We propose that the enigmatic pseudogap phase of cuprate superconductors is characterized by a hidden broken symmetry of d x 2 Ϫy 2-type. The transition to this state is rounded by disorder, but in the limit that the disorder is made sufficiently small, the pseudogap crossover should reveal itself to be such a transition. The ordered state breaks time-reversal, translational, and rotational symmetries, but it is invariant under the combination of any two. We discuss these ideas in the context of ten specific experimental properties of the cuprates, and make several predictions, including the existence of an as-yet undetected metal-metal transition under the superconducting dome.

§ These authors contributed equally to this research project. The Cooper pairing mechanism of heavy-fermion superconductors 1-4 , while long hypothesized as due to spin fluctuations 5-7 , has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap (k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure (k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging 8-10 , a proven technique for measuring the energy gaps of high-T c superconductors 11-13 , has recently been proposed 14 as a new method to measure (k) in heavy-fermion superconductors, specifically CeCoIn 5 15 . By implementing this method, we immediately detect a superconducting energy gap whose nodes are oriented along k||()/a 0 directions 16-19 . Moreover, we determine the complete k-space structure of the (k) of a heavy-fermion superconductor. For CeCoIn 5 , this novel information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that highest magnitude (k) opens on a high-k band so that gap nodes occur at quite unanticipated k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with d x 2y 2 gap symmetry. The availability of such quantitative heavy band-and gap-structure data will be critical in identifying the microscopic mechanism of heavy fermion superconductivity in this material, and perhaps in general. 29 Yuan, T., Figgins, J., and Morr, D. K. Hidden order transition in URu 2 Si 2 and the emergence of a coherent Kondo lattice. Phys. Rev. B 86, 035129 (2012) 30 Petrovic C. et al., J. Phys. Condens. Matter 13, L337 (2001) 31 McCollam, A., et al. Anomalous de Haas-van Alphen Oscillations in CeCoIn 5 . Phys. Rev. Lett. 94, 186401 (2005) 32 Aynajian, P., et al. Visualizing heavy fermions emerging in a quantum critical Kondo lattice. Nature 486, 201 (2012) 33 Koitzsch, A., et al. Electronic structure of CeCoIn 5 from angle-resolved photoemission spectroscopy. Phys. Rev. B 79, 075104 (2009) 34 Jia, X. -W., et al, Growth characterization and Fermi surface of heavy-fermion CeCoIn 5 superconductor. Chinese Phys. Lett. 28 057401 (2011)

We show that a new resonant magnetic excitation at incommensurate momenta, observed recently by inelastic neutron scattering experiments on YBa2Cu3O6.85 and YBa2Cu3O6.6, is a spin exciton. Its location in the Brillouin zone and its frequency are determined by the momentum dependence of the particle-hole continuum. We identify several features that distinguish this novel mode from the previous resonance mode observed near Q=(pi,pi).

We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around $Q =(\pi,\pi)$. We show that as the coupling increases, the shape of the quasiparticle Fermi surface and the spin-fermion vertex undergo a substantial evolution. At strong couplings, $g \gg \omega_0$, where $\omega_0$ is the upper cutoff in the spin susceptibility, the hole Fermi surface consists of small pockets centered at $(\pm \pi/2, \pm \pi/2)$. Simultaneously, the full spin-fermion vertex is much smaller than the bare one, and scales nearly linearly with $|q-Q|$, where $q$ is the momentum of the susceptibility. At intermediate couplings, there exist both, a large hole Fermi surface centered at $(\pi,\pi)$, and four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the origin of the Brillouin zone. The relevance of these results for recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.Comment: 19 pages, RevTeX, 15 figures embedded in the text, submitted to Phys. Rep., ps-file is also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm