Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ±e 2 /2h at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.

The intraorbital repulsive Hubbard interaction cannot lead to attractive superconducting pairing states, except through the Kohn-Luttinger mechanism. This situation may change when we include additional local interactions such as the interorbital repulsion U ′ and Hund's interactions J. Adding these local interactions, we study the nature of the superconducting pairs in systems with tetragonal crystal symmetry including the dxz and dyz orbitals, and in octahedral systems including all three of dxz, dyz, and dxy orbitals. In the tetragonal case, spin-orbit interactions can stabilize attractive pairing channels containing spin triplet, orbital singlet character. Depending on the form of spinorbit coupling, pairing channels belonging to degenerate, non-trivial irreducible representations may be stabilized. In the octahedral case, the pairing interactions of superconducting channels are found to depend critically on the number of bands crossing the Fermi energy.

A variety of heavy fermion superconductors, such as UCoGe, UGe2, and URhGe exhibit a striking coexistence of bulk ferromagnetism and superconductivity. In these systems, the magnetic moment decreases with pressure, and vanishes at a ferromagnetic quantum critical point (qcp). Remarkably, the superconductivity in UCoGe varies smoothly with pressure across the qcp and exists in both the ferromagnetic and paramagnetic regimes. We argue that in UCoGe, spin-orbit interactions stabilize a time-reversal invariant odd-parity superconductor in the high pressure paramagnetic regime. Based on a simple phenomenological model, we predict that the transition from the paramagnetic normal state to the phase where superconductivity and ferromagnetism coexist, is a first-order transition.

We introduce a new method for the inverse design of nanophotonic devices that guarantees that the resulting designs satisfy strict length scale constraints, including minimum width and spacing constraints required by commercial semiconductor foundries. The method adopts several concepts from machine learning to transform the problem of topology optimization with strict length scale constraints to an unconstrained stochastic gradient optimization problem. Specifically, we introduce a conditional generator for feasible designs and adopt a straight-through estimator for the backpropagation of gradients to a latent design. We demonstrate the performance and reliability of our method by designing several common integrated photonic components.

We have examined the intrinsic spin-orbit coupling (SOC) and orbital depairing in thin films of Nb-doped SrTiO3 by superconducting tunneling spectroscopy. The orbital depairing is geometrically suppressed in the two-dimensional limit, enabling a quantitative evaluation of the Fermi level spinorbit scattering using Maki's theory. The response of the superconducting gap under in-plane magnetic fields demonstrates short spin-orbit scattering times τso ≤ 1.1 ps. Analysis of the orbital depairing indicates that the heavy electron band contributes significantly to pairing. These results suggest that the intrinsic spin-orbit scattering time in SrTiO3 is comparable to those associated with Rashba effects in SrTiO3 interfacial conducting layers and can be considered significant in all forms of superconductivity in SrTiO3. arXiv:1805.00047v1 [cond-mat.supr-con]