Diffusion Monte Carlo Study of Electrons in Two-dimensional Layers

Abstract

We investigate the phase diagram of electrons in two dimensions at T = 0 by means of accurate diffusion Monte Carlo simulations within the fixed-node approximation. At variance with previous studies, we find that in an isolated layer Slater-Jastrow nodes yield stability of the fully polarised fluid at intermediate coupling, before freezing into a triangular crystal sets in. We have also studied coupled layers of electrons and of electrons and holes. Preliminary results show that at large coupling, as two layers are brought together from infinity, inter-layer correlation first stabilises the crystalline phase at distances of the order of the in-plane inter-particle spacing. As the distance is further decreased the effect of correlation, as expected, turns into an enhanced screening, which disrupts the crystalline order in favour of liquid phases.

Effective interaction in two-dimensional electron systems

“…6 and in Table V as ͗g skm ͘, together with the RPA and the QMC results. 26,27 We can see that Eq. ͑28͒ underestimates the correlation energy of the QMC by about 20%, which is the same order of the magnitude as the estimated contribution of the three-body correlation, (h/d) 4 , in Table IV.…”

Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

“…Note that most of these values depend on the QMC calculations of the correlation energy and structure factors as reported in Ref. 16 values of q as in the case of r s ϭ10. This suggests that, at least in two dimensions, the higher-order diagrams excluded from Fig.…”

Pair Densities in a Two-dimensional Electron Gas (Jellium) at Strong Coupling from Scattering Theory with Kukkonen-Overhauser Effective Interactions

“…This shows that d ( ) is slightly positive at short distance, corresponding to a [16]. The crosses are from QMC results in [19].…”

“…4 reports the spin-averaged pair distribution function ( ) in 2D jellium at s = 10 , in comparison with the QMC data of Rapisarda and Senatore [19] and with those obtained within the Hartree approximation. It is evident that the present approach yields a fully quantitative account of the QMC data, and in particular reproduces the presence of a firstneighbour shell at this value of the coupling strength which is instead completely missed in the Hartree approximation to the scattering potentials.…”

“…We do so by recourse to the electron-electron effective interactions derived by Kukkonen and Overhauser [18] and focus on 2D jellium in the strong-coupling regime corresponding to s = 10, where QMC data by Rapisarda and Senatore [19] allow a quantitative test of our results for ( ). We also examine the behaviour of the spin-resolved pair densities, in relation to the first-order transition from the paramagnetic to the fully spin-polarized state that has been reported to occur in 2D jellium at s 20 from QMC studies [20].…”