Van Hove Points Research Articles

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 $\tau \equiv t'/t = \tau_\ast$, corresponding to the change of isoenergetic surface topology, the formation of van Hove $\bf k$ 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 $\bf k$-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 $\bf k$-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 $\bf k$-point), maximal value of the density of states is always achieved at energies corresponding to \textit{inner} $\bf k$-points of the Brillouin zone positioned in high-symmetry directions, and not at zone faces.

Anisotropic Quantum Emitter Interactions in Two-Dimensional Photonic-Crystal Baths

Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole-dipole interactions with tuneable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state which inherits the anisotropic properties of the original dissipation, and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.

Nematic phase in a two-dimensional Hubbard model at weak coupling and finite temperature

We apply the self-consistent renormalized perturbation theory to the Hubbard model on the square lattice, at finite temperatures in order to study the evolution of the Fermi-surface (FS) as a function of temperature and doping. Previously, a nematic phase for the same model has been reported to appear at weak coupling near a Lifshitz transition from closed to open FS at zero temperature where the self-consistent renormalized perturbation theory was shown to be sensitive to small deformations of the FS. We find that the competition with the superconducting order leads to a maximal nematic order appearing at non-zero temperature. We explicitly observe the two competing phases near the onset of nematic instability and, by comparing the grand canonical potentials, we find that the transitions are first-order. We explain the origin of the interaction-driven spontaneous symmetry breaking to a nematic phase in a system with several symmetry-related Van Hove points and discuss the required conditions.

Inter-valley spiral order in the Mott insulating state of a heterostructure of trilayer graphene-boron nitride

Recent experiment has shown that the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at half-filling is a Mott insulator. Based on symmetry analysis and effective band structure calculation, we propose a valley-contrasting chiral tight-binding model with local Coulomb interaction to describe this Moire super-lattice system. By matching the positions of van Hove points in the low-energy effective bands, the valley-contrasting staggered flux per triangle is determined around π/2. When the valence band is half-filled, the Fermi surfaces are found to be perfectly nested between the two valleys. Such an effect can induce an inter-valley spiral order with a gap in the charge excitations, indicating that the Mott insulating behavior observed in the trilayer graphene-boron nitride Moire super-lattice results predominantly from the inter-valley scattering.

Thermal Hall conductivity of spin-triplet superconductor with time reversal symmetry breaking

The thermal Hall conductivity is investigated for the superconductor Sr2RuO4 assuming a time reversal symmetry breaking order parameter. The γ band of Sr2RuO4 has its Fermi level near the van Hove points, close to the Lifshitz transition. Within a Bogoliubov-de Gennes approach we calculate the thermal Hall conductivity for pairing symmetries including two exemplary cases, the usual chiral p-wave phase and a fx2−y2-wave phase of the structure . In the chiral p-wave phase the thermal Hall conductivity consists of a universal temperature-linear term and an exponential correction due to quasiparticle activation with a full excitation gap. Due to line-nodes in the gap we find a correction which is quadratic in temperature for fx2−y2-wave state. This difference in the corrections allows to analyze the gap structure of the superconducting phase.

Antiferromagnetism,f-wave, and chiralp-wave superconductivity in a kagome lattice with possible application tosd2graphenes

We investigate the electronic instabilities in a Kagome lattice with Rashba spin-orbital coupling by the unbiased singular-mode functional renormalization group. At the parent $1/3$-filling, the normal state is a quantum spin Hall system. Since the bottom of the conduction band is near the van Hove singularity, the electron-doped system is highly susceptible to competing orders upon electron interactions. The topological nature of the parent system enriches the complexity and novelty of such orders. We find $120^o$-type intra-unitcell antiferromagnetic order, $f$-wave superconductivity and chiral $p$-wave superconductivity with increasing electron doping above the van Hove point. In both types of superconducting phases, there is a mixture of comparable spin singlet and triplet components because of the Rashba coupling. The chiral $p$-wave superconducting state is characterized by a Chern number $Z=1$, supporting a branch of Weyl fermion states on each edge. The model bares close relevance to the so-called $sd^2$-graphenes proposed recently.

Phonons in graphene with point defects

The phonon density of states (DOS) of graphene with different types of point defects(carbon isotopes, substitution atoms, vacancies) is considered. Using a solvable modelwhich is based on the harmonic approximation and the assumption that the elasticforces act only between nearest neighboring ions we calculate corrections to thegraphene DOS dependent on the type and concentration of defects. In particular thecorrection due to isotopic dimers is determined. It is shown that a relatively smallconcentration of defects may lead to significant and specific changes in the DOS,especially at low frequencies, near the Van Hove points and in the vicinity of the Kpoints of the Brillouin zone. In some cases defects generate one or several narrowgaps near the critical points of the phonon DOS as well as resonance states inthe Brillouin zone regular points. All types of defects are characterized by theappearance of one or more additional Van Hove peaks near the (Dirac) K points andtheir singular contribution may be comparable with the effect of electron–phononinteraction. Besides, for low frequencies and near the critical points the relativechange in density of states may be many times higher than the concentration ofdefects.

