Supersymmetry in the Majorana Cooper-pair box

Abstract

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high-energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4π -periodic Majorana-Josephson coupling realizes supersymmetry for a certain characteristic ratio of the conventional Josephson to the Majorana-Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a nontrivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of a Majorana-Josephson coupling of the characteristic strength.

Exact ground states and topological order in interacting Kitaev/Majorana chains

“…The recent surge of interest in condensed-matter realizations of Majorana fermions includes the investigation of the effects of disorder [13][14][15][16][17] or dimerization 18 on the topological phase, the study of nanostructures possess-ing Majorana zero modes, [19][20][21][22][23] and strongly correlated systems showing Kondo physics. [24][25][26][27][28][29] Furthermore, generalizations to higher symmetries including supersymmetry [30][31][32][33][34] and parafermion modes were analyzed. 12,[35][36][37][38][39] Here we focus on interaction effects.…”

Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study

“…The MZM is stable against weak perturbations including the interaction and disorder. However, the generic interaction effect remains an open question, although lots of efforts have been made, which includes the exact solution [50],topological classification [32,51], entanglement entropy investigation [52], many-body MZM operator [53,54], supersymmetry approaches [55,56,57,34] and parafermion edge zero mode [58,59,60,61,62].…”

Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus

“…This proposal combines ideas of implementing supersymmetry in purely bosonic systems 16 with the quantummechanical supersymmetry that has recently been proposed for superconductors hosting fermionic Majorana bound states. 12 The only nonstandard component of our proposal is the Josephson rhombus. The Josephson rhombus is a junction between two superconductors that allows only tunneling of pairs of Cooper pairs.…”

“…Supersymmetry on the other hand does not simply forbid different states to couple but it makes sure that in each order of perturbation theory there is always a pair of terms canceling each other. 11,12 It is intriguing that the degeneracies of supersymmetric quantum mechanics occur by the same mechanism 11 that leads to a miraculous cancellation of divergences in supersymmetric field theories and makes supersymmetries an important tool of particle physics. 13 In trivial cases like the free particle 14 or the Jaynes-Cummings model, 15 however, the supersymmetric structure is irrelevant since the spectrum is exactly solvable.…”