Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect

Abstract

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 sub-gap 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 2π and 4π 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.

Hydrodynamic Approach to Electronic Transport in Graphene

“…In graphene, the linearity of the Dirac spectrum once again plays an important role: as the speed of sound is much smaller than the electron velocity v g , leading-order scattering on acoustic phonons is kinematically suppressed. Consequently, scattering off the optical branch is usually considered [35,36]. In contrast, we argue that there is another process, the disorder-assisted electron-phonon scattering [37] or "supercollisions" [38][39][40][41], that is responsible for both quasiparticle recombination and energy relaxation.…”

Multiterminal Josephson Effect

“…Recently, the physics of multiterminal ABSs became the subject of numerous theoretical proposals . The first category of proposals explores the band topology of multiterminal Josephson junctions [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. These papers explore the structure of the ABS energies in the (N − 1)dimensional Brillouin zone, where the phase differences ϕ j − ϕ N play a role of quasimomenta.…”

“…These papers explore the structure of the ABS energies in the (N − 1)dimensional Brillouin zone, where the phase differences ϕ j − ϕ N play a role of quasimomenta. Theoretical studies of such multiterminal junctions predicted band structures with topologically protected states [9][10][11][12][13] and Weyl nodes [14][15][16][17]. In the second category of theoretical proposals, a junction of more than two topological superconductors is used to perform braiding operations on the zero-energy Majorana bound states [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], as these operations are essential for realization of topologically protected quantum computation [37].…”

Nodal Andreev spectra in multi-Majorana three-terminal Josephson junctions

“…This was recently proposed in Ref. [96,97] for multiterminal Josephson junctions consisting of 1D TSCs with a single MBS per edge. Such junctions have been shown to exhibit finite-energy Weyl crossings between the two lowest ABSs.…”