We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrysta
ls with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional $s$-wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confirmed by the existence of a zero-energy surface bound state and the chiral propagation of a wave packet projected onto the midgap bound state along the surfaces. Furthermore, we confirm the existence of a single Majorana zero mode each in a vortex at the center of the system and along the surfaces, signifying the non-Abelian character of the system when the Bott index is unity.
Motivated by the recently discovered time-reversal symmetry-breaking superconductivity in epitaxial Bi/Ni bilayer system with transition temperature $T_capprox 4.2$K and the observation of zero-bias anomaly in tunneling measurements, we show that gap
-filling states can appear in the fully gapped $d_{xy}pm id_{x^2-y^2}$ superconducting states. We consider a model of helical electron states with d-wave pairing. In particular, we show that both magnetic and non-magnetic impurities can create states within the superconducting gap. Alternatively, we also show that the coupling of the electron spins to the in-plane Zeeman field provided by nickel can also create gap-filling states by producing Bogoliubov Fermi surfaces. Our findings may explain the origin of zero-bias anomaly observed in the point-contact tunneling measurements.
In this work we study interacting electrons on square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consid
er the repulsive onsite Hubbard and nearest-neighbor coulomb interactions, the so called extended Hubbard model. To examine the superconducting instability we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings, and found that while the $d_{xy}$ and $d_{x^2-y^2}$ symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instability. The possibility of topological superconductivity and triplet pairing is also discussed.
