Bulk disorder in the superconductor affects proximity-induced topological superconductivity

Abstract

We investigate effects of ordinary nonmagnetic disorder in the bulk of a superconductor on magnetic adatom-induced Shiba states and on the proximity-induced superconductivity in a nanowire tunnel-coupled to the bulk superconductor. Within the formalism of self-consistent Born approximation we show that, contrary to the widespread belief, the proximity-induced topological superconductivity can be adversely affected by the bulk superconducting disorder even in the absence of any disorder in the nanowire (or the superconductor-nanowire interface) when the proximity tunnel-coupling is strong. In particular, bulk disorder can effectively randomize the Shiba state energies. In the case of a proximate semiconductor nanowire, we numerically compute the dependence of the effective disorder and pairing gap induced on the wire as a function of the semiconductorsuperconductor tunnel coupling. We find that the scaling exponent of the induced disorder with respect to coupling is always larger than that of the induced gap, implying that at weak coupling, the proximity induced pairing gap dominates whereas at strong coupling the induced disorder dominates. These findings bring out the importance of improving the quality of the bulk superconductor itself (in addition to the quality of the nanowire and the interface) in the experimental search for solid state Majorana fermions in proximity-coupled hybrid structures and, in particular, points out the pitfall of pursuing strong coupling between the semiconductor and the superconductor in a goal toward having a large proximity gap. In particular, our work establishes that the bulk superconductor in strongly-coupled hybrid systems for Majorana studies must be in the ultra-clean limit, since otherwise the bulk disorder is likely to completely suppress all induced topological superconductivity effect.

Disorder robustness and protection of Majorana bound states in ferromagnetic chains on conventional superconductors

“…This is remarkable, especially considering the dramatic disorder vulnerability of the Yu-Shiba-Rusinov (YSR) states [28][29][30] created by single magnetic impurity. 24 More specifically, by performing self-consistent calculations also taking into account the effect of disorder on the superconducting state, we find that the MBS exist and are stable as long as the surrounding (conventional s-wave) SC shows only moderate signs of inhomogeneity. Thus simply measuring the local density of states (LDOS) in the surrounding SC gives a very good prediction of the MBS disorder stability.…”

“…They also have the added benefit of keeping the effective chemical potential constant in the whole sample, which leads to better control of the topological phase. For comparison we here also report results for a single type of impurity, such that the chemical potential is changed by a fixed amount δµ i = w, but only on randomly selected sites with a fixed disorder concentration n. This type of disorder has been considered for topological superconducting nanowires 24 but not, to the best of our knowledge, for magnetic impurity chains deposited on a superconducting surface. Figure 11 show the results for two chains W 18 and W 28 using the same parameters as in Fig.…”

Transport signatures of topological superconductivity in a proximity-coupled nanowire

“…There has been significant discussion of the importance of treating the parent superconductor explicitly when analyzing the proximity effect theoretically, as the proximity coupling can strongly renormalize the bulk properties of the nanowire. 28,[41][42][43][44][45][46][47][48][49] As the experimentally achievable coupling strength continues to increase, it becomes more important to understand the effect of the parent superconductor on the transport properties of the nanowire as well.…”

Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

“…Recently, it was suggested that disorder in the underlying superconductor may lead to variation in this parameter [36]. In addition, variation of the exchange coupling J , originating from different microscopic coupling configurations between the atom and the substrate, will also translate into variation of α.…”

“…Since the early work on the subject [30][31][32][33], the effects of disorder in the nanowire systems [34] and Kitaev's toy model [35] have been studied extensively. However, the special properties of magnetic chains have received relatively little attention [36,37].…”