Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

We describe computational methods for the theoretical study of explicit correlations beyond the mean field in excitons confined in semiconductor quantum dots in terms of the Auxiliary-Field Monte Carlo (AFMC) method. Using AFMC, the many-body problem is formulated as a Feynman path integral at finite temperatures and evaluated to numerical precision. This approach is ideally suited for implementation on high-performance parallel computers. Our strategy is to generate a set of...

This paper investigates interaction-induced symmetry breaking in circular quantum dots. We explain that the anisotropic static Wigner molecule ground states frequently observed in simulations are created by interference effects that occur even in the non-interacting limit. They have nothing in common with the interaction-driven crystallization of the uniform electron gas described by Wigner. This leads us to define the term Wigner molecule more carefully, via a finite analog ...

We use the variational quantum Monte Carlo (VMC) method to study the wire width ($b$) and electron density ($r_\text{s}$) dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density, and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2k_\text{F}$ to...

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...

Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N-electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 <= N <= 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. A...

Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood. For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner c...

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 liquid like properties) is more stable than both the liquid and the crystal phase. Here we confirm this result both in the thermo...

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...

Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the inter-electron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron...

We present extensive new direct path-integral Monte Carlo results for electrons in quantum dots in two and three dimensions. This allows us to investigate the nonclassical rotational inertia (NCRI) of the system, and we find an abnormal negative superfluid fraction [Phys. Rev. Lett. 112, 235301 (2014)] under some conditions. In addition, we study the structural properties by computing a sophisticated center-two particle correlation function. Remarkably, we find no connection ...