Evolution of Density of States and a Spin-Resolved Checkerboard-Type Pattern Associated with the Majorana Bound State.

In terms of the Bogoliubov-de Gennes approach, we investigate the Majorana bound state (MBS) in a vortex of proximity-induced superconductivity on the surface of a topological insulator. Mapping out the local density of states (LDOS) of quasiparticle excitations as a function of energy and distance from the vortex center, it is found that the spectral distribution evolves from a V shape to a Y shape with the emergence of a MBS upon variation of the chemical potential, consistent with the STM/STS measurement in a very recent experiment [Xu et al., Phys. Rev. Lett. 114, 017001 (2015)] on a Bi(2)Te(3) thin layer on the top of NbSe(2). Moreover, we demonstrate that there is a checkerboard-type pattern in the relative LDOS between the spin-up and -down channels, where the quantum mechanical wave function of the MBS manifests itself clearly as a single quantum state. Therefore, a spin-resolved STM/STS technique is expected to be able to provide phase-sensitive evidence for a MBS in the vortex core of a topological superconductor.

Imaging Josephson vortices on the surface superconductor Si(111)-(√7×√3)-In using a scanning tunneling microscope.

We have studied the superconducting Si(111)-(√7×√3)-In surface using a ³He-based low-temperature scanning tunneling microscope. Zero-bias conductance images taken over a large surface area reveal that vortices are trapped at atomic steps after magnetic fields are applied. The crossover behavior from Pearl to Josephson vortices is clearly identified from their elongated shapes along the steps and significant recovery of superconductivity within the cores. Our numerical calculations combined with experiments clarify that these characteristic features are determined by the relative strength of the interterrace Josephson coupling at the atomic step.

Stable Skyrmions in SU(2) gauged Bose-Einstein condensates.

We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions are physically understandable with the concept of the helical modulation in a unified way. These topological objects might potentially be realizable in two-component Bose-Einstein condensates experimentally.