The “pair” Fermi contour and high-temperature superconductivity

Superconducting pairing of holes with a large (on the order of doubled Fermi) total pair momentum and small relative motion momenta is considered taking into account the quasi-two-dimensional electronic structure of high-T _c cuprates with clearly defined nesting of the Fermi contour situated in an extended neighborhood of the saddle point of the electronic dispersion law (the momentum space region with a hyperbolic metric) and the arising of a spatially inhomogeneous (stripe) structure as a result of the redistribution of current carriers (holes) that restores regions with antiferromagnetic ordering. The superconducting energy gap and condensation energy were determined, and their dependences on the doping level were qualitatively studied. The energy gap was shown to exist in some hole concentration region limited on both sides. The superconducting state with a positive condensation energy appears in a narrower range of doping within this region. The reason for the arising of the superconducting state at a repulsive screened Coulomb interaction between holes is largely the redistribution of hole pairs in the momentum space related to the special features of the hyperbolic metric, which is responsible for the formation of the “pair” Fermi contour, and the renormalization of the kinetic energy of holes when the chemical potential changes because of the condensation of pairs. Hole pairs of the type under consideration exist not only in the condensate but also in the form of quasi-stationary states with very weak decay at temperatures substantially exceeding the superconducting transition temperature. The pseudogap region of the phase diagram of high-T _c cuprates is related to such states. The pairing mechanism under consideration allows not only the principal characteristics of the phase diagram but also key experimental data on high-T _c cuprate materials to be qualitatively explained.     

Mirror nesting of the Fermi contour and zero line of the superconducting order parameter

The superconducting order parameter that emerges owing to pairing of charge carriers with a large total momentum of the pair during screened Coulomb repulsion in a degenerate quasi-two-dimensional electronic system is determined as a function of the momentum of relative motion of the pair. In view of the kinematic constraint associated with Fermi filling, the ordered state exists in a limited domain of the momentum space, the shape and size of this domain being determined by the total momentum of the pair. The order parameter is not a constant-sign function of the momentum and reverses its sign on a certain line in a kinematically allowed domain. Superconducting instability arises for an arbitrarily small value of the repulsive interaction for certain momenta of the pair, for which the mirror nesting condition is satisfied; this results in the formation of a pair Fermi contour, i.e., the line of coincidence of segments of the Fermi contour with the isoline of the kinetic energy of relative motion of the pair. The temperature dependence of the superconducting order parameter is studied. Owing to the proximity effect in the momentum space, superconducting ordering is extended to the kinematically forbidden domain.     

Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

It has been shown that the strong coupling model taking into account a rise in the spin antiferromagnetic insulating state explains the doping dependence of the topology and shape of the Fermi contour of superconducting cuprates. Hole pockets with shadow bands in the second Brillouin zone form the Fermi contour with perfect ordinary and mirror nesting, which ensures the coexistence of orbital antiferromagnetism and superconductivity with a large pair momentum for T < T_C. The weak pseudogap region (T_* < T < T*) corresponds to the orbital antiferromagnetic ordering, which coexists with the incoherent state of superconducting pairs with large momenta in the strong pseudogap region (T_C < T < T_*).     

Coulomb pairing of like-charged particles with negative effective mass in high-temperature superconductors

Quasi-steady states of pairs of like-charged quasi-particles can be formed because the electronic structure of compounds exhibiting high-temperature superconductivity has various important characteristics: a quasi-two-dimensional electron spectrum, clearly defined nesting of constant-energy lines, and the presence of a logarithmic singularity of the density of states in the immediate vicinity of the Fermi level. Thus, a situation is achieved where, in an extensive region of the Brillouin zone adjacent to the Fermi level, the principal values of the tensor of the reciprocal effective masses have opposite signs and differ appreciably in absolute value. As a result, the nature of the Coulomb correlation interaction between charge carriers of the same sign (holes in p-cuprates) varies: effective attraction may predominate, leading to the formation of long-lived states of relative motion of quasi-particles which form a pair having a quasi-momentum approximately equal to twice the Fermi quasi-momentum typical of this direction (focused pairs). Assuming that the correlation interaction is short-range (screened Coulomb interaction attenuated by filling of states inside the Fermi contour), we determine the energies and envelope functions of the relative motion of a hole pair which correspond to the density-of-states maxima of the pairs attributable to these quasi-steady states. The dependence of these quantities on the polar angle in the plane of the conducting layer reflects the symmetry of the electronic structure of the compound in the normal state and is generally consistent with a mixture of states assigned to s and d types of orbital symmetry. The quasi-steady state as a function of the doping level of the system agrees qualitatively with the concentration dependence of the temperature for the appearance of a pseudogap observed in p-cuprates at below-optimum doping levels. An estimate of the pair concentration above which a gain in correlation energy occurs gives a value which corresponds to the onset of effective pair overlap (for which the characteristic spatial scale is a few or a few tens of interatomic distances).     

Pair-density-wave pseudogap and superconducting states in cuprates

Bogoliubov quasiparticle interference and localized high-energy excitations observed in cuprates in nodal and antinodal regions of the momentum space, respectively, would lead to a conclusion that only the nodal region might give rise to superconductivity whereas the antinodal one might be associated with the pseudogap. We argue that both pseudogap and superconducting states arise exactly in the antinodal region with pronounced nesting feature of the Fermi contour as spatially inhomogeneous incoherent and coherent states of pairs with large momentum. The nodal region gives rise to conventional superconducting pairing with zero momentum which, together with the pairing with large momentum in the antinodal region, forms a biordered superconducting state in the whole of the Brillouin zone. This coherent state with complicated momentum dependence of the order parameter manifests itself as a pair-density wave that can exist without any driving insulating order. We believe that quasiparticle interference, other than observed in the nodal region, should be observable in the antinodal region as well.     

Mirror nesting: A superconducting pairing of carriers with a large momentum

The coincidence of Fermi contour portions with isolines of zero kinetic energy of the relative pair motion (the pair Fermi contour) is a necessary condition for superconducting pairing of carriers with a large total pair momentum. In high?T _c cuprates, this situation can occur either due to the formation of a stripe structure or in the absence of the stripe structure when the Fermi contour satisfies the mirror nesting condition. A gradual deviation from this condition leads to a decrease in the superconducting energy gap to zero.     

Mirror nesting and electron-hole asymmetry at repulsive superconducting pairing

The dependence of the superconducting order parameter Δ(k) on the momentum of the relative motion of a pair with a large total momentum K is numerically studied for the case of repulsive pairing with allowance for the kinematic and insulator constraints on the momentum transfer at scattering. The Fermi contour with nesting and mirror nesting, which is typical of cuprates and optimal for repulsion-induced superconductivity, lies in an extended vicinity of the saddle points of the dispersion law. A deviation from the mirror nesting cuts off the logarithmic singularity from below and bounds the pre-exponent in Δ(k). The effective coupling constant is determined by the degree of the electron-hole asymmetry. The suppression of the contribution of small momentum transfer processes by the impurity and electron-phonon scattering favors an increase in the order parameter amplitude. The nesting of the Fermi contour causes a Peierls singularity in the Coulomb interaction. The self-consistency equation allows the solutions that may be both antisymmetric and symmetric with respect to the momentum inversion. The maximum-amplitude antisymmetric solution in the case of a singlet pairing can be realized only for K ≠ 0.     

Insulating in-plane modulation induced superconductivity of heterostructures

Superconductivity of artificial two-dimensional insulator-metal heterostructure composed of two non-superconducting monolayers is explained by a renormalization of the electron spectrum of the metal layer due to inter-layer electron-hole pairing. Charge or charge current density wave in the insulating monolayer restores mirror nesting feature of the Fermi contour in the metal one that results in a rise of in-plane superconducting ordering with large momentum.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

Crossover from a pseudogap state to a superconducting state

This paper deduces that the particular electronic structure of cuprate superconductors confines Cooper pairs to be first formed in the antinodal region which is far from the Fermi surface,and these pairs are incoherent and result in the pseudogap state.With the change of doping or temperature,some pairs are formed in the nodal region which locates the Fermi surface,and these pairs are coherent and lead to superconductivity.Thus the coexistence of the pseudogap and the superconducting gap is explained when the two kinds of gaps are not all on the Fermi surface.It also shows that the symmetry of the pseudogap and the superconducting gap are determined by the electronic structure,and non-s wave symmetry gap favours the high-temperature superconductivity.Why the high-temperature superconductivity occurs in the metal region near the Mott metal-insulator transition is also explained.     

