BCS Model with Long Range Interaction

Richard M. Fye

We prove the existence of ground-state BCS off-diagonal long-range order (ODLRO) in a nontrivial interacting-electron model of dimension d=1. Somewhat surprisingly, the BCS ODLRO is induced here by a magnetic field. Our existence results extend to all dimensions (d\ensuremath{\ge}1) recent work that proved the existence of BCS ODLRO in nontrivial interacting-electron models for dimensions d\ensuremath{\ge}2.

Yu-Liang Liu, Tai Kai Ng

In this paper we study a model of s-wave marginal Fermi liquid superconductor at two dimensions. Besides the usual Bardeen-Cooper-Schrieffer(BCS) point attractive interaction, the fermions in our system also interact {\em via} a long range repulsive interaction $v(q)=g_{D}/q^2$. We find that although superconductivity is not destroyed by the long-ranged repulsion interaction (demonstrated by the existence of Meissner effect), nevertheless the BCS pairing function $Δ_{BCS}$ is strongly suppressed resulting in power-law correlation $\sim|\vec{x}|^{-2γ}$. This observation is explained within a general picture of marginal Fermi liquid.

I. A. Bernadskii, R. A. Minlos

Emmanuel Buffet, Philippe A. Martin

Yu-Liang Liu, Tai Kai Ng

In this paper we study a model of an $s$-wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction $v(q){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{D}/{q}^{2}$. We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function ${\ensuremath{\Delta}}_{\mathrm{BCS}}$ is strongly suppressed, resulting in a power-law correlation $〈{\ensuremath{\Delta}}_{\mathrm{BCS}}(\stackrel{\ensuremath{\rightarrow}}{x}){\ensuremath{\Delta}}_{\mathrm{BCS}}(0)〉\ensuremath{\sim}|\stackrel{\ensuremath{\rightarrow}}{x}{|}^{\ensuremath{-}2\ensuremath{\gamma}}$. This observation is explained within a general picture of the marginal Fermi liquid.