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

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 τ ≡ t '/ t = τ*, corresponding to the change in isoenergetic surface topology, the formation of Van Hove k lines takes place. At small deviations from these special values, the weakly dispersive spectrum in the vicinity of Van Hove lines is replaced by a weak k -dependence in the vicinity of a few van Hove points which possess huge masses proportional to |τ – τ*| –1 . The singular contributions to the density of states that originate from Van Hove points and lines are considered, as well as the change in the topology of isoenergetic surfaces in the k -space with the variation of τ. The closed analytical expressions for the density of states as a function of energy and τ in terms of elliptic integrals and power-law asymptotics at τ = τ* are obtained. Apart from the case of sc lattice with small τ (maximum of density of state corresponds to the energy level of X k -point), maximal value of the density of states is always achieved at energies corresponding to inner k -points of the Brillouin zone positioned in high-symmetry directions, and rather than at zone faces.