Electronic energy-band structure of(SN)xandS2N2crystals

Abstract

First-principles calculations of the electronic energy-band structures of an isolated one-dimensional ${(\mathrm{SN})}_{x}$ chain and of a three-dimensional ${(\mathrm{SN})}_{x}$ crystal have been made by using the method of linear combinations of atomic orbitals (LCAO). The crystal potential is taken as a superposition of the atomic potentials at each site with a Slater-type exchange approximation. The basis functions consist of the Bloch sums of the nitrogen $1s$, $2s$, $2p$ orbitals and sulfur $1s$, $2s$, $2p$, $3s$, $3p$ orbitals and single-Gaussian Bloch sums. The technique of orthogonalization is used so that the core-state Bloch sums can be deleted from the basis set. All the multicenter integrals occurring in the Hamiltonian matrix elements are evaluated exactly by means of the Gaussian technique and the summation of the multicenter integrals over the lattice is carried to convergence. The calculated density of states (DOS) of the crystal is in good agreement with the x-ray photoemission measurements. Studies of Fermi surfaces show an electron pocket near the $\ensuremath{\Gamma}Z$ line and a hole pocket near the $\mathrm{CY}$ line of the Brillouin zone. While the DOS shows a shallow and flat minimum at the Fermi energy for the one-dimensional ${(\mathrm{SN})}_{x}$ chain, in the case of the three-dimensional crystal, a very steep valley is found in the DOS curve near the Fermi energy. This steep valley is a direct consequence of the interchain coupling. The very small theoretical value of DOS at the Fermi energy [0.01 states/(eV spin molecule)] is consistent with the ultraviolet-photoemission-spectra measurements but is much less than the value deduced from the specific-heat experiment. Because the DOS at the Fermi energy [$N(0)$] is very near the minimum of the steep valley, one may speculate that a slight change in the atomic distances may bring about a large increase in $N(0)$. This would provide a simple explanation for the observed increase in the superconducting transition temperature as well as the normal-state conductivity under pressure. Energy bands and DOS for the ${\mathrm{S}}_{2}$${\mathrm{N}}_{2}$ crystal calculated by the same LCAO procedure are also presented.