Majorana fermions on the quantum Hall edge

Abstract

Superconductivity and the quantum Hall effect are considered to be two cornerstones of condensed matter physics. The realization of hybrid structures where these two effects coexist has recently become an active field of research. In this work, we study a Josephson junction where a central region in the quantum Hall regime is proximitized with superconductors that can be driven to a topological phase with an external Zeeman field. In this regime, the Majorana modes that emerge at the ends of each superconducting lead couple to the chiral quantum Hall edge states. This produces distinguishable features in the Andreev levels and Fraunhofer patterns that could help in detecting not only the topological phase transition but also the spin degree of freedom of these exotic quasiparticles. The current phase relation and the spectral properties of the junction throughout the topological transition are fully described by a numerical tight-binding calculation. In pursuance of the understanding of these results, we develop a low-energy spinful model that captures the main features of the numerical transport simulations in the topological phase.

Nonequilibrium edge transport in quantum Hall based Josephson junctions

“…The fluxes and voltages which satisfy these constraints are precisely given by Eq. (20). When taking into account the mirror processes of transferring holes from the right to the left lead, the same result can be found, indicating the degeneracy between these two mechanisms.…”

“…Several theoretical works have studied the mechanisms by means of which an equilibrium supercurrent flow can be established in Josephson junctions bridged by one-way edge states [16][17][18][19][20]. The insulating nature of the bulk of the sample and the breaking of time-reversal symmetry causes the transfer of Cooper pairs to be realized via hybrid electron-hole edge modes that propagate chirally along the perimeter of the Hall bar [1,15].…”

Edge-induced pairing states in a Josephson junction through a spin-polarized quantum anomalous Hall insulator

“…Notice that in our setup the bulk of a QAHI is not influenced by the proximity effect, which may cause a topological phase transition to a topological superconductor phase [59][60][61]. In addition, we consider only conventional superconductors, while the Josephson junction between unconventional ones has been studied in [62]. This paper is organized as follows.…”