Multi-terminal Josephson junctions as topological matter.

Roman-Pascal Riwar,Yuli V Nazarov,Manuel Houzet,Julia S Meyer

doi:10.1038/ncomms11167

Abstract

Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n−1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n−1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant.

Highlights

Topological materials and their unusual transport properties are at the focus of modern experimental and theoretical research
We show that multi-terminal Josephson junctions may be topologically nontrivial even if the superconducting leads are topologically trivial and no exotic materials are used to make the junction
By randomly generating scattering matrices from the circular orthogonal ensemble[28], we find that about 5% of scattering matrices give rise to four Weyl points (Supplementary Note 4)

Summary

Introduction

Topological materials and their unusual transport properties are at the focus of modern experimental and theoretical research. The junction itself may be regarded as an artificial topological material, which displays Weyl singularities, when the energy of the lowest ABS goes to zero at certain values of the superconducting phases such that the gap in the spectrum closes. The total phase-dependent energy of the junction reads E 1⁄4 ks(nks À 1/2)Ek, nks 1⁄4 0, 1 being the occupation of the state k with spin s.

Results

Conclusion