Quantum Monte Carlo Study of electrons in low dimensions

We report on a diffusion Monte Carlo investigation of model electron systems in low dimensions, which should be relevant to the physics of systems obtainable nowadays in semiconductor heterostructures. In particular, we present results for a one dimensional electron gas, at selected values of the coupling strength and confinement parameter, briefly analyzing the pair correlations and relating them to predictions by Schulz for a Luttinger liquid with long-range interactions. We find no evidence of the the Bloch instability yielded by approximate treatments such as the STLS and DFT schemes.Comment: 6 pages, 3 figures. To appear in the proceedings of the 1999 International Conference on Strongly Coupled Coulomb Systems, Saint-Malo, Franc

Charge and spin correlations of a one dimensional electron gas on the continuum

We present a variational Monte Carlo study of a model one dimensional electron gas on the continuum, with long-range interaction (1/r decay). At low density the reduced dimensionality brings about pseudonodes of the many-body wavefunction, yielding non-ergodic behavior of naive Monte Carlo sampling, which affects the evaluation of pair correlations and the related structure factors. The problem is however easily solved and we are able to carefully analyze the structure factors obtained from an optimal trial function, finding good agreement with the exact predictions for a Luttinger-like hamiltonian with an interaction similar to the one used in the present study.Comment: 4 pages, 3 figure

Ground state properties of the one dimensional Coulomb gas

We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows to sample the exact ground state of the system, even in the low density regime when the exchange between electrons is extremely small. For different values of the width parameter b (0.1 a*_0 <= b <= 4 a*_0), we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi one dimensional systems. Moreover we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long range interactions.Comment: 15 pages, 13 figures, to appear in Phys. Rev.

Dielectric matrix and plasmon dispersion in strongly coupled electronic bilayer liquids

We develop a dielectric matrix and analyze plasmon dispersion in strongly coupled charged-particle bilayers in the quantum domain. The formulation is based on the classical quasi-localized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development, which parallels that of 2D companion paper [Phys. Rev. E 70, 026406 (2004)] by three of the authors, generalizes the single-layer scalar formalism therein to a bilayer matrix formalism. Using pair correlation function data generated from diffusion Monte Carlo simulations, we calculate the dispersion of the in-phase and out-of-phase plasmon modes over a wide range of in-layer coupling values and layer spacings. The out-of-phase spectrum exhibits an exchange-correlation induced long-wavelength energy gap in contrast to earlier predictions of acoustic dispersion softened by exchange-correlations. The energy gap is similar to what has been previously predicted for classical charged-particle bilayers and subsequently confirmed by recent molecular dynamics computer simulations.Comment: 53 pages including 15 Figures with their captions. Submitted to Physical Review

Quadriexciton binding energy in electron-hole bilayers

Excitonic condensation and superfluidity have recently received a renewed attention, due to the fabrication of bilayer systems in which electrons and hole are spatially separated and form stable pairs known as indirect excitons. Dichalcogenides- and graphene- based bilayers are nowadays built and investigated, giving access to systems with (i) only spin degeneracy, (ii) spin and valley degeneracy. Simulation studies performed in the last decade at $T=0$ for simple, model electron-hole bilayers, as function of inter-layer distance and in-layer carrier density, have revealed in case (i) the formation of biexcitons in a tiny region of parameter space and in case (ii) the formation of stable compounds made of 4 electrons and 4 holes (quadriexcitons) in a sizable region of parameter space. Of some interest is the relation of the properties of isolated biexcitons (quadriexcitons) and those of their finite density counterpart. In fact, the isolated biexciton has been repeatedly studied in the last years with simulations and other techniques. No simulations, instead, are available to our knowledge for the isolated quadriexciton, for which we present here results of the first quantum Monte Carlo (QMC) study. Stability with respect to the dissociation into biexcitons, and the pair correlations with varying the inter-layer distance $d$ are discussed

Effects of thickness on the spin susceptibility of the 2D electron gas

Using available quantum Monte Carlo predictions for a strictly 2D electron gas, we have estimated the spin susceptibility of electrons in actual devices taking into account the effect of the finite transverse thickness and finding a very good agreement with experiments. A weak disorder, as found in very clean devices and/or at densities not too low, just brings about a minor enhancement of the susceptibility.Comment: 4 pages, 3 figure

Spin Susceptibility of Interacting Two-dimensional Electrons with Anisotropic Effective Mass

We report measurements of the spin susceptibility in dilute (rs up to 10) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses, ml and mt. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to sqrt(ml.mt). Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Correlation Energy and the Spin Susceptibility of the Two-Valley Two-dimensional Electron Gas

We find that the spin susceptibility of a two-dimensional electron system with valley degeneracy does not grow critically at low densities, at variance with experimental results [A. Shashkin et al., Phys. Rev. Lett. 96, 036403 (2006)]. We ascribe this apparent discrepancy to the weak disorder present in experimental samples. Our prediction is obtained from accurate correlation energies computed with state of-the-art diffusion Monte Carlo simulations and fitted with an analytical expression which also provides a local spin density functional for the system under investigation.Comment: 7 pages, 3 figures, accepted for publication in Phys. Rev.

Quadriexcitons and excitonic condensate in a symmetric electron-hole bilayer with valley degeneracy

Using quantum Monte Carlo simulations we have mapped out the zero temperature phase diagram of a symmetric electron-hole bilayer with twofold valley degeneracy, as function of the interlayer distance $d$ and in-layer density $n$. We find that the effect of the valley degeneracy is to shrink the region of stability of the excitonic condensate, in favor of quadriexcitons at small $d$ and of the four-component plasma at large $d$, with minor effects on the value of the excitonic condensate fraction. The enclosure of the condensate in a density window possibly explains why anomalous tunnelling conductivity, interpreted as signature of condensation, is observed only between two finite values of carrier density in graphene bilayers. Our phase diagram may provide directions to select device parameters for future experiments.Comment: paper: 5 pages and 4 figures; supplemental info: 5 pages, 7 figures, 2 table