Giant van Hove Density of States Singularities and Anomalies of Electron and Magnetic Properties in Cubic Lattices

TL;DR

This paper investigates the density of states and topological changes in isoenergetic surfaces of cubic lattices with nearest and next-nearest neighbor hopping, revealing van Hove singularities and their impact on electronic properties.

Contribution

It provides analytical expressions for density of states near van Hove singularities and describes the topology change of isoenergetic surfaces in cubic lattices.

Findings

Van Hove lines form at specific hopping ratios, changing surface topology.

Singular contributions to density of states are characterized analytically.

Maximum density of states occurs at high-symmetry points inside the Brillouin zone.

Abstract

Densities of states for simple (sc) and base-centered (bcc) cubic lattices with account of nearest and next-nearest neighbour hopping integrals $t$ and $t'$ are investigated in detail. It is shown that at values of $\tau \equiv t'/t = \tau_\ast$, corresponding to the change of isoenergetic surface topology, the formation of van Hove $\bf k$ lines takes place. At small deviation from these special values, the weakly dispersive spectrum in the vicinity of van Hove lines is replaced by a weak $\bf k$-dependence in the vicinity of few van Hove points which possess huge masses proportional to $|\tau - \tau_\ast|^{-1}$. The singular contributions to the density of states originating from van Hove points and lines are considered, as well as the change in the topology of isoenergetic surfaces in the $\bf k$-space with the variation of $\tau$. Closed analytical expressions for density of states as a function of energy and $\tau$ in terms of elliptic integrals, and power-law asymptotics at $\tau = \tau_\ast$ are obtained. Besides the case of sc lattice with small $\tau$ (maximum of density of states corresponds to energy level of X $\bf k$-point), maximal value of the density of states is always achieved at energies corresponding to \textit{inner} $\bf k$-points of the Brillouin zone positioned in high-symmetry directions, and not at zone faces.