Antiferromagnetic Phase of Wigner Electron Crystal

Abstract

The ground state energies of the 3-dimensional antiferromagnetic Wigner crystal corresponding to sc, bcc, fcc, diamond and perovskite structures are computed and the structural stability is analyzed. It is found that the bcc structure has the lowest energy. The possibility of the antiferromagnetic phase of the Wigner crystal having cubic or spherical surface as the region of occupation is analyzed. The effect of correlation is suitably taken into account. This still lowers the ground state energy. The calculations are done for the whole range of the density parameter rs from 1 to 200. The low density region favorable for Wigner crystallization is found to be above rs = 10. The structure dependent Wannier function is approximated by orthonormalized Gaussian and it is employed in the calculation. The orbital exponent of the Gaussian is used as a variational parameter. The calculations are also done for the non-uniform positive background case.

Structural stability analysis of Wigner crystal with Gaussian and Yukawa‐type positive background

“…This has been detailed in our earlier works 12, 13, 22, however, here we give a brief account. In this, we transform the Gaussians into orthogonalized atomic orbitals using the method given by Lowdin 23 and Calais and Appel 24.…”

“…For the bcc lattice, the expression for the edge of the cubic surface is 12, 13 where and the radius of the spherical surface in k space is …”

“…Recently, a lot of experimental and theoretical works are being reported on the Wigner crystal 6–20. But, only a few calculations were performed to analyze the structural stability by assuming different structures for Wigner crystal 8–11.…”