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 ′ are investigated in detail. It is shown that at values of τ ≡ t ′ /t = τ * , corresponding to the change of isoenergetic surface topology, the formation of van Hove 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 k-dependence in the vicinity of few van Hove points which possess huge masses proportional to |τ − τ * | −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 k-space with the variation of τ . Closed analytical expressions for density of states as a function of energy and τ in terms of elliptic integrals, and powerlaw asymptotics at τ = τ * are obtained. Besides the case of sc lattice with small τ (maximum of density of states corresponds to 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 not at zone faces.

Incommensurate magnetic order in rare earth and transition metal compounds with local moments

“…5a. One can see a strong square root van Hove singularity for the Q = Q R point owing to nesting, and a more weak van Hove line singularity with diverging mass [65,66] for the Q = Q M point. Γ(0, 0, 0), H(2π, 0, 0), N(π, π, 0), P(π, π, π), ∆(qx, 0, 0), Σ(qx, qx, 0), Λ(qx, qx, qx), D(π, π − δqy, 0), G(2π − δqx, δqx, 0), F (2π − δqx, δqx, δqx).…”

“…9a. (Such a sharp drop can lead to interesting effects in electronic properties [65,66]). Thus the rest of the peak in DOS generally leads to a wide region of saturated ferromagnetic ordering at n s near 2.…”

Metal-insulator transition and antiferromagnetism in the generalized Hubbard model: Treatment of correlation effects

“…2b,c), where the deviation of τ from special values τ * corresponding to topological transitions (for which the van Hove singularity line is present) results in destroying van Hove singularity lines (see details in Refs. 35,36). For the square lattice at τ = 0 the Fermi level corresponding to half-filling coincides with the van Hove singularity position; at finite τ this is not the case, but the van Hove singularity holds its impact.…”

“…( 56), (55), we use the explicit expressions for exact density of states at finite τ for the square, sc and bcc lattices derived in Refs. 35,36, where the presence of van Hove singularity lines at finite τ was found (at τ = 0.25 for sc lattice and τ = 1.0 for bcc lattice), which allows to solve Eqs. ( 50) and ( 51) numerically with extremely high precision.…”

“…1. Physically, the difference of two-and three-dimensional cases is crucial: while in threedimensional case strong van Hove singularity in the density of states (DOS), generally speaking, does not exist (or, for body-centered cubic lattice, occurs only in nearest-neighbor hopping approximation, apart from the giant van Hove singularity line in the peculiar case t ′ = t [35,36]), for the square lattice the logarithmic van Hove singularity is always present [37], which results in non-analytic dependence on t ′ and, therefore, strong lowering the energy of PM metal phase at finite t ′ . At the same time, the energy of AFM insulator phase also acquires non-analytical contributions from van Hove singularity of DOS in nearest-neighbor approximation at the center of the band.…”