Symmetry Considerations for the Detection of Second-Harmonic Generation in Cuprates in the Pseudogap phase

A proposal to test the proposed time-reversal and inversion breaking phase in the Pseudogap region of the Cuprate compounds through the variation of Second-harmonic generation intensity with temperature and polarization and angle of incidence is presented.Comment: 7 pages, 2 figures include

Theory of Superconductivity in the Cuprates

The quantum critical fluctuations of the time-reversal breaking order parameter which is observed in the pseudogap regime of the Cuprates are shown to couple to the lattice equivalent of the local angular momentum of the fermions. Such a coupling favors scattering of fermions through angles close to $\pm \pi/2$ which is unambiguously shown to promote d-wave pairing. The right order of magnitude of both $T_c$ and the normalized zero temperature gap $\Delta/T_c$ are calculated using the same fluctuations which give the temperature, frequency and momentum dependence of the the anomalous normal state properties for dopings near the quantum-critical value and with two parameters extracted from fit to such experiments.Comment: Accepted for publication in PRB with the title "Theory of the coupling of quantum-critical fluctuations to fermions and d-wave superconductivity in the cuprates

Detecting Dichroism in Angle Resolved Photoemission

Recently, the time-reversal violation predicted for the pseudogap phase of the cuprates, which was observed by dichroism experiments using Angle-Resolved Photoemission has also been observed by polarized neutron diffraction. Earlier derivation of dichroism in angle resolved photoemission due to time-reversal violation relied on existence of mirror planes in the crystal. Here the theory of the effect is generalized to the case that mirror plane symmetry is weakly violated due to perturbing potentials such as a superstructure.Comment: Addenda to Simon and Varma, Phys. Rev. Lett. vol. 89, 247003-1 (2002) and A. Kaminski, et al., Nature, vol. 416, 610 (2002

Gyrotropic Birefringence in the Under-doped Cuprates

The optical effects due to the loop-current order parameter in under-doped cuprates are studied in order to understand the recent observation of unusual birefringence in electromagnetic propagation in under-doped cuprates. It is shown why birefringence occurs even in multiple domains of order with size of domains much smaller than the wave-length and in twinned samples. Not only is there a rotation of polarization of incident light but also a rotation of the principal optical axis from the crystalline axes. Both are calculated in relative agreement with experiments in terms of the same parameters. The magnitude of the effect is orders of magnitude larger than the unusual Kerr effect observed in under-doped cuprates earlier. The new observations, including their comparison with the Kerr effect, test the symmetry of the proposed order decisively and confirm the conclusions from polarized neutron scattering

Some Experimental Signatures to look for Time-reversal Violating superconductors

We discuss some experimental signatures associated with the topological structures of unconventional superconductor order parameters of form $d_{x^2-y^2}+ix$, where $x=s,p_x \pm p_y$, or $d_{xy}$. Specifically, we study the topological surface states on the $(110)$ and equivalent surfaces of such superconductors which are observable in Andreev tunneling experiments, as well as evaluate the magnetic flux trapped in superconducting rings of such superconductors with multiple grain-boundary Josephson junctions. Previous experiments are examined and several new experiments suggested.Comment: 11 pages, 3 figure