Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models.

Abstract

Based on extensions of quantum Monte Carlo algorithms to incorporate magnetic fields, two criteria to detect superconductivity in two-dimensional Hubbard models are investigated. In order to provide such criteria, we calculate both the internal energy E(\ensuremath{\Phi},T) as well as the ground-state energy, ${\mathit{E}}_{0}$(\ensuremath{\Phi}), for Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. The temperature derivative of the superfluid density, \ensuremath{\partial}\ensuremath{\beta}${\mathit{D}}_{\mathit{s}}$(\ensuremath{\beta})/\ensuremath{\partial}\ensuremath{\beta}, is obtained from the difference in internal energy of systems which differ by a phase twist \ensuremath{\pi}/2 in the boundary condition along one lattice direction. In the framework of a Kosterlitz-Thouless transition, \ensuremath{\partial}\ensuremath{\beta}${\mathit{D}}_{\mathit{x}}$(\ensuremath{\beta})/\ensuremath{\partial}\ensuremath{\beta} scales to a Dirac \ensuremath{\delta} function at the transition temperature. On finite-sized lattices, \ensuremath{\partial}\ensuremath{\beta}${\mathit{D}}_{\mathit{s}}$(\ensuremath{\beta})/\ensuremath{\partial}\ensuremath{\beta} shows a response which increases with lattice size. Flux quantization is a T=0 method. From the functional form of ${\mathit{E}}_{0}$(\ensuremath{\Phi}), superconducting or nonsuperconducting ground states may be identified. In both approaches, superconductivity may be detected without prior knowledge of the symmetry and nature of the pairing correlations. For single-band Hubbard models, our main quantum Monte Carlo results include numerical data which (a) confirm the existence and pin down the transition temperature of a Kosterlitz-Thouless-type transition in the attractive Hubbard model away from half-band filling and (b) show that the quarter-filled repulsive Hubbard model is not superconducting. For the three-band Hubbard model we consider two parameter sets which take into account the differences in static magnetic structure and Fermi surfaces between La-Sr-Cu-O and Y-Ba-Cu-O materials. For both parameter sets, the finite-temperature approach showed no sign of a Kosterlitz-Thouless-type transition up to inverse temperatures \ensuremath{\beta}=17.5, in units of the Cu-O hopping, and hole doping \ensuremath{\delta}=0.25. Flux quantization results for the Y-Ba-Cu-O parameters on clusters up to 8\ifmmode\times\else\texttimes\fi{}8 unit cells equally showed no sign of superconductivity at a hole doping \ensuremath{\delta}=0.25.