Abstract
Interplay between superconductivity, spin-orbit coupling and magnetic field can lead to realisation of the topologically non–trivial states which in finite one dimensional nanowires are manifested by emergence of a pair of zero-energy Majorana bound states. On the other hand, in two dimensional systems the chiral edge states can appear. We investigate novel properties of the bound states in a system of mixed dimensionality, composed of one-dimensional nanowire connected with two-dimensional plaquette. We study this system, assuming either its part or the entire structure to be in topologically non–trivial superconducting state. Our results show delocalisation of the Majorana modes, upon leaking from the nanowire to the plaquette with some tendency towards its corners.
Highlights
We have investigated quasiparticle spectra of the hybrid system, comprising the 1D-nanowire attached to the 2D-plaquette, both proximitized to the s-wave superconductor
Selfconsistent numerical determination of the quasiparticle spectra has revealed, that under such circumstances the zero-energy Majorana quasiparticles would be (i) localised near the ends of 1D-nanowire or (ii) one of them would leak into the plaquette region
For the latter case we have inspected the spatial profile of the delocalised Majorana mode and found its signatures distributed along boundaries of the 2D-plaquette, with some preference towards its corners
Summary
The first term describes the kinetic energy:. The chemical potential μi can be tuned in-situ by some external gate voltage. Accounts for the proximity induced on-site pairing, where Δ is the uniform energy gap in the system. Where σi are the Pauli matrices and λ stands for the Rashba potential. Since the nanowire is oriented along xaxis, only the second part of SOC term survives. Where γn, γn† are the new quasi-particle fermionic operators and uinσ, vinσ are the corresponding eigenvectors. From this transformation (4) we get the Bogoliubov–de Gennes (BdG) equations. Refer to probability of the n-th quasiparticle energy and spin σ to exist at i-th site of the system[61]
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