Polarons near Van Hove points in 2D charge or spin density waves

Abstract We study theoretically the effects of impurities and of gap distortions in binding and self-trapping of particles added or excited over the insulating state of an antiferromagnetic Mott insulator. Wave functions of single particles or of bound excitons are affected by interactions with collective degrees of freedom, as shown by ARPES and optics experiments. The resulting self-localized state lowers the total particle energy, enhances its effective mass and splits off the electronic level below the nominal insulating gap. Most of the features measured experimentally in lightly n-doped cuprates are related to electronic states originated by anti-nodal points ( π , 0 ) of the Brillouin zone. In these points the van Hove singularity plays a major role by enhancing bound states of the electron with neutral and charged impurities and of inter-gap excitons.

SINGULAR FERMI SURFACES II: THE TWO-DIMENSIONAL CASE

We consider many-fermion systems with singular Fermi surfaces, which contain Van Hove points where the gradient of the band function k ↦ e(k) vanishes. In a previous paper, we have treated the case of spatial dimension d ≥ 3. In this paper, we focus on the more singular case d = 2 and establish properties of the fermionic self-energy to all orders in perturbation theory. We show that there is an asymmetry between the spatial and frequency derivatives of the self-energy. The derivative with respect to the Matsubara frequency diverges at the Van Hove points, but, surprisingly, the self-energy is C1 in the spatial momentum to all orders in perturbation theory, provided the Fermi surface is curved away from the Van Hove points. In a prototypical example, the second spatial derivative behaves similarly to the first frequency derivative. We discuss the physical significance of these findings.

SINGULAR FERMI SURFACES I: GENERAL POWER COUNTING AND HIGHER DIMENSIONAL CASES

We prove regularity properties of the self-energy, to all orders in perturbation theory, for systems with singular Fermi surfaces which contain Van Hove points where the gradient of the dispersion relation vanishes. In this paper, we show for spatial dimensions d ≥ 3 that despite the Van Hove singularity, the overlapping loop bounds we proved together with E. Trubowitz for regular non-nested Fermi surfaces [J. Stat. Phys.84 (1996) 1209–1336] still hold, provided that the Fermi surface satisfies a no-nesting condition. This implies that for a fixed interacting Fermi surface, the self-energy is a continuously differentiable function of frequency and momentum, so that the quasiparticle weight and the Fermi velocity remain close to their values in the noninteracting system to all orders in perturbation theory. In a companion paper, we treat the more singular two-dimensional case.

Phase diagram and quasiparticle properties of the Hubbard model within cluster two-site dynamical mean-field theory

We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's "two-site" method [Phys. Rev. B. 64, 165114 (2001)] where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electron-like Fermi surface away from the Mott transition, to a hole-like one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-Tc superconductors). This leaves Fermi arcs which are closed into pockets by lines with very small quasiparticle residue.

Non-BCS pairing in anisotropic strongly correlated electron systems in solids

The problem of pairing in anisotropic electron systems possessing patches of fermion condensate in the vicinity of the van Hove points is analyzed. Attention is directed to opportunities for the occurrence of non-BCS pairing correlations between the states belonging to the fermion condensate. It is shown that the physical emergence of such pairing correlations would drastically alter the behavior of the single-particle Green function, the canonical pole of Fermi-liquid theory being replaced by a branch point.

Electron spectral functions of two-dimensional high-T c superconductors in the model of fermion condensation

Spectral functions of strongly correlated two-dimensional (2D) electron systems in solids are studied on the assumption that these systems undergo a phase transition, called fermion condensation, whose characteristic feature is flattening of the electron spectrum e(p). Unlike the previous models, the decay of single-particle states in our study is properly taken into account. Results of our calculations are shown to be in qualitative agreement with ARPES data. The universal behavior of the ratio ImΣ(p, e, T)/T as a function of x=e/T, uncovered in [3] for the single-particle states around the diagonal of the Brillouin zone, are found to be reproduced reasonably well. However, in our model this behavior is destroyed in vicinities of the van Hove points, where the fermion condensate resides.

On the singularity structure of the 2D Ising model susceptibility

Some simplifications of the integrals (2n+1), derived by Wu et al (1976 13 316), that contribute to the zero field susceptibility of the 2D square lattice Ising model are reported. In particular, several alternate expressions for the integrands in (2n+1) are determined which greatly facilitate both the generation of high-temperature series and analytical analysis. One can show that as series, (2n+1) = 22n(s/2)4n(n+1)(1+O(s)) where s is the high-temperature variable sin(2K) with K the conventional normalized inverse temperature. Analysis of the integrals near symmetry points of the integrands shows that (2n+1)(s) is singular on the unit circle at sk = exp(ik) where 2cos(k) = cos(2 k/(2n+1))+cos(2/(2n+1)), -n k, n. The singularities, k = 0 excepted, are logarithmic branch points of order 2n(n+1)-1ln() with = 1-s/sk. There is numerical evidence from series that these van Hove points, in addition to the known points at s = ?1 and ?i, exhaust the singularities on the unit circle. Barring cancellation from extra (unobserved) singularities one can conclude that |s| = 1 is a natural boundary for the susceptibility.

