Lattice Effects in Flux Phases

Abstract

The uniform flux phases of the t-J model are studied using a slave boson representation. The gaussian fluctuations around the mean field saddle point are calculated. A key feature is the cancellation of Hall conductances of the spinons and the holons, in the limit of small doping. This cancellation leads to a pole in the global electromagnetic response function, in a mechanism which is very similar to anyon superconductivity. Our main focus has been to evaluate the Hall conductance of the global system as a function of frequency and wave vector. Using various examples, we show that because of the cancellation of the two Hall conductances in the static and long wave-length limit, the behaviour of the global system is very sensitive to lattice effects. For instance, P. Wiegmann has found that the global Hall conductance vanishes in the static and long wave length limit, if one uses the response functions for the two dimensional continuous system. However, a direct calculation of the response functions starting from the Hofstadter spectrum leads to a finite Hall conductance in the absence of an external field. We show how this formalism can be used to calculate the local magnetic field which muons are expected to measure. The electric field of the muons induces a finite Hall current which in turn creates a finite magnetic field at the muon sites. Screening of the magnetic field by the Meissner effect has been taken into account and dielectric screening as well. Preliminary results indicate that the predicted fields are approximately one order of magnitude larger than the upper bound from experimental results obtained by the Vancouver group.