Type-I and type-II topological nodal superconductors with s -wave interaction

Abstract

Topological nodal superconductors are generally realized based on unconventional pairings. In this work, we propose a minimal model to realize these topological nodal phases with only s-wave interaction. In our model the linear and quadratic spin-orbit couplings along the two directions break the isotropy in momentum space and introduce effective unconventional pairings on the Fermi surface. This model may support different nodal superconducting phases characterized by either winding number in BDI class or Pfaffian in D class at the particle-hole invariant axes. In the vicinity of the nodal points the effective Hamiltonian can be described by either type-I or type-II Dirac equation; and the crossover between these two nodal points can be driven by external Zeeman fields. We show that these nodal phases are robust against weak disorders, thus are possible to be realized in experiments with real materials. The smoking-gun evidences to verify these phases based on scanning tunneling spectroscopy are also briefly discussed.

Classifying superconductivity in Moiré graphene superlattices

“…Laughlin [48] twenty years ago for HTS cuprates. We only mention [13,14,[49][50][51][52][53][54][55][56] where models and extended reference lists can be found.…”

Higher-order symmetry-protected topological states for interacting bosons and fermions

“…Such a symmetry-protected topological (SPT) phase can essentially be defined by its topological bulk-boundary correspondence: if the boundary does not break the symmetry, it must be gapless or (for 3 dimensional systems) topologically ordered. In parallel to the exploration of SPT phases, the concept of symmetry protection has been extended to spatial symmetries and point group symmetries in common crystalline materials [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Topological states protected by spatial symmetries come with a much richer bulkboundary correspondence: in addition to gapless surfaces (or edges), depending on the protecting symmetries, they also admit boundaries where the edges and surfaces are gapped, but protected gapless modes appear at corners or hinges of the system.…”

“…Third, an important feature of HOSPT phases protected by spatial symmetries (together with some internal symmetry) is the interplay between symmetry and geometric defects. In the study of conventional SPT phases, a rich phenomenology including the existence of symmetry protected zero modes was uncovered at geometrical defects, such as cross-caps, dislocations, or disclinations [31,33,[61][62][63][64]. In addition, for SPT phases protected by global unitary symmetries, gauging these symmetries reveals nontrivial braiding statistics between flux defects [65][66][67][68][69][70], suggesting that a similar form of braiding arises between lattice defects and symmetry fluxes when the internal symmetries of an HOSPT are gauged.…”

On the SERS quantitative determination of organic dyes

“…Classical electrodynamics calculation can show that if two metal NPs are very close, when they are excited in the plasmonic resonance, the electric field in the gap between them is extremely high. [17] Then, if a molecule is placed in this gap, an extremely strong Raman signal can be obtained. [1,5] Similar local conditions are referred as "hot spots" in * Also at LENS, University of Florence, via N. Carrara 1, 50019 Sesto Fiorentino (FI), Italy.…”