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Topological Phases of Inhomogeneous Superconductivity

Silas Hoffman

We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions in one-dimensional systems brought into close proximity with an s-wave superconductor. When the magnetic exchange is larger than the Fermi energy of the bulk superconductor we model the system as a chain of coupled Shiba states. While in the opposite regime, the system is accurately described by a quantum wire. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange field, the system is a 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 field, 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.

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