Recent experimental discoveries have brought a diverse set of broken symmetry states to the center stage of research on cuprate superconductors. Here, we focus on a thematic understanding of the diverse phenomenology by exploring a strong-coupling me
chanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a variational study of a three-band model of the CuO$_2$ plane with Kondo-type exchange couplings between doped oxygen holes and classical copper spins. Two main findings from this strong-coupling multi-band perspective are 1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order and isotropic phases are all accessible microscopically within the model, 2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. These results indicate that the diverse phenomenology of broken-symmetry states in hole-doped antiferromagnetic charge-transfer insulators may indeed arise from hole-doped frustration of antiferromagnetism.
Recent $mu$SR measurements on SrPtAs revealed time-reversal-symmetry breaking with the onset of superconductivity [Biswas et al., Phys. Rev. B 87, 180503(R) (2013)], suggesting an unconventional superconducting state. We investigate this possibility
via functional renormalization group and find a chiral $(d+mathrm{i}d)$-wave order parameter favored by the multiband fermiology and hexagonal symmetry of SrPtAs. This $(d+mathrm{i}d)$-wave state exhibits significant gap anisotropies as well as gap differences on the different bands, but only has point nodes on one of the bands at the Brillouin zone corners. We study the topological characteristics of this superconducting phase, which features Majorana-Weyl nodes in the bulk, protected surface states, and an associated thermal Hall response. The lack of extended nodes and the spontaneously broken time-reversal symmetry of the $(d+mathrm{i}d)$-wave state are in agreement with the $mu$SR experiments. Our theoretical findings together with the experimental evidence thus suggests that SrPtAs is the first example of chiral $d$-wave superconductivity.
