Majorana-Weyl crossings in topological multiterminal junctions

Abstract

We analyze the Andreev spectrum in a four-terminal Josephson junction between one-dimensional topological superconductors in class D. We find that a topologically protected crossing in the space of three superconducting phase differences can occur between the two lowest Andreev bound states. This crossing can be detected through the transconductance quantization, in units of 2e 2 /h, between two voltage-biased terminals. Our prediction provides yet another example of topology in multiterminal Josephson junctions. We discuss possible realizations of such junctions with semiconducting crossed nanowires and with quantum-spin Hall insulators.

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.…”

Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime

“…A partial answer using the Kitaev spinless model was recently found in Ref. [28] for the case of a four-terminal device (see also [29]). Yet, a complete description of the transition from the s-wave to the p-wave regime within a spinful approach in the entire parameter space is still missing.…”

“…This is a necessary condition to obtain a unified topological phase diagram that could be experimentally tested. Even more, the calculation of the topological invariant associated with the ATC has so far been mainly based on the Chern numbers of the Andreev bound states (ABS) [12,16,[28][29][30] despite the fact that in many regions of the parameter space they cannot be disentangled from the continuum spectrum above the superconducting gap (which might also contribute to the ATC [15]).…”

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

“…See also Refs. [60,96]. By employing the Pauli matrices λ and κ, the so(3) generators read J 1 = (λ 1 κ 2 , λ 2 , λ 3 κ 2 )/2 and J 2 = (λ 2 κ 1 , κ 2 , λ 2 κ 3 )/2.…”

“…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.…”