Energy band structure of a two-dimensional liquid with nearest-neighbour angular correlations

Abstract

The electronic energy bands of a two-dimensional liquid in which there are angular correlations between the positions of nearest-neighbour atoms are investigated, using an extension of the Greenian formalism of Phariseau and Ziman and a generalized coherent-wave approximation Near k = 0, and when the number of nearest neighbours is odd, it is found that, in addition to the normal bands in which the wave function has the same sign on each atom, bands occur in which the wave function is essentially of opposite sign on nearest-neighbour atoms. The energy bands in such liquids therefore closely resemble those in the corresponding crystal having two atoms per unit cell In particular, different band edges can be identified with wave functions possessing bonding or antibonding properties.

As the degree of angular correlation is decreased, the imaginary part of the wave vector or energy in these new bands increases and the bands ultimately disappear as the nearest-neighbour environment approaches spherical symmetry The energy states associated with these bands presumably become added to the symmetric-sign bands as states of large wave vector

The extension of these findings to three dimensions is conjectured and the results are applied briefly to a discussion of the energy band structure of amorphous germanium, which is a semiconductor, and of liquid germanium, which is a metal.