The Majorana fermion, which is its own anti-particle and obeys non-abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor, due to contamination from impurity states or other closely-packed Caroli-de Gennes-Matricon (CdGM) states, which hampers further manipulations of MZMs. Here using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect free regions of (Li0.84Fe0.16)OHFeSe, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can be naturally attributed to a MZM arising from this chiral topological surface states of a bulk superconductor. (Li0.84Fe0.16)OHFeSe thus provides an ideal platform for studying MZMs and topological quantum computing. 2

We constructed tight-binding models for the new superconductor SrPtAs according to first principle calculations, and by functional renormalization group we investigated the effect of electron correlations and spin-orbital coupling (SOC) in Cooper pairing. We found that out of the five d-orbitals, the (dxz, dyz)-orbitals are the active ones responsible for superconductivity, and ferromagnetic spin fluctuations enhanced by the proximity to the van Hove singularity triggers f -wave triplet pairing. The superconducting transition temperature increases as the Fermi level approaches the van Hove singularity until ferromagnetism sets in. Because of SOC, the spin fluctuations have easy-plane anisotropy, and the d-vector of the triplet pairing component is pinned along the out-ofplane direction. Experimental perspectives are discussed.

The supercurrent in a Josephson junction composed of the zigzag edged graphene nanoribbon (ZGNR) lying between two superconducting leads [superconductor-graphene-superconductor (SGS) junction] has been studied by the Green's function method. It is found that a small transverse electric field applied on the ZGNR can reverse the supercurrent direction, leading to a so-called 0-pi phase transition. The 0-pi phase transition can happen periodically with a change in the ZGNR's length, and, more importantly, can be easily and electrically controllable by a gate voltage, which is absent in the conventional superconducting pi junction and would make the SGS junction very promising for future application in superconducting electronics, as well as quauntum information and computation.

CuxBi2Se3 hosts both topological surface states and bulk superconductivity. It has been identified recently as a topological superconductor (TSC) with an extraordinary nematic, i. e. C2-symmetric, superconducting state and odd-parity pairing. Here, using scanning tunneling microscopy (STM), we directly examine the response of the superconductivity of CuxBi2Se3 to magnetic field. Under outof-plane fields (B⊥), we discover elongated magnetic vortices hosting zero-bias conductance peaks consistent with the Majorana bound states expected in a TSC. Under in-plane fields (B//), the average superconducting gap exhibits two-fold symmetry with field orientation; the long C2 symmetry axes are pinned to the dihedral mirror planes under B//=0.5 T but rotate slightly under B//=1.0 T. Moreover, a nodeless Δ4x gap structure is semi-quantitatively determined for the first time. Our data paint a microscopic picture of the nematic superconductivity in CuxBi2Se3 and pose strong constraints on theory.