Electron Spectrum Topology and Giant Density-of-States Singularities in Cubic Lattices

TL;DR

This paper investigates the topology of isoenergetic surfaces in cubic lattices within the tight-binding model, revealing giant density-of-states singularities and their impact on electronic and magnetic properties.

Contribution

It provides analytical expressions for density of states near topological transitions in cubic lattices, highlighting the formation of van Hove lines and surfaces with giant effective masses.

Findings

Density of states peaks at internal Brillouin zone points.

Giant effective masses near van Hove singularities.

Analytical formulas involving elliptic integrals for DOS.

Abstract

The topology of isoenergetic surfaces in reciprocal space for simple (sc), body-centered (bcc), and face-centered (fcc) cubic lattices is investigated in detail in the tight-binding approximation, taking into account the transfer integrals between the nearest and next neighbors $t$ and $t'$. It is shown that, for values $\tau = t'/t = \tau_\ast$ corresponding to a change in the topology of surfaces, lines and surfaces of $\mathbf k$-van Hove points can be formed. With a small deviation of $\tau$ from these singular values, the spectrum in the vicinity of the van Hove line (surface) is replaced by a weak dependence on $\mathbf k$ in the vicinity of several van Hove points that have a giant mass proportional to $|\tau - \tau_ \ast|^{-1}$. Singular contributions to the density of states near peculiar $\tau$ values are considered; analytical expressions for the density of states being obtained in terms of elliptic integrals. It is shown that in a number of cases the maximum value of the density of states is achieved at energies corresponding not to $\mathbf{k}$-points on the Brillouin zone edges, but to its internal points in highly symmetrical directions. The corresponding contributions to electron and magnetic properties are treated, in particular, in application to weak itinerant magnets.