Lattice vibrations and elastic constants of three- and two-dimensional quantal Wigner crystals near melting

Abstract

The phonon dispersion relations and the elastic constants are evaluated for Wigner electron crystals near the critical coupling strength for melting in the fully quantal regime at zero temperature. The structures considered are the body-centred and face-centred cubic lattices in dimensionality D = 3 and the triangular lattice in D = 2. The calculations are based on a density functional approach requiring as input the linear density response function of the fluid phase at freezing and the Debye - Waller factor of the crystal at melting. These are known from quantal Monte Carlo simulations both for D = 3 and for D = 2. Comparison with earlier results of harmonic calculations shows appreciable softening from anharmonicity, which is mainly associated with the exchange and correlation contributions to the effective force constants of the quantal crystal near melting. Mechanical stability of the body-centred cubic electron crystal at melting is demonstrated through a self-consistent calculation of the lattice vibrations and the mean square particle displacement entering the Debye - Waller factor, as well as by calculations of the elastic constants using the methods of long waves and of homogeneous deformations. Finally, a relationship is displayed between phonon dispersion curves in the triangular Wigner crystal near melting and plasmon excitations in the two-dimensional electron fluid near freezing.

Electron–electron Interactions in the 2d Ferromagnetic Electron Fluid

“…For the local field factor G(q, 0) we have used a simple representation of simulation data through two intersecting straight lines embodying the compressibility sum rule at low q and the exact kinetic energy at high q, as proposed in earlier work on phonons in the 2D Wigner crystal. 30 That is,…”

Polaron in the Wigner lattice

“…It seems that these effects are not important for the Wigner lattice at r s Ͼ20, 9 but various approaches still do not give a clear answer. 4,21 Of course, all the effects can be taken into account in the first-principle numerical calculations, 9,22 but then we lack a simple physical picture.…”

“…Obviously, one can add an external electron among lattice electrons and ask for the interaction of this free-like electron with lattice vibrations, i.e., for the polaron in the Wigner lattice. While the lattice vibrations are known, 3,4 here we wish to investigate the properties of a Wigner polaron. There are some obvious differences between this and the standard polaron problem.…”

Study of Structural Stability of Wigner Electron Crystal

“…48 We then minimize the energy functional ε given in Eq. (33), with appropriate H eff . R(m, n) -which has a matrix like structure is evaluated using Eqs.…”

“…[2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] On the theoretical side attempts have been made to understand the character of the ground state of the electron crystal -an electron gas with periodic density and positive background. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] Only a few calculations were performed to ascertain the structural stability by assuming different crystal structures namely simple cubic (sc), body centered cubic (bcc), face centered cubic (fcc), diamond (dd) and perovskite (pst) structures for the Wigner crystal. [37][38][39][40] All these calculations lead to the conclusion that Wigner crystal favours bcc structure compared to other structures.…”