Chih-Chun Chien, Qijin Chen, Yan He, Kathryn Levin
We present results for the transition temperature $T_c$ as afunction of the hopping $t$ and inter-site attraction $U$and filling $n$,where $0 \leq n \leq 1$, in the attractiveHubbard model. As expected, at small $n$ we find $T_c \approxt^2 / |U|$ in the strong coupling regime. However, at larger$n$ we find a novel phase (for sufficiently strong attraction)associated with a localization of the Cooper pairs. Thisinsulating rather than superfluid ground state arises becausepairs cannot readily hop due to Pauli principle repulsion inthe presence of large $n$. Our theory is based on a selfconsistent pairing fluctuation scheme which addresses BCS-BECcrossover on a lattice. This T-matrix approach can becalibrated by noting that unlike alternatives in theliterature it leads to a consistent behavior for thesuperfluid density $n_s/m$ from $T=0$ to $T=T_c$. [Othercrossover schemes lead to first order transitions at $T_c$ ormulti-valued $n_s/m$]. Finally, we speculate that the novelinsulating phase may beassociated with \"pair density wave\" order which has beenconjectured to be present in the pseudogap state (when $T_c$vanishes) of the copper oxide superconductors.
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