Types of topological surface states in nodal noncentrosymmetric superconductors

Abstract

Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at their surface. We show that the presence of certain inversion-type lattice symmetries can give rise to additional topological features of the gap nodes, resulting in surface states forming one-dimensional arcs connecting the projections of two nodal rings. In addition, we demonstrate that Majorana surface states can appear at time-reversal-invariant momenta of the surface Brillouin zone, even when the system is not fully gapped in the bulk. Within a continuum theory we derive the topological invariants that protect these different types of zero-energy surface states. We independently derive general conditions for the existence of zero-energy surface bound states using the complementary quasiclassical scattering theory, explicitly taking into account the effects of spin-orbit splitting of the bands. We compute surface bound-state spectra for various crystal point-group symmetries and orbital-angular-momentum pairing states. Finally, we examine the signatures of the arc surface states and of the zero-energy surface flat bands in tunneling-conductance spectra and dicuss how topological phase transitions in noncentrosymmetric superconductors could be observed in experiments.

Ballistic transport in one-dimensional random dimer photonic crystals

“…The upper critical field B c2 (T ) curves taken at different pressures collapse in a reduced plot onto a single curve with an unusual linear variation and values that largely exceed the model values for a weak-coupling spin-singlet superconductor [21]. These B c2 data point to the presence of an odd-parity Cooper pair component in the superconducting order parameter, in agreement with predictions for noncentrosymmetric and topological superconductors [3,22,23].…”

Surface instability in nodal noncentrosymmetric superconductors

“…For T > T s , the zero-energy flat band predicted in Refs. [2,11] is clearly visible for 0.5 k m 1.5; the zero-energy states at k m 0.5 form an arc connecting the projections of the nodal rings [2,11]. The TRSB for T < T s removes the topological protection of the zero-energy flat bands of the TRS state, which are consequently pushed away from zero energy, with a low-temperature energy shift on the order of T s .…”

“…We find that the singlet and triplet gaps have the same phase, which can be set to zero, so that TRS is preserved. SOC splits the bands and thus also the Fermi surface according to the helicity of states [2]. Since the triplet order parameter is parallel to the SOC, pairing only occurs between states with the same helicity.…”

Entanglement entropy and entanglement spectrum of triplet topological superconductors

“…Various experimental signatures have been proposed and considerable experimental evidence has by now been found [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . The absence of a local order parameter and the impossibility to use Landau symmetry breaking arguments turn topological phases into one of the most successful examples where entanglement measures, such as the entanglement entropy, bring new insights that could be hardly achieved by other more traditional methods.…”