Consequences of time-reversal-symmetry violation in models of high-Tcsuperconductors

Abstract

We consider some observable consequences of the possible breaking of the discrete space-time symmetries $P$ and $T$ in high-$T_c$ superconducting materials, as occurs in anyon models. It is argued, within these models, that at least two species of anyons are expected to occur, as a result of a quasimagnetic modification of the algebra of translations. We find that there is an intrinsic orbital magnetic moment perpendicular to each anyon layer, whose sign depends on the sign of the broken symmetry in the layer. If the coupling between layers is ferromagnetic, there should be a number of observable bulk effects, including optical rotation and anomalous transport properties analogous to a Hall conductance, which would occur even in the absence of an external magnetic field. Depending on the sample geometry, there may be a magnetic domain structure and/or fringing magnetic fields, and there may be a difference in the value of $H_{\mathrm{c}1\mathrm{}}$ for positive and negative magnetic fields. If the coupling between planes is antiferromagnetic, so that the sign of the broken $P$ and $T$ symmetry alternates between planes, the bulk effects are absent, but the broken symmetry may be detected in principle by surface-sensitive probes or by weak effects in neutron scattering. Measurements of muon spin relaxation provide a local probe that should be a sensitive detector of broken $P$ and $T$ symmetry in either the ferromagnetic or antiferromagnetic case. For the model of dilute, weakly interacting anyons, we show that the magnitude of the intrinsic orbital magnetic moment can be obtained exactly by a direct physical argument. Our analysis determines all of the coefficients in the effective London Lagrangian, including the Chern-Simons-type terms, if the value of the compressibility is known.