We propose a realization of the Weyl semimetal phase that is invariant under time reversal and occurs due to broken inversion symmetry. We consider both a simple superlattice model and a more realistic tight-binding model describing an experimentally reasonable HgTe/CdTe multilayer structure. The two models have the same underlying symmetry, therefore their low-energy features are equivalent. We find a Weyl semimetal phase between the normal insulator and the topological insulator phases that exists for a finite range of the system parameters and exhibits a finite number of Weyl points with robust band touching at the Fermi level. This phase is experimentally characterized by a strong conductivity anisotropy and topological surface states. The principal conductivities change in a complementary fashion as the system parameters are varied, and the surface states only exist in a region of momentum space that is determined by the positions of the Weyl points.

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κxx due to phonons is much larger than the expected quantized thermal Hall conductance κ q xy = πT 12 k 2 B of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L , where is a thermalization length. We obtain ∼ T −5 for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κxy/κxx ∼ 10 −3 , in α-RuCl3. arXiv:1805.10532v2 [cond-mat.str-el]

π coupling may arise when a ferromagnet forms a link between two superconductors of an artificial Josephson junction. Using a trilayer Fe/Cr/Fe barrier in which the Cr thickness determines the alignment of the Fe layers, we show that the critical currents are substantially enhanced in the antiparallel configuration. The result agrees with existing superconductor-ferromagnet proximity theory according to which the phase-controlling effects of ferromagnets on Cooper pairs can be minimized by arranging their moments in a nonparallel way [Bergeret, Phys. Rev. Lett. 86, 3140 (2001); Blanter, Phys. Rev. B 69, 024525 (2004)].