It has been noted that certain surfaces of Weyl semimetals have bound states forming open Fermi arcs, which are never seen in typical metallic states. We show that the Fermi arcs enable them to support an even more exotic surface state with crossed flat bands in the superconducting state. We clarify the topological origin of the crossed flat bands and the relevant symmetry that stabilizes the cross point. We also discuss their possible experimental verification by tunneling spectroscopy.

The proximity induced pair potential in a topological insulator-superconductor hybrid features an interesting superposition of a conventional spin-singlet component from the superconductor and a spin-triplet one induced by the surface state of the topological insulator. This singlet-triplet superposition can be altered by the presence of a magnetic field. We study the interplay between topological order and superconducting correlations performing a symmetry analysis of the induced pair potential, using Green functions techniques to theoretically describe ballistic junctions between superconductors and topological insulators under magnetic fields. We relate a change in the conductance from a gapped profile into one with a zero-energy peak with the transition into a topologically nontrivial regime where the odd-frequency triplet pairing becomes the dominant component in the pair potential. The nontrivial regime, which provides a signature of odd-frequency triplet superconductivity, is reached for an out-of-plane effective magnetization with strength comparable to the chemical potential of the superconductor or for an in-plane one, parallel to the normal-superconductor interface, with strength of the order of the superconducting gap. Strikingly, in the latter case, a misalignment with the interface yields an asymmetry with the energy in the conductance unless the total contribution of the topological surface state is considered.

We study the system of double Rashba wires brought into the proximity to an s-wave superconductor. The time reversal invariant topological superconductivity is realized if the interwire pairing corresponding to crossed Andreev reflection dominates over the standard intrawire pairing. We derive the topological criterion and show that the system hosts zero energy Andreev bound states such as a Kramers pair of Majorana fermions. We classify symmetry of the Cooper pairs focusing on the four degrees of freedom, i.e., frequency, spin, spatial parity inside wires, and spatial parity between wires. The magnitude of the odd-frequency pairing is strongly enhanced in the topological state. We also explore properties of junctions occurring in such double wire systems. If one section of the junction is in the topological state and the other is in the trivial state, the energy dispersion of Andreev bound states is proportional to ∼ ± sin ϕ, where ϕ denotes the macroscopic phase difference between two sections. This behavior can be intuitively explained by the couplings of a Kramers pair of Majorana fermions and spin-singlet s-wave Cooper pair and can also be understood by analyzing an effective continuum model of the s + p/s-wave superconductor hybrid system.

We study the influence of nonmagnetic impurity scatterings on the tunneling conductance of a junction consisting of a normal metal and a disordered unconventional superconductor by solving the quasiclassical Eilenberger equation self-consistently. We find that the impurity scatterings in both the Born and the unitary limits affect the formation of the Andreev bound states and modify strongly the tunneling spectra around zero bias. Our results are interpreted well by the appearance of odd-frequency Cooper pairs near the interface and by the divergent behavior of the impurity self-energy. The present paper provides a useful tool to identify the pairing symmetry of unconventional superconductors in experiments.

We propose an all-electrical experimental setup to detect and manipulate the amplitude of oddfrequency pairing in a double quantum dot. Odd-frequency pair amplitude is induced from the breakdown of orbital symmetry when Cooper pairs are injected in the double dot with electrons in different dots. When the dot levels are aligned with the Fermi energy, i.e., on resonance, nonlocal Andreev processes are directly connected to the presence of odd-frequency pairing. Therefore, their amplitude can be manipulated by tuning the level positions. Detection of nonlocal Andreev processes by conductance measurements contributes a direct proof of the existence of odd-frequency pair amplitude and is available using current experimental techniques. Introduction.-The symmetry analysis of Cooper pairs is a key element in the study of superconductivity. For example, Cooper pairs at conventional BCS superconductors form a spin-singlet even-parity state, where the electrons have opposite spins and are coupled in momentum space by the isotropic s-wave channel. A current trend in the study of superconductivity is to engineer unconventional superconductors by breaking down symmetries of a BCS superconductor. Consequently, a new type of pairing emerges which is odd in frequency, i.e., odd under an exchange of the time coordinates [1][2][3][4]. Plenty of theoretical studies suggest ubiquitous presence of odd-frequency superconductivity at inhomogeneous superconducting systems [5][6][7][8][9][10][11][12][13][14][15]. Unfortunately, experimental evidence for odd-frequency pair amplitude is very limited. Odd-frequency spin-triplet swave superconductivity can explain the long-range proximity effect [16,17], the intrinsic paramagnetic Meissner effect [18][19][20][21], and the subgap structure [22] observed in ferromagnet-superconductor hybrids. However, oddfrequency pairs are mixed with conventional ones and their amplitude is not tunable but accidentally determined by the configuration of magnetic moments realized at the junction. To unambiguously establish the presence of odd-frequency pairing, new proposals that filter oddfrequency pairs and allow to control their amplitude are required.