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(Φ,T) as well as the ground-state energy, E0(Φ), for Hubbard models on a cylinder geometry threaded by a flux Φ. The temperature derivative of the superfluid density, ∂βDs(β)/∂β, is obtained from the difference in internal energy of systems which differ by a phase twist π/2 in the boundary condition along one lattice direction. In the framework of a Kosterlitz-Thouless transition, ∂βDx(β)/∂β scales to a Dirac δ function at the transition temperature. On finite-sized lattices, ∂βDs(β)/∂β shows a response which increases with lattice size. Flux quantization is a T=0 method. From the functional form of E0(Φ), 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 β=17.5, in units of the Cu-O hopping, and hole doping δ=0.25. Flux quantization results for the Y-Ba-Cu-O parameters on clusters up to 8×8 unit cells equally showed no sign of superconductivity at a hole doping δ=0.25.

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