Topological phases and surface flat bands in superconductors without inversion symmetry

Abstract

We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value of any of these topological numbers indicates the appearance of zero-energy Andreev surface states. We find that some of these boundary modes in nodal superconducting phases are dispersionless, i.e., they form a topologically protected flat band. The region where the zero-energy flat band appears in the surface Brillouin zone is determined by the projection of the nodal lines in the bulk onto the surface. These dispersionless Andreev surface bound states have many observable consequences, in particular, a zerobias conductance peak in tunneling measurements. We also find that in the gapless phase there appear Majorana surface modes at time-reversal invariant momenta which are protected by a Z2 topological invariant. 03.65.Vf, 74.55.+v, 74.45.+c, 73.20.Fz The hallmark of topological insulators and superconductors (SCs) is the existence of topologically protected conducting boundary modes. The recent experimental observation of these edge and surface states in spin-orbit induced Z 2 topological insulators in two and three dimensions [1], respectively, has lead to a surge of interest and excitement [2]. An exhaustive classification of topologically protected boundary modes occurring in gapped free fermion systems in terms of symmetry and spatial dimension was given in Refs. [3][4][5]. Interestingly, this classification scheme, which is known as the "periodic table" of topological insulators and SCs, predicts a three dimensional (3D) topological SC which satisfies time-reversal symmetry, but breaks spin-rotation symmetry. Indeed, the B phase of 3 He is one example of this so-called "class DIII" topological superfluid, whose different topological sectors can be distinguished by an integer topological invariant. Recent transverse acoustic impedance measurements in 3 He-B confirmed the existence of the predicted surface Majorana bound state [6].However, finding an electronic analog of the superfluid B phase of 3 He remains an outstanding challenge. In this paper we argue that some of the 3D non-centrosymmetric SCs might be examples of electronic topological SCs in symmetry class DIII [7]. We analyze the topological phase diagram of these systems and demonstrate quite generally that adjacent to fully gapped topological phases there exist non-trivial gapless superconducting phases with topologically protected nodal lines (rings). To characterize these gapless lines we introduce a set of topological invariants and show that, due to the bulkboundary correspondence, the presence of topologically stable nodal rings implies the appearance of dispersionless zeroenergy Andreev surface states. These topologically protected surface flat bands manifest themselves in scanning tunneling spectroscopy (STS) as a zero bias conductance peak, a feature which could be used as an experimental signatu...

Scanning tunneling measurements of layers of superconducting 2H-TaSe2: Evidence for a zero-bias anomaly in single layers

“…A zero voltage conductance peak can appear thus close to impurities, at a surface or close to crystal boundaries. 7,50,[53][54][55][56][57][58][59] An intriguing possibility is that some sort of unconventional superconductivity appears within the 2H -TaSe 2 sheets, either in the form of a d-wave order parameter or of sign changing superconductivity between different sheets. 47,60 Such a possibility would imply that the superconducting properties change from conventional s-wave in multilayers to unconventional reduced symmetry superconductivity when decreasing the thickness of the sample down to a single layer.…”

Conductance oscillations and zero-bias anomaly in a single superconducting junction to a three-dimensional Bi 2 Te 3 topological insulator

“…It was previously connected with disorder effects 31 or with more exotic scenarios like Majorana fermions [32][33][34] and Andreev surface states 35 . It also appears for ballistic transport l e >> L, if there is some restricted area within N region [36][37][38] .…”

Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures

“…Recently, several authors have demonstrated that surface Andreev bound states with flat dispersion arise in certain topological superconductors, for example Cu x Bi 2 Se 3 [16] and noncentrosymmetric superconductors [17,18]. Their existence can be traced back to the nontrivial topology associated with the gapped bulk, and thus are topologically protected.…”