We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor UPt3 and calculate the anomalous ac Hall conductivity in a simplified two-band model. From the ac Hall conductivity and optical data we estimate the polar Kerr rotation angle and compare it to the measured results for UPt3 [E. R. Schemm et al., Science 345,190(2014)].

We consider quantum oscillation experiments in YBa 2 Cu 3 O 6+δ from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard–Landauer formula for the conductivity. The specific density wave order responsible for reconstruction is a period-8 d -density wave in which the current density is unidirectionally modulated, which is also naturally accompanied by a period-4 charge order, consistent with recent nuclear magnetic resonance experiments. This scenario leads to a natural explanation as to why only oscillations from a single electron pocket of a frequency of about 500 T is observed, and a hole pocket of roughly twice the frequency as dictated by the twofold commensurate order and the Luttinger sum rule is not observed. In contrast period-8 d -density wave leads to a hole pocket of roughly half the frequency of the electron pocket. The observation of this slower frequency will require higher, but not unrealistic, magnetic fields than those commonly employed. There is already some suggestion of the slower frequency in a measurement in fields as high as 85 T.

In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, , can give rise to different kinds of Pfaffian states. In addition to the well known Moore-Read Pfaffian and anti-Pfaffian states, a new putative particle-hole symmetric Pfaffian state, corresponding to the s−wave pairing channel, was also proposed. However, the possible underlying pairing mechanism is not clear at all. In this work we provide a specific pairing mechanism for realizing some of these Pfaffian states. We show that there can be nonzero pairing in angular momentum channels | | ≥ 1 depending on the magnitude of a coupling constant. There is a quantum phase transition from the Dirac composite fermi liquid state to Cooper pairing states in angular momentum channels | | ≥ 1 as the coupling constant is tuned across its critical point value. Surprisingly the particle-hole symmetric = 0 channel pairing turns out to be impossible irrespective of the size of the coupling constant. arXiv:1606.00899v2 [cond-mat.str-el]

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current-current interactions. Our results show that there can be a continuous transition from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that = 1 angular momentum channel is quite different from higher angular momenta ≥ 3. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction ν = is quantitatively changed from the previously established results but not qualitatively.

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