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.     

Lifetime analysis of quasibound states in coupled quantum wells

A simple time-dependent model is presented to investigate lifetimes of the quasibound states in coupled quantum wells (CQWs). The transfer matrix approach is employed to discretize the conduction-band profile of the heterostructure and form a dispersion equation whose zeros correspond to the complex eigenenergies. Both the bound and quasibound states are extracted numerically in the complex plane by Newton's method. The lower and higher well subbands are found to have negative and positive energy shift, respectively, as following the no level crossing theorem. Besides, the decay rate of the quasibound state is approximately proportional to the absolute energy shift. The quasibound states, which have larger energy shift, have shorter lifetime and decay more quickly. Furthermore, the differences in lifetime between the quasibound states in CQWs can be easily realized as all the wave functions are specially adjusted to form the relative probability density distributions.     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.     

Interplay among superconductivity,charge density waves,and magnetism in EuMo6S8

In a one-dimensional metal, the energy of the electrons can always be lowered by opening an energy gap around the Fermi energy (the Peierls instability): all occupied states are then in the lower-energy band, while the higher-energy band is empty. The opening of such a gap requires a structural distortion, resulting in the formation of a charge density wave. In a three-dimensional system, the gapping takes place in the region where the Fermi surface is nested (i.e., large parallel areas of the Fermi surface are spanned by a certain wave vector), giving rise to partial gapping of the Fermi surface, accompanied by a structural distortion. In this case, a charge density wave can coexist with superconductivity. Both charge-density-wave and superconducting transitions involve the formation of an energy gap at the Fermi energy. A charge-density-wave gap is formed at a region of the Fermi surface where there is a high density of electronic states. In such a material, there is also a strong electronphonon interaction. A region with high density of states and a high electron-phonon interaction is just the portion of the Fermi surface that will enhance the superconducting transition temperature, according to the BCS (Bardeen-Cooper-Schrieffer) theory. When a charge-density-wave gap opens up at the Fermi surface these electronic states are no longer available to form Cooper pairs and to enhance the superconducting transition temperature. The opposite is also true; if a superconducting gap opens, the states involved in forming this gap are no longer available to take part in a charge-density-wave transition. It appears that charge density waves and superconductivity compete for the same portion of the Fermi surface and thus inhibit each other. In this paper, we will review a unique situation with respect to the competition between these two ground states and will also discuss how this competition affects the anomalous behavior of critical field in EuMo6S, at high pressure.     

Single-particle spectral function of the Hubbard chain: frustration induced

The one-electron spectral function of a frustrated Hubbard chain is computed by making use of the cluster perturbation theory. The spectral weight we found turns out to be strongly dependent on the frustrating next-nearest-neighbor hopping t'. A frustration induced pseudogap arises when the system evolves from a gapful Mott insulator to a gapless conductor for an intermediate value of the frustration parameter |t'|. Furthermore, the opening of a pseudogap in the density of states already in the metallic side leads to a continuous opening of the true gap in the insulator. For the hole-doped case, the pseudogap is pinned at the Fermi energy, while the Mott gap is shifted in energy with increasing Hubbard interaction U. The separation of the pseudogap and Mott gap in the hole-doped system demonstrates the validity of the existence of a pseudogap.     

Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by an Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.     

The origin of the pseudogap in α-Ga

Density functional theory, the free-electron empty lattice approximation and the nearly free-electron approximation are employed to investigate the electronic properties of partially covalent α-Ga. Whereas free-electron-like properties are revealed over a large energy range, a deep pseudogap at the Fermi level is characteristic of α-Ga. We explain the origin of the pseudogap in terms of a delicate interplay between the electronic states and the specific Brillouin zone geometry.