Effect of van Hove singularities on a spin liquid.

We determine the properties and leading instabilities of a spin liquid with a Fermi surface passing near a van Hove singularity. Our study is motivated by recent photoemission experiments on high $T_c$ cuprates in which it is found that for the optimally doped material the experimental Fermi surface passes near a van Hove singularity, while for underdoped materials, a pseudogap in the electron spectral function is formed in the vicinity of the van Hove point. We show theoretically that proximity to the van Hove singularity suppresses the inelastic scattering due to the gauge field and permits the formation of a d-wave RVB state in which the gap exists only near the van Hove points while finite regions of the Fermi surface remain gapless. This $d$-wave pairing provides a natural explanation of the pseudogap observed in photoemission. We also discuss the relation of the pseudogap observed in the spectral function to the pseudogaps observed in the magnetic susceptibility.

Superconducting order parameter symmetry in multilayer cuprates.

We discuss the allowed order parameter symmetries in multi-layer cuprates and their physical consequences using highly non-specific forms of the inter- and intra-plane interactions. Within this framework, the bi-layer case is discussed in detail with particular attention paid to the role of small orthorhombic distortions as would derive from the chains in YBCO or superlattice effects in BSCCO. In the orthorhombic bi-layer case the (s,-s) state is of special interest, since for a wide range of parameters this state exhibits pi phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d_{x^2 - y^2}-like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d_{x^2 - y^2}-like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.

Superconductive states in the two-dimensional repulsive Hubbard model

The investigation of the two-dimensional repulsive Hubbard model is continued for the case in which the Fermi level is close to one of the saddle Van Hove points of the quasiparticle energy function. The Bethe-Salpeter equation for the two-particle scattering amplitude and the system of Dyson-Gor'kov equations for normal and anomalous Green functions are considered. The closeness of the Van Hove point to the Fermi level makes the investigation substantially simpler. A new method of evaluating the kernel of the equations, i.e., the oneloop polarization diagram, is suggested. It is shown that a nontrivial Cooper pairing (the superposition of the pairings with odd angular momenta) appears in the model if and only if the Fermi level is close to one of the Van Hove points. The temperature of the superconductive phase transition is maximal for some special mutual location of the Fermi level and the Van Hove point. Two different superconductive solutions (modes) are found which are antisymmetric functions in the momentum representation. These modes coexist in close vicinity of the doping parameter value corresponding to the intersection of the Van Hove point and the Fermi level. The values of the energy gap for these modes are, generally speaking, different (the two different gap values are observed in some experiments). Bibliography: 18 titles.

The superstructure effect on the superconducting phase diagrams and on the electron spectrum singularities near van Hove points

We propose a possible mechanism of the superstructure effect on an electron spectrum near its singular points. The two-dimensional electron spectrum of the tight-binding model and of the spin-polaron model, which describes the motion of a hole in CuO 2 planes, are considered. For the latter model we show, that the dependence of the superconducting transition temperature on the position of the Fermi level can have two maxima both near the bottom of the spin-polaron band and near its boundary. This dependence has also a discontinuity of slope near the magnetic Brillouin band boundary. The existence of a discontinuity as well as the presence of the maxima are caused by the electron spectra transformations under a long-wave perturbation.

Superconductive states with odd angular momentum pairing in the 2D repulsive Hubbard model

The earlier suggested superconductive state in the two-dimensional repulsive Hubbard model is investigated. Cooper pairing in this state arises due to an effective attraction of fermions in channels with odd angular momenta. It is shown that superconductivity can exist only if one of the Van Hove saddle points of the quasiparticle energy lies near the Fermi level. Equations are obtained for the phase transition curve and for the order parameter in the superconductive state. The optimal relative position of the Van Hove point and the Fermi level corresponding to the maximal critical temperature is found. It is argued that two superconductive modes with threefold spin degeneration and, in principle, with different values of the gap parameter can exist in the model under consideration.

Antiferromagnetism, ferromagnetism and superconductivity in the Hubbard model with repulsion

A study has been made, using Green's functions for temperature, of the Hubbard model with repulsive interaction. The existence is demonstrated of an antiferromagnetic state in the case of a half-filled zone. The existence of a superconducting state with p-pairing in the three-dimensional model is shown for low densities of electrons or holes. The highest superconducting transition temperature is reached in a two-dimensional model when the saddle point of the energy function (Van Hove point) is situated on the Fermi surface. The type of superconducting pairing can be called “superposition pairing with odd angular momenta” (to a first approximation this is p-pairing). The problem of competition between superconductivity and ferromagnetism is discussed. It is shown that superconductivity is favored for u/t ≳ 8.