Ground state of a partially melted Wigner molecule

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at lo...

We reply to the Comment by Mobius and Richter [arXiv:0908.3092, Phys. Rev. Lett. 105, 039701 (2010)] on "Density of States and Critical Behavior of the Coulomb Glass" [arXiv:0805.4640, Phys. Rev. Lett. 102, 067205 (2009)] and address the issues raised with our results on the density of states. In addition, we correct our statements about the random displacement version of the Coulomb glass model where the Wigner crystal is not as robust to disorder as stated. Still, our main ...

We investigate the behaviour of dipolar bosons in two dimensions. We describe the large density crystalline limit analytically while we use quantum Monte-Carlo to study the melting toward the Bose-Einstein condensate. We find strong evidence for a first order transition. We characterize the window of experimentally accessible parameters in the context of ultracold bosons and show that observing the quantum melting should be within grasp once one is able to form cold heteronuc...

approaches. We demonstrate that the Wigner regime can be reached using small values of the confinement parameter. To obtain physical insight in our results we analyze them with a semi-analytical model for two electrons. Thanks to electronic-structure properties such as the one-body density and the particle-hole entropy, we are able to define a path that connects the Wigner regime to the Fermi-gas regime by varying the confinement parameter. In particular, we show that the par...

We determine the ground state of the two-dimensional, fully polarized electron gas within the Hartree-Fock approximation without imposing any particular symmetries on the solutions. At low electronic densities, the Wigner crystal solution is stable, but for higher densities ($r_s$ less than $\sim 3$) we obtain a ground state of different symmetry: the charge density forms a triangular lattice with about 11% more sites than electrons. We argue that this conducting state with b...

Quantum Monte Carlo methods are used to calculate various ground state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at $r_s\simeq 60$. Results for the ground state energy and the momentum distribution are summarized in analytic interpolation formulas embodying known asymptotic behaviors. Near freezing, the condensate fraction is less than 1%. The static structure factor ...

Relationship among Wigner crystal, charge order and Mott insulator is studied by the path-integral renormalization group method for two-dimensional lattices with long-range Coulomb interaction. In contrast to Hartree-Fock results, the solid stability drastically increases with lattice commensurability. The transition to liquid occurs at the electron gas parameter $r_s \sim 2$ for the filling $n=1/2$ showing large reduction from $r_s \sim 35$ in the continuum limit. Correct ac...

Coupled semiconductor quantum dots form artificial molecules where relevant energy scales controlling the interacting ground state can be easily tuned. By applying an external magnetic field it is possible to drive the system from a weak to a strong correlation regime where eventually electrons localize in space in an ordered manner reminiscent of the two-dimensional Wigner crystal. We explore the phase diagram of such "Wigner molecules" analyzing the angular correlation func...

How the two dimensional (2D) quantum Wigner crystal (WC) transforms into the metallic liquid phase remains to be an outstanding problem in physics. In theories considering the 2D WC to liquid transition in the clean limit, it was suggested that a number of intermediate phases might exist. We have studied the transformation between the metallic fluid phase and the low magnetic field reentrant insulating phase (RIP) which was interpreted as due to WC formation [Qiu et al, PRL 1...

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic ...