Ground state of a partially melted Wigner molecule

The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio r_s=a/a_B*. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r_s* below which the lattice spacing s becomes a relevant scale and r_s ceases to be the scaling parameter. For systems of small ratios s/a_B*, s becomes only relevant at small r_s (large densities) where one has a quantum fluid with a de...

A Bethe-Ansatz spin-density functional approach is developed to evaluate the ground-state density profile in a system of repulsively interacting spin-1/2 fermions inside a quasi-one-dimensional harmonic well. The approach allows for the formation of antiferromagnetic quasi-order with increasing coupling strength and reproduces with high accuracy the exact solution that is available for the two-fermion system.

We investigate the stability, the dynamical properties and melting of a two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a bi-layer structure. Compared to the single-layer WC, this system shows a rich phase diagram. Five different crystalline phases are stable; the energetically favoured structure can be tuned by changing either the inter-layer distance or the particle density. Phase boundaries consist of both continuous and discontinuous transitio...

We analyze the quantum melting of two-dimensional Wigner molecules (WM) in confined geometries with distinct symmetries and compare it with corresponding thermal melting. Our findings unfold complementary mechanisms that drive the quantum and thermal crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale $n_X$. This is because the zero-point motion screens the boundary effects within short distance...

Recent experiments have established that semiconductor-based moir\'e materials can host incompressible states at a series of fractional moir\'e-miniband fillings. These states have been identified as generalized Wigner crystals in which electrons localize on a subset of the available triangular-lattice moir\'e superlattice sites. In this article, we use momentum-space exact diagonalization to investigate the many-body ground state evolution at rational fillings from the weak-...

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different...

We consider 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...

We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario --including critical phenomena-- can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hithert...

We modify the "floating crystal" trial state for the classical Homogeneous Electron Gas (also known as Jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground state energy of Jellium coincid...

In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function we use a regular distribution in space of gaussian-type orbitals and we take advantage of the tra...