Ground state of a partially melted Wigner molecule

We show that a triangular lattice consisting of dipolar molecules pointing orthogonal to the plane undergoes a first-order defect melting transition.

We considered a two dimensional three electron quantum dot in a magnetic field in the Wigner limit. A unitary coordinate transformation decouples the Hamiltonian (with Coulomb interaction between the electrons included) into a sum of three independent pair Hamiltonians. The eigen-solutions of the pair Hamiltonian provide a spectrum of pair states. Each pair state defines the distance of the two electrons involved in this state. In the ground state for given pair angular momen...

For intermediate Coulomb energy to Fermi energy ratios $r_s$, spinless fermions in a random potential form a new quantum phase which is nor a Fermi glass, neither 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.

The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (< 1%) in the energy due to...

We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy, the system forms a Wigner crystal undergoing a first-order quantum phase transition. This transition is a condensation in the space of the states and belongs to the class of quantum phase transitions discussed in J. Phys.~A \textbf{54}, 05500...

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized...

The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives rise to a rich sequence of structural transitions upon varying the particle density. In addition, the concurrence of low-dimensional electron motion and isotropic Coulomb interactions leads to a sizeable stabilization of the Wigner crystal, wh...

We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of the Wigner crystal phases are considerably smaller than those of the fluid phases at the same density.

We study by means of exact-diagonalization techniques the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays at strong coupling very well pronounced Friedel oscillations with a `4k_F periodicity', the pair correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also ...

We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total energy per electron which correspond to the classical energy and the harmonic correction due to the zero-point motion of the Wigner crystals, respectively. Our approach employs Clifford periodic boundary conditions to simulate the infinite el...