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.
We derive the polarizability of an electron system in (i) the superconducting phase, with
d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the
d-density-wave (dDW) state, characterized by a
d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-
Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azimuthal modulation, consistent with the
d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, albeit imperfect, due to a nonzero value of the hopping ratio ${t}^{\ensuremath{'}}∕t$ in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the $(\mathbf{q},\ensuremath{\omega})$ dependence of the retarded polarizability.
We study a short coherence length d-wave superconductor with a finite density of unitary scatterers using the Bogoliubov-deGennes technique. We find that the low-energy density of states is reduced, the superfluid stiffness is significantly larger, and off-diagonal long-range order is more robust than the conventional self-consistent T-matrix prediction. These results are a consequence of the inhomogeneous pairing amplitude in the ground state and of the low-lying excitations formed by hybridized impurity resonances. This inhomogeneous response accounts for the insensitivity of high-
Tc superconductors to impurities.