Wigner crystallization in quantum electron bilayers

Abstract

The phase diagram of quantum electron bilayers in zero magnetic field is obtained using density functional theory. For large electron densities the system is in the liquid phase, while for smaller densities the liquid may freeze (Wigner crystallization) into four different crystalline phases; the lattice symmetry and the critical density depend on the the inter-layer distance. The phase boundaries between different Wigner crystals consist of both first and second order transitions, depending on the phases involved, and join the freezing curve at three different triple points. 73.20.Dx, 64.70.Dv, 64.70.Kb Typeset using REVT E X 1

Enhancement of Wigner crystallization in quasi-low-dimensional solids

“…6 that both the sequence of phases and the critical melting densities obtained within the present quadratic approximation are in satisfactory agreement with the more sophisticated numerical results of Refs. 21,22,23 (the melting density is slightly underestimated as compared with QMC, but quite similar to the DFT result). It is interesting to see that the same trends observed in the preceding Section for the layered solids are already present in the single bilayer.…”

Wigner crystallization in semiconductor quantum wires

“…As remarked by Choudhury and Ghosh, 15 the success of the method relies on various cancellations. We choose to follow the previous examples [15][16][17] which yield reasonable estimates for Wigner crystallization in higher dimensions. The kinetic energy functional within the Thomas-Fermi-Weizsäcker approximation in one dimension can be described in atomic units ͑a.u.͒ as…”

“…It has been commented 20 that the above procedure of using a modulated density results in a rather poor density profile, although a reasonable estimate of the fluid-solid transition is obtained. Another popular form for the density distribution is a Gaussian with variational parameters, 15,17 which predicts the transition density rather well and gives reasonable density profiles in 2D electron systems. Since our primary aim here is to obtain an estimate for the freezing densities in 1D structures, we have not attempted a Gaussian ansatz for (z).…”

Analytical expressions for the local-field corrections in double-layer electron systems

“…Recently, Dong and Lei [16] utilized a similar approach to calculate the interlayer local field correlations in weakly coupled electron-electron and electron-hole layers and studied the Coulomb drag effect. It should even be possible to study the Wigner crystallization in double-layer systems using our results as input to density-functional theories [17]. Our approach lends itself to further generalizations to cover other situations as well.…”