Study of Structural Stability of Wigner Electron Crystal

Abstract

The ground state energies of the non-magnetic Wigner electron crystals corresponding to sc, bcc, fcc, diamond and perovskite structures are estimated and it is found that the bcc lattice still remains to be the stable known arrangement for three-dimensional Wigner electron crystal. Perovskite structure is not the stablest as claimed in a previous work, it is preferred only after fcc and sc. The stability is analysed taking different structures and assuming the possibility of the Wigner electrons having cubic or spherical constant energy surface, the region of occupation in momentum space, for a whole range of rs values (rs = 20 to 200). The structure dependent Wannier functions, which give a proper localized representation for the Wigner electrons in the crystals are constructed and employed in the present calculation.

Antiferromagnetic Phase of Wigner Electron Crystal

“…He concluded that, at low density, the ground state is a ferromagnetic crystal of the Wigner type. To compare our present work with our previous works, 19,20 we have tabulated the ground state energies for the non-magnetic, ferromagnetic and antiferromagnetic phase of Wigner crystal in Table 6. From Table 6, it is found that, at very low For the non-uniform positive background case also, the ground state energy is minimum for bcc structure.…”

“…In an antiferromagnetic Wigner electron crystal the bcc structure has the minimum energy with spherical surface as the region of occupation in momentum space for the uniform neutralizing positive background similar to non-magnetic crystal. 7,19 For almost all the r s values, the Wigner crystal energy is less than the electron gas energy. The fcc structure has the minimum energy next to bcc for both cubic and spherical surface cases.…”

INVESTIGATION OF NON-MAGNETIC AND FERROMAGNETIC PHASES OF 3D ELECTRON CRYSTAL WITH NaCl AND CsCl STRUCTURES

“…In our previous work, [14][15][16][17][18] we have analyzed the electron crystallization with sc, bcc, fcc, perovskite, and diamond structures for non-magnetic and ferromagnetic cases. In the present work, we have investigated the whole problem adopting a more realistic approach, which has been developed and used successfully for Wigner electron crystallization 14 and the ground state energies of the non-magnetic and ferromagnetic phases of 3D Wigner electron crystal corresponding to sodium chloride (NaCl) and cesium chloride (CsCl) structures with uniform neutralizing and Yukawa type positive backgrounds are computed.…”