Flux quantization and superfluid weight in doped antiferromagnets

Abstract

Doped antiferromagnets, described by a model and a suitable expansion, exhibit a metallic phase-modulated antiferromagnetic ground state close to half-filling. Here we demonstrate that the energy of the latter state is an even periodic function of the external magnetic flux threading the square lattice in an Aharonov-Bohm geometry. The period is equal to the flux quantum entering the Peierls phase factor of the hopping matrix elements. Thus flux quantization and a concomitant finite value of superfluid weight occur along with metallic antiferromagnetism. We argue that in the context of the present effective model, whereby carriers are treated as hard-core bosons, the charge q in the associated flux quantum might be set equal to 2e. Finally, the superconducting transition temperature is related to linearly, in accordance to the generic Kosterlitz-Thouless type of transition in a two-dimensional system, signalling the coherence of the phase fluctuations of the condensate. The calculated dependence of on hole concentration is qualitatively similar to that observed in the high-temperature superconducting cuprates.