Phase diagram of the electron-doped La2-xCexCuO4 cuprate superconductor from Andreev bound states at grain boundary junctions

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

After a recent series of rapid and exciting developments, the long search for the Majorana fermion-the elusive quantum entity at the border between particles and antiparticles-has produced the first positive experimental results, but is not over yet. Originally proposed by E Majorana in the context of particle physics, Majorana fermions have a condensed matter analogue in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, namely, vortices for thin films and wire ends for the nanowire. These Majorana bound states are expected to manifest non-Abelian quantum statistics, which makes them ideal building blocks for fault-tolerant topological quantum computation. This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire-superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling, which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances.

Spin accumulation in triplet Josephson junction

We employ a Hamiltonian method to study the equal-spin pairing triplet Josephson junction with different orbital symmetries of pair potentials. Both the spin/charge supercurrent and possible spin accumulation at the interface of the junction are analyzed by means of the Keldysh Green's function. It is found that a spontaneous angle-resolved spin accumulation can form at the junction's interface when the orbital symmetries of Cooper pairs in two triplet superconductors are different, the physical origin is the combined effect of the different orbital symmetries and different spin states of Cooper pairs due to the misalignment of two d vectors in triplet leads. An abrupt current reversal effect induced by misalignment of d vectors is observed and can survive in a strong interface barrier scattering because the zero-energy state appears at the interface of the junction. These properties of the p-wave Josephson junction may be helpful for identifying the order parameter symmetry.

Anomalous Andreev bound state in noncentrosymmetric superconductors

We study edge states of noncentrosymmetric superconductors where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spin-orbit coupling. For d(xy)-wave pairing, the obtained Andreev bound state has an anomalous dispersion as compared to conventional helical edge modes. A unique topologically protected time-reversal invariant Majorana bound state appears at the edge. The charge conductance in the noncentrosymmetric superconductor junctions reflects the anomalous structures of the dispersions, particularly the time-reversal invariant Majorana bound state is manifested as a zero bias conductance peak.