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

Abstract

PACS 74.20. ÀZ, 71.28.þD, 74.20.Mn Penson-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 ¼ Q (h-phase), which can develop in this model for the case of repulsive J(J < 0). The evolutions of the phase diagrams, the critical temperatures and superfluid characteristics with particle concentration and pairing strength are discussed.General formulation The Penson-Kolb (PK) model is one of the conceptually simplest models for studying superconductivity of the narrow band systems with short coherence length [1][2][3][4][5]. The model Hamiltonian has the form:where n is ¼ c þ is c is ; t is the single electron hopping integral, J is the pair hopping (intersite charge exchange) interaction, m is the chemical potential, the limit hiji restricts the sum to nearest neighbors (nn).The model includes a nonlocal pairing mechanism (the pair hopping term J) that is distinct from the on-site interaction in the attractive Hubbard (AH) model and that is the driving force of pair formation and also of their condensation.In our recent work [2] we have studied thermodynamic and electromagnetic properties of the PK model in the case of attractive J(J > 0), which stabilizes s-wave pairing state (S) analogous to that driven by the on-site attraction in the AH model. Here, we focus on the case of repulsive J(J < 0), which favorizes the h-phase, i.e. superconducting state with Cooper-pair center of mass momentum As in Ref.[2] our analysis is based on the (broken symmetry) HFA and the linear response theory. The free energy of the h-phase F h is calculated to be:wherecos k a , a ¼ x; y; . . . ;J 0 ¼ zJ, z is the number of nn, b ¼ 1=k B T. The h-pairing order parameter x h ¼

Phase Diagrams of the Penson-Kolb-Hubbard Model with Repulsive Pair-Hopping Interaction

“…The electronic spectrum of the η-phase consists of two branches E [9,16,17], which is in contrast with the s-wave phase, where E g > 0 for any T < T c .…”

“…For more detailed discussion of these two η states see Ref. [9,[16][17][18]. In addition to the ground state phase boundaries, we denote in the figures the crossovers to the BEC regimes (dasheddotted lines).…”

“…also [2,[16][17][18]). This behaviour is in contrast with the properties of the isotropic s-wave state, which for U ≤ 0 is stable for any attractive J > 0, and the system exhibits a smooth crossover from the BCS-like limit to the BEC regime with increasing J [2,6,[19][20][21][22].…”

Ground State Phase Diagram of the Extended Hubbard Model with Pair-Hopping Interaction in the Limit of Very Narrow Bandwidth

“…Model (1) is a generalization of the Penson-Kolb model (e.g. [13][14][15][16]) to the case of U = 0.…”

Superconductivity in the Penson-Kolb Model on a Triangular Lattice

“…In such approach, the Coulomb repulsion leads to the repulsive pair hopping interaction J. However, the pair hopping integral may also be considered as the effective model parameter that takes on both positive and negative values [2][3][4]. In the case of a square lattice the superconducting correlations occur independently of the sign of J. Superconductivity that occurs for repulsive pair hopping interaction is usually referred to as η-type pairing.…”