Identifying s-wave pairing symmetry in single-layer FeSe from topologically trivial edge states.

Determining the pairing symmetry of single-layer FeSe on SrTiO3 is the key to understanding the enhanced pairing mechanism. It also guides the search for superconductors with high transition temperatures. Despite considerable efforts, it remains controversial whether the symmetry is the sign-preserving s- or the sign-changing s±-wave. Here, we investigate the pairing symmetry of single-layer FeSe from a topological point of view. Using low-temperature scanning tunneling microscopy/spectroscopy, we systematically characterize the superconducting states at edges and corners of single-layer FeSe. The tunneling spectra collected at edges and corners show a full energy gap and a substantial dip, respectively, suggesting the absence of topologically non-trivial edge and corner modes. According to our theoretical calculations, these spectroscopic features can be considered as strong evidence for the sign-preserving s-wave pairing in single-layer FeSe.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal.

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking the P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Gapless vortex bound states in superconducting topological semimetals.

We find that the vortex bound states in superconducting topological semimetals are gapless owing to topological massless excitations in their normal states. We demonstrate this universal result in a variety of semimetals, including Dirac and Weyl semimetals, three-fold degenerate spin-1 fermions, spin-3/2 Rarita-Schwinger-Weyl fermion semimetals and other exotic fermion semimetals. The formation of these gapless bound states is closely related to their Andreev specular reflection and propagating Andreev modes in π-phase superconductor-normal metal-superconductor junctions. We further demonstrate that these gapless states are topologically protected and can be derived from a topological pumping process.

Topological Weyl semimetal phases in a time reversal invariant spinless model.

We investigate the topological Weyl semimetal phases in a time reversal invariant spinless lattice model which has C 4v or C 2v point group symmetries. For the C 4v case, the model is characterized by eight Weyl points in the k z = π plane, while for the C 2v case, it is characterized by four Weyl points in the k z = π plane. For both cases, Fermi arcs can be realized on their surfaces. We find that the topological Weyl semimetal can be viewed as an intermediate phase between the topological crystalline insulator (TCI) and normal insulator, and they all can be described by the so-called bent mirror Chern numbers. What's more, in the C 2v case, the TCI phase is still present when the perturbation is small, though the Z 2 invariant is not well-defined then, however, it can be well described by the bent mirror Chern number.

Quasi-1D Topological Nodal Vortex Line Phase in Doped Superconducting 3D Dirac Semimetals.

We study vortex bound states in three-dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. We find that there exist robust gapless vortex bound states propagating along the vortex line in the s-wave superconducting state. We refer to this newly found phase as the quasi-1D nodal vortex line phase. According to the Altland-Zirnbauer classification, the phase is characterized by a topological index (ν;N) at k_{z}=0 and k_{z}=π, where ν is the Z_{2} topological invariant for a 0D class-D system and N is the Z topological invariant for a 0D class-A system. Furthermore, we show that the vortex end Majorana zero mode can coexist with the quasi-1D nodal phase in certain types of Dirac semimetals. The possible experimental observations and material realization of such nodal vortex line states are discussed.

Topological vortex phase transitions in iron-based superconductors.

We study topological vortex phases in iron-based superconductors. Besides the previously known vortex end Majorana zero modes (MZMs) phase stemming from the existence of a three dimensional (3D) strong topological insulator state, we show that there is another topologically nontrivial phase as iron-based superconductors can be doped superconducting 3D weak topological insulators (WTIs). The vortex bound states in a superconducting 3D WTI exhibit two different types of quantum states, a robust nodal superconducting phase with pairs of bulk MZMs and a full-gap topologically nontrivial superconducting phase which has single vortex end MZM in a certain range of doping level. Moreover, we predict and summarize various topological phases in iron-based superconductors, and find that carrier doping and interlayer coupling can drive systems to have phase transitions between these different topological phases.

Dirac semimetal in ß-CuI without surface Fermi arcs.

Anomalous surface states with Fermi arcs are commonly considered to be a fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals, however, Fermi arcs of DSMs are not topologically protected. Using first-principles calculations, we predict that ß-cuprous iodide (ß-CuI) is a peculiar DSM whose surface states form closed Fermi pockets instead of Fermi arcs. In such a fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to Fermi pockets stems from a large cubic term preserving all crystal symmetries and from the small energy difference between the surface and bulk Dirac points. The cubic term in ß-CuI, usually negligible in prototypical DSMs, becomes relevant because of the particular crystal structure. As such, we establish a concrete material example manifesting the lack of topological protection for surface Fermi arcs in DSMs.

Electronic physics and possible superconductivity in layered orthorhombic cobalt oxychalcogenides.

We suggest that cobalt-oxychalcogenide layers constructed by vertex sharing CoA2O2 (A=S, Se, Te) tetrahedra, such as BaCoAO, are strongly correlated multi-orbitals electron systems that can provide important clues on the cause of unconventional superconductivity. Differing from cuprates and iron-based superconductors, these systems lack of the D4h symmetry classification. However, their parental compounds possess antiferromagnetic (AFM) Mott insulating states through pure superexchange interactions and the low energy physics near Fermi surfaces upon doping is mainly attributed to the three t2g orbitals that dominate the AFM interactions. We derive a low energy effective model for these systems and predict that a d-wave-like superconducting state with reasonable high transition temperature can emerge by suppressing the AFM ordering even if the pairing symmetry can not be classified by the rotational symmetry any more.