Properties of electrons near a Van Hove singularity

The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.     

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

The topology of energy surfaces in reciprocal space is studied in detail for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in the tight-binding approximation, taking into account hopping integrals t and t′ between the nearest and next-nearest neighbor sites, respectively. It is shown that lines and surfaces formed by van Hove k points can arise at values τ = t′/t = τ* corresponding to a change in the surface topology. At a small deviation of τ from these special values, the spectrum near the van Hove line (surface) only slightly depends on k. This corresponds to a giant effective mass proportional to |τ - τ*|⁻¹ near several van Hove points. Singular contributions to the density of states near these special t values are analyzed and explicit expressions are obtained for the density of states in terms of elliptic integrals. It is shown that, in some cases, the maximum density of states is achieved at energies corresponding to k points in high-symmetry directions inside the Brillouin zone rather than at its edges. The corresponding contributions to electronic and magnetic characteristics are discussed, in particular, in application to itinerant weak magnets.

     

Contributions to the theory of ferromagnetism in the degenerate Hubbard model

The possibility of ferromagnetic ordering in a generalized Hubbard model with allowance for degeneracy and for infinite Hubbard energy is studied. The region of existence of ferromagnetism for electron density greater than 1 is determined. It is shown that for electron density less than 1 ferromagnetism exists only in special cases when the Fermi surface passes near van Hove singularities. Zh. éksp. Teor. Fiz. 112, 2223–2236 (December 1997)     

Note on the equivalence of different approximations in the relaxation theory

We briefly discuss relations between different variants of the second order generalized master equations (GME), in particular among different types of the Markov-Born approximation of time-convolution GME and Born approximation in time-convolutionless one. We prove that equivalence valid in the van Hove limit does not in general apply for other types of scaling. On the other hand, for other scalings one appropriate form of the interaction representation always exist that reproduces this equivalence known from the weak-coupling (van Hove) one.     

Critical temperature of a van Hove superconductor with spin–charge separation

We studied a spin–charge separation superconductor with a van Hove density of states. The critical temperature and the influence of the Coulomb interaction have been calculated in the mean field model. We also calculated the Ginzburg–Landau coefficients as a function of temperature.     

The electrical conductivity for inhomogeneous electric fields by the Liouville operator method

A derivation is given of the electrical conductivity for a metal in a space- and time-dependent electric field. Thereby it is assumed that the electrons are scattered elastically by randomly distributed impurities. The derivation starts from the Kubo-Nakajima formula and is based on a perturbation expansion with Liouville operators, where use is made of van Hove's diagonal singularity property of the scattering potential. The formulae obtained are compact and the method is simpler and more transparent than the perturbation formalism developed by van Hove. It is shown that the lowest order approximation corresponds to the Boltzmann equation for electrons in inhomogeneous electric fields.     

Probability distributions for the run-and-tumble bacterial dynamics: An analogy to the Lorentz model

In this paper, we exploit an analogy of the run-and-tumble process for bacterial motility with the Lorentz model of electron conduction in order to obtain analytical results for the intermediate scattering function. This allows to obtain an analytical result for the van Hove function in real space for two-dimensional systems. We furthermore consider the 2D circling motion of bacteria close to solid boundaries with tumbling, and show that the analogy to electron conduction in a magnetic field allows to predict the effective diffusion coefficient of the bacteria. The latter is shown to be reduced by the circling motion of the bacteria.     

Electron-phonon interaction in tetrahedral semiconductors

Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The one-electron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T=0).In this paper, we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T⁴ law (contrary to the Varshni T² result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g. CuCl) and possibly Ag (e.g. AgGaS₂). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.     

What is the highest T c for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.     

What is the highest Tc for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.      

Ultrarelativistic electron-hole pairing in graphene bilayer

We consider the ground state of an electron-hole graphene bilayer composed of two independently-doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only the conduction band of the electron-doped layer and the valence band of the hole-doped layer, thus the ground state is similar to an ordinary BCS condensate. At strong coupling, an ultrarelativistic character of the electron dynamics reveals itself and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. Analysis of the instability of the unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. The relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of a separable potential. It is shown that, if the characteristic width of the pairing region is of the order of magnitude of the chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.     

