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

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 $t^{\prime }$ are investigated in detail. It is shown that at values of $\tau \equiv t^{\prime }/t={\tau }_{\ast }$, corresponding to the change of isoenergetic surface topology, the formation of van Hove $\mathbf{k}$ 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 $\mathbf{k}$-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 $\mathbf{k}$-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 $\mathbf{k}$-point), maximal value of the density of states is always achieved at energies corresponding to \textit{inner} $\mathbf{k}$-points of the Brillouin zone positioned in high-symmetry directions, and not at zone faces.

arXiv commentInvited Talk on EASTMAG-2019, Ekaterinburg, 9 pages

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• Metal-insulator transition and antiferromagnetism in the generalized Hubbard model: Treatment of correlation effects
• Incommensurate magnetic order in rare earth and transition metal compounds with local moments
• Ferromagnetic instability in itinerant fcc lattice electron systems with higher order van Hove singularities: Functional renormalization group study
• Itinerant electron metamagnetism for lattices with van Hove density-of-states singularities near the Fermi level