Ground-state energy and Wigner crystallization in thick two-dimensional electron systems

Abstract

The ground state energy of the 2-D Wigner crystal is determined as a function of the thickness of the electron layer and the crystal structure. The method of evaluating the exchange-correlation energy is tested using known results for the infinitely-thin 2D system. Two methods, one based on the local-density approximation (LDA), and another based on the constant-density approximation (CDA) are established by comparing with quantum Monte-Carlo (QMC) results. The LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at rs = 38 and 32 respectively, compared with rs = 35 ± 5 from QMC. For thick-2D layers as found in Hetero-junction-insulatedgate field-effect transistors, the LDA and CDA predictions of the Wigner transition are at rs = 20.5 and 15.5 respectively. Impurity effects are not considered here.

The classical‐map hyper‐netted‐chain (CHNC) method and associated novel density‐functional techniques for warm dense matter

“…In mapping an inhomogeneous system of density n ( r ) to a homogeneous slab of density $\bar n$ we have used the form20, 55, 25, in dealing with 2D systems. The same method has been used by Gori‐Giorgi and Savin for defining a uniform density in dealing with densities of atoms56.…”

“…In mapping an inhomogeneous system of density n(r) to a homogeneous slab of density n we have used the form [19,24,50], n =< n(r)n(r) >< n(r) > (28) in dealing with 2D systems. The same method has been used by Gori-Giorgi and Savin for 3D systems [51].…”

Dimensionality dependence of the self-interaction correction in the local-density approximation to density functional theory

“…The necessary self-interaction correction on an input many-body term to LDA in DFT is, therefore, smaller in 2D at this limit. Immediate applications of the result found in our study could be a modification of the LDA-based input exchange-correlation in thicknessdependent modeling 13 of an electron layer, and in the fundamental problem of bound states 18 around a negative point charge in a 2D electron system at low densities. In the attractive, so-called interaction strength interpolation modeling 19,20 of exchange and correlation, the input at strong coupling rests on the details of the Wigner limit, as well.…”

“…Considering the common scaling ͓ϳ͑1 / r s ͔͒ of the leading terms in the energies of the many-body system at low densities, one has to use the ⑀ xc ͑LDA͒ ͑D͒ =−␤ / r s form to design properly a local input-construction to numerical applications. 7,13 In the Wigner lattice, a pointlike electron sees only the normalized compensating charge density of the rigid background. Thus, in an LDA treatment, the spurious selfinteraction term, which is one-half the integrated 6,7 electrostatic interaction of a normalized electronic chargedistribution with the potential field generated by itself, must cancel the energy-contribution calculated via a local ͑input͒ exchange-correlation term ͓⑀ xc ͑LDA͒ ͑r͔͒.…”

Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

“…Maybe the most important phenomenon is the competition between electrostatic and kinetic energies in the quantum range. Within the idealized model of a 2D homogeneous electron gas and charge-compensating rigid background the competition leads to different phases, such as unpolarized and polarized liquids, 1-3 possible intermediate states, [4][5][6] and the Wigner crystal. [7][8][9][10] In this work we are interested in a possible Cooper channel with effective electron-electron attraction in 2D.…”