2018/12/31 by Hong-Yi Xie, Alex Levchenko
Mathematics · Physics and Astronomy · #Berry connection and curvature #Bound state #Condensed matter physics #Geometric phase #Josephson effect #MAJORANA #Mathematics #Parity (physics) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Scattering #Superconductivity #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.99.094519
published as Phys. Rev. B 99, 094519 (2019) · 8+ pages, 6 figures
arxiv created 2019/03/23 · openalex publication_date 2019/03/26 · arxiv updated 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the Josephson effect in the multiterminal junction of topological superconductors. We use the symmetry-constrained scattering matrix approach to derive band dispersions of emergent subgap Andreev bound states in a multidimensional parameter space of superconducting phase differences. We find distinct topologically protected band crossings that serve as monopoles of finite Berry curvature. Particularly, in a four-terminal junction the admixture of 2\ensuremathπ and 4\ensuremathπ periodic levels leads to the appearance of finite-energy Majorana-Weyl nodes. This topological regime in the junction can be characterized by a quantized nonlocal conductance that measures the Chern number of the corresponding bands. In addition, we calculate current-phase relations, variance, and cross correlations of topological supercurrents in multiterminal contacts and discuss the universality of these transport characteristics. At the technical level these results are obtained by integrating over the group of a circular ensemble that describes the scattering matrix of the junction. We briefly discuss our results in the context of observed fluctuations of the gate dependence of the critical current in topological planar Josephson junctions and comment on the possibility of parity measurements from the switching current distributions in multiterminal Majorana junctions.