Yu. V. Kopaev

Hyperbolic pairing and stripes in high-temperature superconductors

Abstract We suggest that pairing of holes in high-TC cuprates is directly related to special features of the electronic structure of such quasi-two-dimensional compounds, namely, strong nesting of the Fermi contour situated in extended flat-band vicinity of saddle points of electron dispersion and specific spatial stripe hole self-organization partly restoring antiferromagnetic ordering. Due to hyperbolic metrics of k-space, the relative motion of a pair with large momentum may result in a rise of both quasi-stationary states which explains a pseudogap in the quasiparticle spectrum and a condensate of pairs corresponding to the superconducting state with the condensation being mainly driven by kinetic energy of carriers. Repulsion-induced hyperbolic pairing conception allows one to explain qualitatively some fundamental features of high-TC cuprates.

Phase separation and dielectric correlations in HTSC

Abstract A general description of the phase separation (PS) in HTSC is presented based on a concept of “soft” dielectric ordering with respect to the addition of collectivized charge carriers. The possibility of the PS crucially depends on the properties of the screening ion subsystem. The interaction of electron and ion subsystems determines a large variety of manifestations of the PS under different experimental conditions. It is shown that the assumption of the existence of the PS makes it possible to explain on common grounds a number of experiments on different HTSC, which seem to be quite separate from each other, such as anomalous magnetoresistance at T T c in Ba 1- x K x BiO 3 , the appearance of midgap states in cuprate HTSC, the existence of two plateaus in the dependence of T c on composition x in YBa 2 Cu 3 O 6+ x , the appearence of photoinduced superconductivity in yttrium superconductors and others.

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.

Momentum dependence of the dimensionality of the electronic states in heterostructures

Bound states of electrons (holes) in quantum wells and wires with asymmetric barriers can exist in bounded regions of two-and one-dimensional momentum space, respectively. As the corresponding momentum increases, both the disappearance (increase of dimensionality) and appearance (decrease of dimensionality) of bound states as well as the existence of a sequence of several such transformations of dimensionality are possible. In the case of anisotropic effective masses in the quantum wells and barriers, the forms of the lines of disappearance and appearance of bound states are different from the forms of the isoenergy lines. Therefore there is a finite energy interval (i.e., electron density interval) where bound states exist on only a part of an isoenergy line. The dimensionality of the states can be controlled with an electric field; this should be observable in a number of the experiments discussed.

High-frequency response and the possibilities of frequency-tunable narrow-band terahertz amplification in resonant tunneling nanostructures

The characteristics of the high-frequency response of single- and double-well resonant tunneling structures in a dc electric field are investigated on the basis of the numerical solution of a time-dependent Schrödinger equation with open boundary conditions. The frequency dependence of the real part of high frequency conductivity (high-frequency response) in In0.53Ga0.47As/AlAs/InP structures is analyzed in detail for various values of the dc voltage Vdc in the negative differential resistance (NDR) region. It is shown that double-well three-barrier structures are promising for the design of terahertz-band oscillators. The presence of two resonant states with close energies in such structures leads to a resonant (in frequency) response whose frequency is determined by the energy difference between these levels and can be controlled by varying the parameters of the structure. It is shown that, in principle, such structures admit narrow-band amplification, tuning of the amplification frequency, and a fine control of the amplification (oscillation) frequency in a wide range of terahertz frequencies by varying a dc electric voltage applied to the structure. Starting from a certain width of the central intermediate barrier in double-well structures, one can observe a collapse of resonances, where the structure behaves like a single-well system. This phenomenon imposes a lower limit on the oscillation frequency in three-barrier resonant tunneling structures.

Biordered superconductivity and strong pseudogap state

Interrelation between the two-particle and mean-field problems is used to describe the strong pseudogap and superconducting states in cuprates. We present strong pseudogap state as off-diagonal short-range order (ODSRO) originating from quasi-stationary states of the pair of repulsing particles with large total momentum (K - pair). Phase transition from the ODSRO state into the off-diagonal long-range ordered (ODLRO) superconducting state is associated with Bose-Einstein condensation of the K - pairs. A checkerboard spatial order observable in the superconducting state in the cuprates is explained by a rise of the K - pair density wave. A competition between the ODSRO and ODLRO states leads to the phase diagram typical of the cuprates. Biordered superconducting state of coexisting condensates of Cooper pairs with zero momentum and K - pairs explains some properties of the cuprates observed below Tc: Drude optical conductivity, unconventional isotope effect and two-gap quasiparticle spectrum with essentially different energy scales.

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.

The pseudogap mode as long-lived states of noncoherent pairs with large momenta

The mirror nesting of the Fermi contour of a quasi-two-dimensional electronic system and the presence of at least one negative eigenvalue of the Fourier transform of interaction energy are sufficient conditions for the formation of bound states of the relative motion of pairs with large total momenta. As distinct from pairing by attractive interactions, the wave functions of such pairs have alternating signs and lines of zeros that twice intersect the Fermi contour in the regions of definition of relative motion momenta. The total number of intersection points between the line of zeros and the Fermi contour is determined by symmetry of a linear combination of the wave functions of crystallographically equivalent pairs. Long-lived quasi-stationary states exist in the form of noncoherent pairs with different but close momenta and cause substantial suppression of the density of one-particle states (the appearance of a pseudogap) over a fairly wide energy range. The upper tempereture bound of the pseudogap is determined by the decay of pairs, and the lower bound, by phase coherence disturbance when pairs leave the condensate that is formed at some optimum pair momentum value owing to mirror nesting.

Mirror Nesting of the Fermi Contour and Superconducting Pairing from the Repulsive Interaction

We consider the necessary conditions of superconducting pairing at repulsive interaction between particles composing a pair with large total momentum: (1) the existence of, at least, one negative eigenvalue of the repulsion potential and (2) mirror nesting of the Fermi contour. Under these conditions, we represent the solution of the self-consistency equation continuously depending on the momentum of the relative motion of the pair. The corresponding superconducting order parameter changes its sign on a line crossing the Fermi contour inside the domain of definition of the relative motion pair momentum. We argue that repulsive-induced superconducting pairing with large total pair momentum maybe just the case relating to high-temperature superconducting cuprates.

Stark ladder laser with a coherent electron subsystem

A theory of generation in a two-subband “Stark ladder” with a coherent electron subsystem is developed. In the proposed model, electrons reach the upper level of a quantum well due to resonant tunneling and pass to the lower level of the well (vertical transitions), emitting a photon ℏω, then tunnel resonantly to the upper level of a neighboring well, performing a radiative transition, and so on until electrons leave the lower level of the last well. A static electric field applied to the superlattice shifts the levels so that the lower level of the nth well coincides with the upper level of the (n+1)th well. Analytic expressions are derived for the wave functions and polarization currents of an N-well structure. The possibility of bulk oscillation of the N-well structure in the optimal mode with an efficiency close to unity, weak reflection, and a linear dependence of the power on the pumping current is demonstrated. The total generation power is proportional to the number of wells. For structures with an even number of wells, the energy of electrons from the emitter must simply coincide with the resonance energy for any laser fields; i.e., the energy tuning which is necessary in a single-well structure is not required. Universal relations are derived for parameters of the N-well structure, which ensure the simultaneous fulfillment of resonance conditions in all the wells. The possibility of coherent lasing in a one-subband Stark ladder with a lower gain is also indicated.