In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center-of-mass momentum. This is indeed enforced by self-consistency if the pairing interaction is momentum independent. Here, we show that for an attractive nearest-neighbor interaction, this is different. In this case, stable solutions with pairs with momenta $\mathbf{q}$ and $\ensuremath{-}\mathbf{q}$ coexist and, for a sufficiently strong interaction, one of these states becomes the ground state of the superconductor. The possibility for a finite-momentum pairing state emerges only for nodal superconductors and is accompanied by a charge order with wave vector $2\mathbf{q}$ . For a weak pairing interaction, the ground state is a $d$ -wave superconductor.In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center-of-mass momentum. This is indeed enforced by self-consistency if the pairing interaction is momentum independent. Here, we show that for an attractive nearest-neighbor interaction, this is different. In this case, stable solutions with pairs with momenta $\mathbf{q}$ and $\ensuremath{-}\mathbf{q}$ coexist and, for a sufficiently strong interaction, one of these states becomes the ground state of the superconductor. The possibility for a finite-momentum pairing state emerges only for nodal superconductors and is accompanied by a charge order with wave vector $2\mathbf{q}$. For a weak pairing interaction, the ground state is a $d$-wave superconductor.

arXiv:0907.4345Physical Review BJan 28, 201057 citations

The Generalized Bogolyubov-Valatin Transformation of Neutron and Proton System

Y. Takahashi

The charge independent pairing interaction in the system of neutron and proton with many j-configurations is studied using the five-dimensional quasispin formalism, and the generalized BCS the9ry is obtained as a natural generalization of the BCS theory of identical nucleon system.It is shown that a rotation in the five-dimensional quasispin space can be regarded as the generalized Bogolyubov-Valatin transformation in our generalized BCS theory.The normalized BCS ground state and the solutions of the BCS equations for several models are explicitly given in analogy to the case of identical nucleon system.*> The phase of the modified annihilation operator has been taken to be the same as that of Ichimura.The charge independent pairing interaction in the system of neutron and proton with many j-configurations is studied using the five-dimensional quasispin formalism, and the generalized BCS the9ry is obtained as a natural generalization of the BCS theory of identical nucleon system.It is shown that a rotation in the five-dimensional quasispin space can be regarded as the generalized Bogolyubov-Valatin transformation in our generalized BCS theory.The normalized BCS ground state and the solutions of the BCS equations for several models are explicitly given in analogy to the case of identical nucleon system.*> The phase of the modified annihilation operator has been taken to be the same as that of Ichimura.

Progress of Theoretical PhysicsDec 1, 19718 citations

The BCS Functional for General Pair Interactions

Christian Hainzl, Eman Hamza, Robert Seiringer +1 more

arXiv:math-ph/0703086Communications in Mathematical PhysicsApr 30, 200860 citations

Pseudogap phenomena in the BCS pairing model

Satoshi Fujimoto

arXiv:cond-mat/0201380Physica C SuperconductivityMay 1, 20030 citations

Mesoscopic BCS pairing in the repulsive one-dimensional Hubbard model

Luigi Amico A, Andrea Mastellone, Andreas Osterloh

We study mesoscopic pairing in the one-dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper pairs form a noncondensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.We study mesoscopic pairing in the one-dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper pairs form a noncondensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.

arXiv:cond-mat/0509554Physical Review BJun 13, 20063 citations

\mathbf{q}

and $\ensuremath{-}\mathbf{q}$ coexist and, for a sufficiently strong interaction, one of these states becomes the ground state of the superconductor. The possibility for a finite-momentum pairing state emerges only for nodal superconductors and is accompanied by a charge order with wave vector

2\mathbf{q}

. For a weak pairing interaction, the ground state is a

d

-wave superconductor.