Physical Review B

Ground state properties of a laterally confined two-dimensional electron gas

Lucia Dandrea, Francesco Pederiva, E. Lipparini

Published Apr 27, 2009• 0 citations

Abstract

We present an accurate diffusion Monte Carlo computation of the ground state of a two-dimensional electron gas laterally confined by a harmonic potential in the effective mass-dielectric constant approximation. The computation is made explicitly including the second dimension, and can therefore address the occurrence of phase transitions in the system. The system was studied as a function of the one-dimensional Wigner-Seitz parameter ${r}_{s}=1/2{\ensuremath{\rho}}^{1\text{D}}$ in the range $0.5\ensuremath{\le}{r}_{s}\ensuremath{\le}7$. The ground state is found to be spin polarized for ${r}_{s}>3$.

DOI: 10.1103/physrevb.79.155321

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Physical Review B

Ground state properties of a laterally confined two-dimensional electron gas

Lucia Dandrea, Francesco Pederiva, E. Lipparini

Published Apr 27, 2009• 0 citations

Publisher

Abstract

{r}_{s}=1/2{\ensuremath{\rho}}^{1\text{D}}

in the range

0.5\ensuremath{\le}{r}_{s}\ensuremath{\le}7

. The ground state is found to be spin polarized for

{r}_{s}>3

DOI: 10.1103/physrevb.79.155321

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{r}_{s}=1/2{\ensuremath{\rho}}^{1\text{D}}

in the range

0.5\ensuremath{\le}{r}_{s}\ensuremath{\le}7

. The ground state is found to be spin polarized for

{r}_{s}>3

b

$(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, 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.

Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}

{r}_{s}

\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density

{r}_{s}

\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.

{r}_{s}

, respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large

{r}_{s}

(the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small

{r}_{s}

. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if

{r}_{s}>1

. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.