Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of impenetrable electrons is shown to expose a positive charge, resulting in an effective mutual attraction of infinite range. As a result, all electrons are involved in the long-range pairing. A model of spinless fermions with infinitesimal attraction of infinite range is proposed to describe the excitation spectrum and the superconducting gap in low-density 1D electron channels. In contrast with the conventional theory, the energy gap does not contain exponentially small factors. It depends mostly on the Coulombic parameters of the system, which guides practical aspects of high-temperature superconductivity.
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of impenetrable electrons is shown to expose a positive charge, resulting in an effective mutual attraction of infinite range. As a result, all electrons are involved in the long-range pairing. A model of spinless fermions with infinitesimal attraction of infinite range is proposed to describe the excitation spectrum and the superconducting gap in low-density 1D electron channels. In contrast with the conventional theory, the energy gap does not contain exponentially small factors. It depends mostly on the Coulombic parameters of the system, which guides practical aspects of high-temperature superconductivity.
An electronic Hubbard-type model with bond-charge interaction and on-site repulsion U is studied in one and two dimensions. Evidence is provided in favor of superconductivity, without phase separation, for UUc(n), although no explicit attraction between particles is present in the Hamiltonian. The presence of a bound state for two particles in vacuum in D=1 and 2 (but not for D=3) suggests that, at low density and low dimensionality, superconductivity is due to condensation of preexistent pairs (dimers). The one-dimensional (1D) phase diagram is studied analytically as well as numerically and shows a transiiton between a Luttinger liquid and a strong-coupling phase with diverging superconducting susceptibility. Estimates of critical exponents are given at low density and at quarter filling for several values of the parameters. The 2D model at quarter filling is analyzed by Lanczos diagonalization on a 4\ifmmode\times\else\texttimes\fi{}4 cluster. The numerical results are consistent with the phase diagram obtained by BCS mean-field theory and is qualitatively similar to the 1D case: a ground state with spin gap and off-diagonal long-range order at UUc(n); and a Fermi liquid above Uc with no sign of phase separation.
In this letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range Rs that is much greater than the Fermi wavelength λF breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature Tc versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal Tc∗∼0.1EF on the interaction range at Rs≫λF, EF is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
In this Letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range R_{s} that is much greater than the Fermi wavelength λ_{F} breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature T_{c} versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal T_{c}^{*}∼0.1E_{F} on the interaction range at R_{s}≫λ_{F}, E_{F} is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles.
We consider possible superconducting instabilities in a two-dimensional Fermi system with short-ranged repulsive interactions between electrons. The possibility of an unusual superconducting paring due to the Kohn-Luttinger mechanism is examined. The quasiparticle scattering amplitude is shown to possess an attractive harmonic in second-order perturbation theory for finite values of the energy transfer. The corresponding singularity in the pairing vertex leads to a superconducting pairing of the electron excitations with finite energies. We identify the energy transfer in the Cooper channel as the binding energy of the excited pair. At low enough temperatures, the Fermi system is a mixture of normal electron excitations and fluctuating d-wave Cooper pairs possessing a finite gap.
One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.