Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work, we theoretically propose a novel way to attain topological superconductors with non-trivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with j = 3/2 electrons, we investigate the dominant superconducting channels for a multi-orbital quadratic band-touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors d-wave pairing, the absence of the particle-hole symmetry necessarily induces parasitic s-wave pairing. Based on the Landau theory with SO(3) symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with parasitic s wave pairing (d (3z 2 −r 2 ) +s) and time-reversal-symmetry broken phase with parasitic s wave pairing (d (3z 2 −r 2 ,xy) + id x 2 −y 2 + s). These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological winding numbers ±2, leading to non-trivial surface states such as drumhead-like surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-heusler compound YPtBi, and suggest possible future experiments. arXiv:1811.04046v1 [cond-mat.str-el] 9 Nov 2018

Lacunar spinel GaTa4Se8 is a unique example of spin–orbit coupled Mott insulator described by molecular jeff = 3/2 states. It becomes superconducting at Tc = 5.8 K under pressure without doping. In this work, we show, this pressure-induced superconductivity is a realization of a new type topological phase characterized by spin-2 Cooper pairs. Starting from first-principles density functional calculations and random phase approximation, we construct the microscopic model and perform the detailed analysis. Applying pressure is found to trigger the virtual interband tunneling processes assisted by strong Hund coupling, thereby stabilizing a particular d-wave quintet channel. Furthermore, we show that its Bogoliubov quasiparticles and their surface states exhibit novel topological nature. To verify our theory, we propose unique experimental signatures that can be measured by Josephson junction transport and scanning tunneling microscope. Our findings open up new directions searching for exotic superconductivity in spin–orbit coupled materials.

Frustration in spin system can give rise to unique ordered states and as a consequence several physical phenomena are expected such as multiferroics, high temperature superconductors and anomalous hall effect. Here we report the "new magnetic orders" induced by anisotropic spin exchanges on pyrochlore spinels as the interplay of spin orbit coupling and geometrical frustration. Due to complicated superexchange paths of B-site spinels, we claim that anisotropic interaction between next-nearest neighbors play an important role. Based on the systematic studies of generic spin model, we argue that several classical spin states can be explored in spinel systems; local XY state, all-in all-out state, Palmer-Chalker state and coplanar spiral state. In addition, we reveal new types of magnetic phases with finite ordering wavevectors, labeled as 'octagonal (prism)' state and '(distorted) cubic' states. When the 'octagonal prism' state is stabilized, non-zero scalar spin chirality induces alternating net current in addition to finite orbital current and orbital magnetization even in Mott insulators. Finally, we also discuss the relevance of 'distorted cubic' state to the magnetic order of spinel compound GeCo2O4.Magnetic frustration originates from competing interactions between different spin exchanges. Despite the simple spin interactions such as Heisenberg or Ising type, lattice geometries can give rise to frustration, often termed as geometrical frustration. [1,2] Apart from geometrical frustration, anisotropic spin exchanges can also give rise to frustration due to competing interactions. [3][4][5] In general, such anisotropic spin exchanges are expected for spin-orbit coupled system described by the total angular momentum J. When anisotropic spin exchanges meet geometrical frustration, exotic magnetism emerges in Mott insulators.Magnetic properties of the B site spinel compounds (AB 2 X 4 ) own such interplay forming a corner shared tetrahedra, pyrochlore lattice structure.[6-8] Focusing on pyrochlore lattice structure, one can derive the most generic spin model on symmetry grounds and indeed such generic spin model for nearest-neighbor interactions has been studied. Especially for rare-earth pyrochlore magnets (A 2 B 2 O 7 ), A site rare-earth ions also form a pyrochlore lattice and their partially filled 4f electrons can give rise to non-negligible anisotropic spin exchanges between nearest-neighbors.[9-12] However, the situation in B-site spinels with 3d-5d magnetic ions is quite different from the case of rare-earth pyrochlores. In spinels, the superexchange paths induce anisotropic exchanges between next-nearest-neighbor to play an important role, thus generic spin model for B-site spinel compounds is significantly distinct from ones studied before and one could expect new types of magnetic orderings.In this paper, we study the frustrated spin model on a pyrochlore lattice and find new magnetic phases and their unique properties. Focusing on spin orbit coupled B-site spinels, we write down the generic spin exchan...

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