Penson-Kolb Model Research Articles

Thermodynamic and electromagnetic properties of the eta-pairing superconductivity in the Penson–Kolb model

In the paper, we study the thermodynamic and electromagnetic properties of the Penson–Kolb (PK) model, i.e., the tight-binding model for fermionic particles with the pair-hopping interaction J. We focus on the case of repulsive J (i.e., J<0), which can stabilize the eta-pairing superconductivity with Cooper-pair center-of-mass momentum q→=Q→, Q→=(π/a,π/a,…). Numerical calculations are performed for several d-dimensional hypercubic lattices: d=2 (the square lattice, SQ), d=3 (the simple cubic lattice) and d=∞ hypercubic lattice (for arbitrary particle concentration 0<n<2 and temperature T). The ground state J versus n phase diagrams and the crossover to the Bose–Einstein condensation regime are analyzed and the evolution of the superfluid characteristics are examined within the (broken symmetry) Hartree–Fock approximation (HFA). The critical fields, the coherence length, the London penetration depth, and the Ginzburg ratio are determined at T=0 and T>0 as a function of n and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz–Thouless scenario, the critical temperatures TKT are estimated for d=2 SQ lattice and compared with the critical temperature Tc obtained from HFA. We also determine the temperature Tm at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive J are contrasted with those found earlier for the PK model with attractive J (i.e., with J>0).

Superconductivity in the Penson-Kolb Model on a Triangular Lattice

We investigate properties of the two-dimensional Penson{Kolb model with repulsive pair hopping interaction. In the case of a bipartite square lattice this interaction may lead to the ·-type pairing, when the phase of superconducting order parameter changes from one lattice site to the neighboring one. We show that this interaction may be responsible for the onset of superconductivity also for a triangular lattice. We discuss the spatial dependence of the superconducting order parameter and demonstrate that the total momentum of the paired electrons is determined by the lattice geometry.

Eta‐pairing and s‐wave pairing in the Penson–Kolb model with next‐nearest neighbour hopping

AbstractWe study the two‐dimensional Penson–Kolb model, i.e the tight‐binding model with the pair‐hopping interaction J, and analyze the effects of next‐nearest neighbour hopping t2 on the superconductivity in this system. In the analysis we focus on the properties of the superconducting state with Cooper‐pair center‐of‐mass momentum q = Q (eta‐phase), which can develop in this model for the case of repulsive J (J &lt; 0) and q = 0 (s‐wave phase), which develops for the case of attractive J (J &gt; 0). The evolutions of the phase diagrams, ground state characteristics and the transition temperatures with particle concentration and pairing strength are determined for square lattice. Within the Kosterlitz–Thouless scenario the Uemura‐type plots (Tc vs. 1/λ2(0)) are also derived. The results for t2 ≠ 0 are compared with those found for the case with nn hopping only. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Effect of Fibonacci modulation on superconductivity

We have studied finite-sized single band models with short-range pairing interactionsbetween electrons in the presence of diagonal Fibonacci modulation in one dimension. Twomodels, namely the attractive Hubbard model and the Penson–Kolb model, have beeninvestigated at half-filling at zero temperature by solving the Bogoliubov–de Gennesequations in real space within a mean-field approximation. The competition between‘disorder’ and the pairing interaction leads to a suppression of superconductivity (of usualpairs with zero centre-of-mass momenta) in the strong-coupling limit while an enhancementof the pairing correlation is observed in the weak-coupling regime for both models.However, the dissimilarity of the pairing mechanisms in these two models brings aboutnotable differences in the results. The extent to which the bond-ordered wave and theη-paired (of pairswith centre-of-mass momenta = π) phases of the Penson–Kolb model are affected by the disorder has also been studied in thepresent calculation. Some finite size effects are also identified.

A Rigorous Investigation on the Ground State of the Penson–Kolb Model**The project partially supported by the Special Funds for Major State Basic Research Projects (G20000365) and National Natural Science Foundation of China under Grant No. 10174002

By using either numerical calculations or analytical methods, such as the bosonization technique, the ground state of the Penson–Kolb model has been previously studied by several groups. Some physicists argued that, as far as the existence of superconductivity in this model is concerned, it is canonically equivalent to the negative-U Hubbard model. However, others did not agree. In the present paper, we shall investigate this model by an independent and rigorous approach. We show that the ground state of the Penson–Kolb model is nondegenerate and has a nonvanishing overlap with the ground state of the negative-U Hubbard model. Furthermore, we also show that the ground states of both the models have the same good quantum numbers and may have superconducting long-range order at the same momentum q = 0. Our results support the equivalence between these models.

