of fermions BCS wave function [5] of Bouchaud et al The question is to know if a system of unpaired electrons with a reduced Fermi energy can co-exist with an ordered array of charges, the number of sites of the crystalline array being smaller than the total number of electrons. In Ref.…”