Topological phases of inhomogeneous superconductivity

Abstract

We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a one-dimensional system with magnetic impurities brought into close proximity to an s-wave superconductor. When the magnetic exchange energy is larger than the inter-impurity electron hopping we model the effective system as a chain of coupled Shiba states, while in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, that the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions.

Effects of the electrostatic environment on superlattice Majorana nanowires

“…In this case 36 , the topological phase diagram becomes more complex than for the uniformly covered nanowire (due to the presence of longitudinal minibands created by the periodicity of the system), and extends over a wider region in parameter space (to lower Zeeman fields and higher values of the chemical potential). Levine et al 36 considered a minimal 1D model for the nanowire superstructure, in a similar fashion to other previous studies [37][38][39][40] with related periodic structures. However, in the last couple of years it has been shown that the electrostatic environment and the three-dimensionality of these wires play an important role in all aspects concern-ing the trivial/topological phases and the appearance of MBSs.…”

Majorana fermions in magnetic chains

“…Despite the fact that several experiments have discovered zero energy end states in precisely these systems, the mechanism by which the states are conceived is yet in dispute. Firstly, it is unknown if the 1D system furnishing the MZMs at its ends is induced within the bulk superconductor [15,16,17,18,19,20,21,22,23,24] or realized within the atomic chain itself [25,26,27]. When the magnetic exchange between an atom and the quasiparticles in the bulk superconductor is sufficiently strong, a localized Yu-Shiba-Rusinov state [4,5,6] with energy within the superconducting gap is formed.…”

“…When the magnetic exchange between an atom and the quasiparticles in the bulk superconductor is sufficiently strong, a localized Yu-Shiba-Rusinov state [4,5,6] with energy within the superconducting gap is formed. A chain of such magnetic atoms creates many localized states that can hybridize and form a band, which can itself support MZMs at the ends of the chain within the superconductor [15,16,17,18,19,20,21,22,23,24]. Alternatively, if the atoms are sufficiently close together, their orbitals can overlap and the system appears as a 1D quantum wire with proximity-induced superconductivity [25,26,27].…”

Dimerization-induced topological superconductivity in a Rashba nanowire

“…Their robustness against various types of perturbations has been extensively explored, considering e.g. internal disorder [41][42][43][44][45][46][47], disordered superconducting substrates [48], noise [49], inhomogeneous spin-orbit coupling [50], thermal fluctuations [30,[51][52][53], reorientation of the magnetic field [54,55], and correlations [56,57].…”