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Ground state of a partially melted Wigner molecule

Zoltán Ádám Németh(a, Jean‐Louis Pichard

Published Jan 1, 2002• 2 citations
OpenAlex

Abstract

(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

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Ground state of a partially melted Wigner molecule

Z. Á Németh, J.‐L. Pichard

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.

arXiv:cond-mat/0203477•Europhysics Letters (EPL)•Jun 1, 2002•3 citations

Correlated Electrons on Square Lattices

Jean‐Louis Pichard

Using a few electrons interacting via a U/r Coulomb repulsion on two dimensional L ×L square lattices with periodic boundary conditions and nearest neighbor hopping t, I review on results of systematic exact finite size numerical studies of the ground state as a function of the Coulomb energy to kinetic energy ratio rs=UL/(2t√πN). Studies of the persistent currents, of the magnetization, of the inter-particle spacing distributions, of a simple analytical ansatz converge towards the same conclusion: there is a new regime for intermediate values rs, where delocalized electrons co-exist with a solid Wigner molecule. The study of this new regime, first done in the presence of random potentials, is extended to the clean lattice limit. The results are consistent, for a finite size lattice, with a possibility proposed by Andreev and Lifshitz for the continuous thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles.

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Thermal melting of a quantum electron solid in the presence of strong disorder: Anderson localization versus the Wigner crystal

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We consider the temperature-induced melting of a Wigner solid in one-dimensional (1D) and two-dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.

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The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder and spin and including disorder and spin show that the electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings

arXiv:cond-mat/0107500•Jul 24, 2001•0 citations
(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
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.
Using a few electrons interacting via a U/r Coulomb repulsion on two dimensional L ×L square lattices with periodic boundary conditions and nearest neighbor hopping t, I review on results of systematic exact finite size numerical studies of the ground state as a function of the Coulomb energy to kinetic energy ratio rs=UL/(2t√πN). Studies of the persistent currents, of the magnetization, of the inter-particle spacing distributions, of a simple analytical ansatz converge towards the same conclusion: there is a new regime for intermediate values rs, where delocalized electrons co-exist with a solid Wigner molecule. The study of this new regime, first done in the presence of random potentials, is extended to the clean lattice limit. The results are consistent, for a finite size lattice, with a possibility proposed by Andreev and Lifshitz for the continuous thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles.
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.
(received; accepted) PACS. 71.30+h – Metal-insulator transitions and other electronic transitions. PACS. 72.15Rn – Quantum localization. PACS. 71.27+a – Strongly correlated electron systems. Abstract. – Extending finite size scaling theory to the many body ground state, one finds that Coulomb repulsion can drive a system of spinless fermions in a random potential from the Anderson insulator (Fermi glass of localized states) towards a new extended phase in dimension d = 2. The transition occurs at a Coulomb energy to Fermi energy ratio rs ≈ 4, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed 2d metallic phase is suggested. Following the scaling theory of localization [1], all 2d systems of electrons (or holes) are localized when electron-electron interaction is negligible. This absence of metals in two dimensions is nowadays questioned after the observation of a transition towards a metallic behavior in silicon based 2d electron gases [2, 3, 4] when the carrier density is varied. This unexpected phenomenon occurs also for hole gases in GaAs heterostructures [5, 6], SiGe [7]
We consider the temperature-induced melting of a Wigner solid in one-dimensional (1D) and two-dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/rU/rU/r potential. The studies of models without disorder and spin and including disorder and spin show that the electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings