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.     

Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities

A criterion for ferromagnetism in two-dimensional systems with the Fermi level near Van Hove singularities (VHSs) is analyzed. In the quasistatic approximation applied to a spin-fermion model, it is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between the electronic and spin degrees of freedom is sufficiently large (I > I _c). The critical interaction I _c is much greater than its value determined from the Stoner criterion; hence, the latter criterion is not an adequate criterion for ferromagnetism in the presence of Van Hove singularities in the electronic spectrum. By combining the quasistatic approximation with the method of equations of motion, the electronic self-energy is obtained in the first order in the inverse number of spin components.     

Dynamics of water in real space and time

Owing to marked advances in instrumentation in X-ray and neutron scattering the time-dependent pair correlation function, the Van Hove function, can now be determined by inelastic X-ray and neutron scattering measurements. The local dynamics of water in real space and time is visualised by this approach. We discuss how the dynamic properties, such as viscosity and diffusion, can be elucidated through the Van Hove function of water.     

On the enhancement of superconductivity due to Van Hove singularity

We have rigorously solved the standard BCS gap equation with the density of states of Van Hove type. The result shows that the enhancement ofT _c is not as effective as previously estimated. It seems unlikely that Van Hove singularity inN(E) can be theT _c -enhancement mechanism for the high-T _c Cu oxides.     

On the theory of the Kondo effect in two-dimensional metals

The Kondo effect in a (quasi-)two-dimensional metal is studied. The special feature of the two-dimensionality is the Van Hove singularity in the electron density of states. For the band filling choosen such, that the Fermi level is close to the saddle points of the band spectrum, the Van Hove singularity comes into play and changes the usual Kondo log to the log². It turnes out to be possible to carry out the first order parquet summation and to obtain the conditions for the Kondo antiferromagnetic resonance for an arbitrary geometry of the band spectrum. The connection with the Orthogonality Catastrophe is traced and it is shown, that the weak coupling Kondo problem just corresponds to the intermediate asymptotics of the metal's relaxation in a time-dependent external potential.     

Compton profiles of metals and Van Hove singularities

The structures of the Compton profiles of metals, as observed by Platzman et al., are tentatively interpreted as Van Hove singularities for Bloch electrons.     

Asymmetric Features in the Resistivity of Clean Quasi-One-Dimensional Systems: Fano Resonances or Non-Born Effects?

JETP Letters - We show that experimentally observed complex line shapes of smeared Van Hove singularities in the resistivity of a quasi-one-dimensional system may be due to non-Born effects in...     

Solution de l'equation de Boltzmann pour des batonnets durs unidimensionnels

We present the exact solution of the linear Boltzmann equation for one-dimensional hard rods. In particular, we compute the velocity correlation function and the Van Hove self-correlation function.     

Kinetic equations without “memory” for the time-displaced correlation functions

The relations between the kinetic equations with and without convolution in time are discussed on the basis of the kinetic equation for the Van Hove self-correlation function. Formal equivalence of both the equations is shown, and approximate scattering operators for the dilute-gas case and for the Brownian particle are considered.     

Two-dimensional Van Hove singularity in TaS2 band structure

The transverse optical properties of a number of transition metal dichalcogenides have been studied in the 2 eV – 12 eV range. For TaS₂, a two-dimensional Van Hove singularity clearly appears at 7 eV in good agreement with the saddle point case.     

s+d混合波对称性下联合模型的超导电性

提出一个联合模型，在ｓ＋ｄ混合波对称性下，合并考虑电子间配对相互作用的各向异性及二维电子结构上Ｖａｎ Ｈｏｖｅ奇异性对超导电性的影响．理论结果表明：Ｖａｎ Ｈｏｖｅ奇异性及配对相互作用的各向异性都是使Ｔ_c提高的重要因素；各向异性的电子配对相互作用自然导致序参量的ｄ波成分，当此各向异性增强时，ｄ波成分也增大．高温超导体的较高２Δ（０）／ｋ_ＢＴ_c值可能预示着在这些材料中ｓ波的权重远小于ｄ波权重．联合效应模型下的Ｔ_c处比热跳跃行为与经典的ＢＣＳ理论也完全不同 关键词：     

