Correlation energy of coupled double electron layers

doi:10.1016/S0026-2692(03)00050-8

Microelectronics Journal

Volume 34, Issues 5–8, May–August 2003, Pages 569-570

https://doi.org/10.1016/S0026-2692(03)00050-8 Get rights and content

Abstract

The work is aimed to study the interlayer electron–electron correlation energy of the coupled double-layer two-dimensional electron system. Using the variational Monte Carlo and diffusion Monte Carlo method, we calculate the ground state energy in unpolarized liquid phase for r_s=1–30 and different interlayer distances. By fitting the numerical results of the ground state energy as a function of r_s and the interlayer distance d, we successfully separated the energies due to intra- and inter-layer electron–electron interactions. The interlayer correlation energy is found to be of a exponential dependence on d. Furthermore, we obtain a simple function for the r_s dependence of the interlayer correlation energy.

Introduction

Many-body effects in two-dimensional (2D) electron systems have been studied extensively since the first 2D semiconductor structure was realized in the middle of sixties. Advances in the epitaxial growth technique have made it possible recently to fabricate the layered structures with coupled 2D electron gases. These new systems show a number of different effects result from interlayer electron–electron Coulomb interactions [1]. They also provide us more parameters, such as the interlayer separation and the electron density difference between the layers, to study the effects due to the electron–electron correlation.

In this work, by using the variational Monte Carlo and diffusion Monte Carlo (VMC–DMC) technique, we calculate within a high accuracy the ground state energy of double-layer electron gases at low temperature. We obtain the ground state energy with densities varying from r_s=1 to 30 for different distances between the layers. In the limit case of large interlayer separation our results recover well those of single layers obtained by Tanatar and Ceperley [2]. For the interlayer separation d≤1.0r_s where the interlayer electron–electron interaction is of important contribution to the correlation energy, we obtain a simple expression for the interlayer correlation energy of the coupled electron gases by fitting our accurate numeric results. The interlayer correlation energy decays exponentially as the layer separation d with a prefactor being almost inversely proportional to r_s.

Section snippets

The system and numerical technique

The system being simulated is formed by two parallel electron layers $(a and b)$ separated by a distance d. The Hamiltonian is given by $H= 1 r_{s}^{2} ∑ i=1 N_{a,b} ∇_{i}^{2} + 2 r_{s} ∑ i<j N_{a} 1 |r_{i}^{a} −r_{j}^{a} | + 2 r_{s} ∑ i<j N_{b} 1 |r_{i}^{b} −r_{j}^{b} | + 2 r_{s} ∑ i,j N_{a,b} 1 [|r_{i}^{a} −r_{j}^{b} |^{2} +d^{2}]^{1/2},$ where N_a,b is the number of electrons at the layer a and b, energy is in unit of the Rydberg Ry=ℏ/2ma_B², length is in unit of the Wigner–Seitz radius a=(πρ)^−1/2, and a_B is the effective Bohr radius.

The numerical approach is based on the quantum Monte Carlo (QMC) simulation.

Numerical results and discussions

In the following, we present some numerical results obtained for the unpolarized electron system with 26 electrons each layer. We have checked the system with up to 74 electrons/layer which does not change the numerical results within the statistical error.

Fig. 1 shows the total energy per electron as a function of interlayer distance at different r_s. We fitted the MC results by $E=E_{0} +E_{1} exp − d ηr_{s},$ where E₀, E₁, and η are dependent on r_s. For d→∞, E=E₀ which corresponds to the result without

Acknowledgements

This work was supported by the FAPESP and CNPq, Brazil. L. Cândido thanks the support by the IF-UFG and FUNAPE-UFG.

References (4)

L. Zheng et al.
Phys. Rev. B
(1994)
F. Rapisarda et al.
Aust. J. Phys.
(1996)
P.P. Ruden et al.
Appl. Phys. Lett.
(1991)
B. Tanatar et al.
Phys. Rev. B
(1989)

There are more references available in the full text version of this article.

Cited by (0)

View full text