Recent discoveries, as well as open questions, in experimentally realized correlated electron materials are reviewed. In particular, high temperature superconductivity in the cuprates and in the recently discovered iron pnictides, possible chiral p-w
ave superconductivity in strontium ruthenate, the search for quantum spin liquid behavior in real materials, and new experimental discoveries in topological insulators are discussed.
Much excitement surrounds the possibility that strontium ruthenate exhibits chiral p-wave superconducting order. Such order would be a solid state analogue of the A phase of He-3, with the potential for exotic physics relevant to quantum computing. W
e take a critical look at the evidence for such time-reversal symmetry breaking order. The possible superconducting order parameter symmetries and the evidence for and against chiral p-wave order are reviewed, with an emphasis on the most recent theoretical predictions and experimental observations. In particular, attempts to reconcile experimental observations and theoretical predictions for the spontaneous supercurrents expected at sample edges and domain walls of a chiral p-wave superconductor and for the polar Kerr effect, a key signature of broken time-reversal symmetry, are discussed.
The superfluid density near the superconducting transition is investigated in the presence of spatial inhomogeneity in the critical temperature. Disorder is accounted for by means of a random $T_c$ term in the conventional Ginzburg-Landau action for
the superconducting order parameter. Focusing on the case where a low-density of randomly distributed planar defects are responsible for the variation of $T_c$, we derive the lowest order correction to the superfluid density in powers of the defect concentration. The correction is calculated assuming a broad Gaussian distribution for the strengths of the defect potentials. Our results are in a qualitative agreement with the superfluid density measurements in the underdoped regime of high-quality YBCO crystals by Broun and co-workers.
It is widely believed that the perovskite Sr$_2$RuO$_4$ is an unconventional superconductor with broken time reversal symmetry. It has been predicted that superconductors with broken time reversal symmetry should have spontaneously generated supercur
rents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr$_2$RuO$_4$ single crystals using scanning Hall bar and SQUID microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents at edges and domain walls as a function of domain size. For a single domain, this upper limit is below the predicted signal by two orders of magnitude. We speculate on the causes and implications of the lack of large spontaneous supercurrents in this very interesting superconducting system.
The Ginzburg-Landau (GL) equations for a d-wave superconductor are derived within the context of two microscopic lattice models used to describe the cuprates: the extended Hubbard model and the Antiferromagnetic-van Hove model. Both models have pairi
ng on nearest-neighbour links, consistent with theories for d-wave superconductivity mediated by spin fluctuations. Analytical results obtained for the extended Hubbard model at low electron densities and weak-coupling are compared to results reported previously for a d-wave superconductor in the continuum. The variation of the coefficients in the GL equations with carrier density, temperature, and coupling constants are calculated numerically for both models. The relative importance of anisotropic higher-order terms in the GL free energy is investigated, and the implications for experimental observations of the vortex lattice are considered.