Universal absorption of two-dimensional materials within k ⋅ p method

The universal optical absorption is a fascinating property existing in certain two-dimensional (2D) materials. By introducing a general two-band $\mathbf{k}?\mathbf{p}$ effective Hamiltonian, we demonstrate that the absorptance can manifest an universal value at the direct band-edge of 2D materials in three specific cases. However, for general 2D materials, the absorptance becomes nonuniversal. We investigate the dependency of absorptance on the band parameters of general 2D materials. The influences of band-anisotropy and band warping are also considered. Interestingly, we find that the coherent interband coupling and the band warping are responsible for the occurrence of the saddle-point type of Van Hove singularity, which leads to strong light-matter interactions in 2D materials.     

Quantum corrections to liquid correlations

Sudarshan's semi-classical treatment of correlation functions is applied to the study of quantum corrections to the Van Hove function. In its generalised form, it enables one to choose the best correlation function for a given potential. Higher-order correlations are also sketched briefly and the details are similar to those considered by Oppenheim and Bloom.     

On the detection of nuclear spin waves by inelastic neutron scattering

The possibility of measuring nuclear spin waves (NSW) by inelastic neutron scattering is discussed. The differential cross section and scattered state polarization for the scattering of thermal neutrons from systems described by the Suhl-Nakamura Hamiltonian are developed in the Van Hove correlation function formalism; the relevant correlation functions for the Suhl-Nakamura system are computed. The implications of these calculations for the feasibility of detecting nuclear spin wave modes in neutron scattering experiments are discussed.     

The Homogeneous Hamilton–Jacobi and Bernoulli Equations Revisited, II

It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949–1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called compatible if they satisfy the Morette–Van Hove formula and anti-compatible if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf–Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton–Jacobi equation has recently been enlarged.     

Motion of charges and singularities in the vacancy spectrum in crystalline helium

The Van Hove singularities in the vacancy spectrum of ⁴He crystals are manifested as singularities in the field dependence of the drift velocity of charges. In ³He, the field dependence of the drift velocity is determined by the vacancy spectrum in the completely spin-polarized state of the crystal.     

Functorial geometric quantization and Van Hove's theorem

A classical theorem of Van Hove in conjunction with a formalism developed by Weinstein is used to prove that a quantization functor does not exist. In the proof a category of exact transverse Lagrangian submanifolds is introduced which provides a functorial link between Schrödinger quantization and the prequantization/polarization theory of Kostant and Souriau.     

Impurity-induced anisotropic semiconductor-semimetal transition in monolayer biased black phosphorus

Taking into account the electron-impurity interaction within the continuum approximation of tight-binding model, the Born approximation, and the Green's function method, the main features of anisotropic electronic phase transition are investigated in monolayer biased black phosphorus (BP). To this end, we concentrated on the disordered electronic density of states (DOS), which gives useful information for electro-optical devices. Increasing the impurity concentration in both unbiased and biased impurity-infected single-layer BP, in addition to the decrease of the band gap, independent of the direction, leads to the midgap states and an extra Van Hove singularity inside and outside of the band gap, respectively. Furthermore, strong impurity scattering potentials lead to a semiconductor-semimetal transition and one more Van Hove singularity in x-direction of unbiased BP and surprisingly, this transition does not occur in biased BP. We found that there is no phase transition in y-direction. Since real applications require structures with modulated band gaps, we have studied the influence of different bias voltages on the disordered DOS in both directions, resulting in the increase of the band gap.     

Theory of irreversible processes in nonequilibrium quantum systems. I. General formalism

The theory of Van Hove for nonequilibrium quantum statistical mechanics is extensively reformulated in terms of a superspace (a kind of operator space). This reformulation enables us to introduce a diagrammatic method which makes it convenient to deal with practical problems in physical systems. In our formalism, quantum statistical effects are considered on the basis of a systematic rule for the contraction technique. A complicated statistical effect in boson or fermion systems can be treated by starting with a simple unsymmetrized formalism in the Boltzmann statistics.