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arXiv:cond-mat/0012213

Intermediate liquid-solid regime near the quantum melting of a two dimensional Wigner molecule

Georgios Katomeris, Jean‐Louis Pichard

Published Dec 12, 2000• 0 citations
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Abstract

For intermediate values of the Coulomb energy to Fermi energy ratio $r_s$, the ground state of a few spinless fermions confined on a two dimensional torus is the quantum superposition of a floppy Wigner molecule with delocalized vacancies and of a Fermi liquid of intersticial particles. This raises the question of the existence of an unnoticed liquid-solid phase between the Fermi liquid and the Wigner crystal for fermionic systems in two dimensions.

DOI
10.48550/arxiv.cond-mat/0012213

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For intermediate values of the Coulomb energy to Fermi energy ratio rsr_srs​, the ground state of a few spinless fermions confined on a two dimensional torus is the quantum superposition of a floppy Wigner molecule with delocalized vacancies and of a Fermi liquid of intersticial particles. This raises the question of the existence of an unnoticed liquid-solid phase between the Fermi liquid and the Wigner crystal for fermionic systems in two dimensions.
We consider three spinless fermions free to move on 2 d 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.
(received; accepted) PACS. 71.10-w – Theories and models for many-electron systems. PACS. 71.27+a – Strongly correlated electron systems. PACS. 73.20.Qt – Electron solids. Abstract. – 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 rs is large, a rigid Wigner molecule is formed. As rs 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. Ordered arrays of charged particles with long range Coulomb repulsion have been a continuous subject of interest in various branches of physics, including colloidal suspensions, ion rings, atomic-ion Wigner crystals, quantum computers, biophysics, plasmas, electrons deposited on liquid Helium surfaces, charges created in semiconductor or organic field effect devices. These
For intermediate Coulomb energy to Fermi energy ratios rsr_srs​, spinless fermions in a random potential form a new quantum phase which is different from the Fermi glass and the Wigner crystal. From a numerical study of small clusters, we show that this phase is characterized by an ordered flow of enhanced persistent currents and occurs for rsr_srs​ values where a metallic phase has been observed in two dimensions.
The Fermi liquid-Wigner crystal transition in a two-dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum Monte Carlo calculations. Recently, we proposed [Phys. Rev. Lett. 94, 046801 (2005)] that for intermediate densities, a hybrid phase (with the symmetry of the crystal but otherwise liquidlike properties) is more stable than both the liquid and the crystal phase. Here we confirm this result both in the thermodynamic and continuum limit. The liquid-hybrid transition takes place at ${r}_{s}^{*}=31.5\ifmmode\pm\else\textpm\fi{}0.5$. We find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature. We discuss the implications of our results for various transition scenarios (quantum hexatic phase, supersolid, multiple exchange, and microemulsions) as proposed in the literature.