We study a one-dimensional topological superconductor, the Kitaev chain, under the influence of a non-Hermitian but $\mathcal{PT}$-symmetric potential. This potential introduces gain and loss in the system in equal parts. We show that the stability of the topological phase is influenced by the gain/loss strength and explicitly derive the bulk topological invariant in a bipartite lattice as well as compute the corresponding phase diagram using analytical and numerical methods. Furthermore we find that the edge state is exponentially localized near the ends of the wire despite the presence of gain and loss of probability amplitude in that region.Comment: 10 pages, 9 figure

Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic band degeneracies: (i) Weyl points protected by screw rotations with an accordionlike dispersion, and (ii) Weyl nodal lines protected by glide reflections. We report a number of existing materials, where these band crossings are realized near the Fermi energy. This includes Cu2SrSnS4 and elemental tellurium (Te), which exhibit accordion Weyl points; and the telluriumsilicon clathrate Te16Si38, which shows Weyl nodal lines. The ab-initio band structures and surface states of these materials are studied in detail, and implications for experiments are briefly discussed. arXiv:1908.00901v1 [cond-mat.mtrl-sci]

Despite recent efforts to advance spintronics devices and quantum information technology using materials with non-trivial topological properties, three key challenges are still unresolved1–9. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, the identification of generic topological degeneracies in large, multisheeted Fermi surfaces. By combining de Haas–van Alphen spectroscopy with density functional theory and band-topology calculations, here we show that the non-symmorphic symmetries10–17 in chiral, ferromagnetic manganese silicide (MnSi) generate nodal planes (NPs)11,12, which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1,651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs, which can be controlled with a magnetic field, on the FS of MnSi suggests the existence of similar properties—amenable for technological exploitation—in a large number of materials.

Three-dimensional Dirac semimetals with Dirac points carrying Z2 monopole charges can be realized in systems preserving the combined symmetry of space-inversion (P) and time-reversal (T ).Here we systematically study PT -symmetric non-Hermitian Dirac semimetals incorporating different kinds of symmetry-preserving non-Hermitian potentials. These potentials render non-Hermitian semimetals to be in either PT -unbroken or PT -broken phases. Interestingly, with the same kind of non-Hermitian potentials, systems with periodic and open boundary conditions may belong to different PT phases unique to non-Hermitian systems. We find that the topological properties of Z2 monopole charges are retained in non-Hermitian Dirac semimetals with PT -unbroken phases, where the bulk-boundary correspondence can be established. However, these systems exhibit features with no counterpart in Hermitian theory, such as the reflection-symmetric non-Hermitian skin effect and Fermi ribbon surface states. arXiv:1907.10417v1 [cond-mat.mes-hall]

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