Properties of the η‐pairing phase of the Penson–Kolb model

AbstractPenson–Kolb model, i.e. the tight‐binding model with the pair‐hopping (intersite charge exchange) interaction J is considered. In the analysis we focus on the properties of the superconducting state with Cooper‐pair center‐of‐mass momentum q = Q (η‐phase), which can develop in this model for the case of repulsive J(J &lt; 0). The evolutions of the phase diagrams, the critical temperatures and superfluid characteristics with particle concentration and pairing strength are discussed.

Superconductivity of the Two-Dimensional Penson-Kolb Model

Two-dimensional (d = 2) Penson-Kolb model, i.e. the tight-binding model with the pair-hopping (intersite charge exchange) interaction, is considered and the effects of phase fluctuations on the s-wave superconductivity ofthis system are discussed within the Kosterlitz-Thouless scenario. The London penetration depth A at T = 0, the Kosterlitz-Thouless critical temperature T c , and the Hartree-Fock approximation critical temperature Tp are determined as a function of particle concentration and interaction. The Uemura type plots (T c vs. λ - 2 (0)) are derived. Beyond weak coupling and for low concentrations they show the existence of universal scaling: T c ∼ 1/λ 2 (0), as it was previously found for the attractive Hubbard model and for the models with intersite electron pairing.

Thermodynamic and electromagnetic properties of the Penson-Kolb model

Thermodynamic and electromagnetic properties of the Penson-Kolb model

Superconducting Characteristics of the Penson-Kolb Model

We study superconducting properties of the Penson—Kolb model, i.e. the tight-binding model with the pair-hopping ( inters ite charge exchange) interaction J. The evolution of the critical fields, the coherence length, the Ginzburg ratio, and the London penetration depth with particle concentration n and pairing strength are determined. The results are compared with those found earlier for the attractive Hubbard model.

Collective excitations in the Penson-Kolb model: A generalized random-phase-approximation study

The evolution of the superconducting ground state of the half-filled Penson-Kolb model is examined as a function of the coupling constant using a mean-field approach and the generalized random phase approximation (RPA) in two and three dimensions. On-site singlet pairs hop to compete against single-particle motion in this model, giving the coupling constant a strong momentum dependence. There is a pronounced bandwidth enhancement effect that converges smoothly to a finite value in the strong-coupling (Bose) regime. The low-lying collective excitations evaluated in generalized RPA show a linear dispersion and a gradual crossover from the weak-coupling (BCS) limit to the Bose regime; the mode velocity increases monotonically in sharp contrast to the attractive Hubbard model. Analytical results are derived in the asymptotic limits. {copyright} {ital 1997} {ital The American Physical Society}

η-superconductivity in the one-dimensional Penson-Kolb model

Using exact Lanczos diagonalizations we have shown that the pair-hopping model for {\it negative} $W$ exhibits a phase transition into $\eta$-{\it superconducting state}. The transition occurs at {\it any band filling} and the critical value $W_{c}$ varies between $W_{c} \simeq -1.75t$ at half-filling to $W_{c} \simeq -2t$ for two particles on the lattice.

Ground-state instabilities in the one-dimensional Penson-Kolb-Hubbard model.

Different kinds of instabilities (CDW, SDW, SS) in the 1D Hubbard model with pair-hopping interaction are investigated using an approximate Bethe-Salpeter equation. The study is performed at any density of electrons and for arbitrary values of the model parameters. In the absence of the on-site interaction, no transition occurs at half filling for any finite negative pair-hopping parameter, in agreement with recent results; our calculation suggests that the Penson-Kolb model (t,W) with $\mid W/t\mid<\pi/\sin k^{}_F$ behaves qualitatively like the Hubbard model (t,U). Phase diagrams of the Penson-Kolb-Hubbard model (t,U,W) at various densities are presented.