Classification of unconventional electron-hole condensates

Heavy Fermion metals with their very anisotropic quasiparticle states may support unconventional electron-hole (Peierls) pairing in addition to unconventional two electron (Cooper) pairs in the superconducting phase. For two different nesting Fermi surface models the possible types of electron hole condensates are classified according to the symmetries of their order parameters. This is performed within a continuum representation for the electronic states near the van Hove saddle point singularities. The quasiparticle bands and the unitary transformation to Bloch states in the condensed phase are derived for the two Fermi surface models with one and two independent nesting vectors respectively. Emphasis is put on the investigation of electron-hole condensed phases with 2Q-modulated structure. It is shown that in the continuum approximation the gap equations are all equivalent and the critical field curve is calculated in the rigid band model.     

Optical potential and nuclear matter

The relation of the parameters of the optical nucleon-nucleus potential to the characteristics of nuclear matter is established. The existing values of the parameters of the optical potential reflect well the binding energy per nucleon and the symmetry energy of nuclear matter. It is shown that the theorem of Hugenholtz and van Hove is not valid for the real part of the optical potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1978.     

Effects of van Hove Singularities on Transport of Quantum Dot Systems in Kondo Regime

In the present paper, we study the effect of van Hove singularities of conduction electron on the transport of a single quantum dot system in the Kondo regime. By using both the equation-of-motion and the noncrossing approximation techniques, we show that the corrections caused by these singularities are actually minor. It can be explained by observing that the singularities in the equations, which determine the electronic DOS on the dot, are integrable. Furthermore, we find that, although each line width function is divergent at van Hove singular points, the total divergence is canceled out in the final formula to calculate the current through the system. Therefore, as far as the qualitative properties of the system is concerned, these singularities can be ignored and the wide-band approximation can be safely used in calculation.     

Phase diagram of superconductivity and antiferromagnetism in high-Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential (μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap (z), AFM gap (h) and chemical potential (μ) are solved self consistently for different dopant concentrations (x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (?39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.     

Doping and temperature dependence of the spin susceptibility in the p-d model

The spin magnetic susceptibility of the p-d model is calculated by means of a perturbation theory in the hybridization term V through a generalized cumulant expansion (GCE). The analysis is approached from the paramagnetic metallic phase. The results qualitatively reproduce some unusual magnetic properties in the normal state of the hole-doped cuprates, supporting the scenario of a Van Hove singularity near the Fermi level. Received 15 October 1998 and Received in final form 24 March 1999     

Anomalous Fermi-surface dependent pairing in a self-doped high-Tc superconductor

We report the discovery of a self-doped multilayer high Tc superconductor Ba2Ca3Cu4O8F2 (F0234) which contains distinctly different superconducting gap magnitudes along its two Fermi-surface sheets. While formal valence counting would imply this material to be an undoped insulator, it is a self-doped superconductor with a Tc of 60 K, possessing simultaneously both electron- and hole-doped Fermi-surface sheets. Intriguingly, the Fermi-surface sheet characterized by the much larger gap is the electron-doped one, which has a shape disfavoring two electronic features considered to be important for the pairing mechanism: the van Hove singularity and the antiferromagnetic (pi/a, pi/a) scattering.     

A new method to study phase transition in 3D Heisenberg model

It is shown that partial entropy, which is the classical analog of von Neumann entropy in quantum theory, is an effective tool to study the thermodynamic phase transitions in the physical systems. This method captures the intrinsic characters of critical fluctuations and does not need the pre-assumed order parameter. As an example, the finite temperature phase transition in the quantum three-dimensional spin-1/2 Heisenberg model is studied, where the stochastic series expansion quantum Monte Carlo method with operator-loop update is used. It is found that close to the critical temperature, the derivative of partial entropy displays a maximum value and shows finite size scaling behaviors, from which the critical temperature and critical exponents are determined.     

Superconducting instability of a non-centrosymmetric system

The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.