Majorana states in a p-wave superconducting ring

Abstract

The spectrum of excitations of the chiral superconducting ring with internal and external radii R i , R e (comparable with coherence length ξ) trapping a unit flux Φ 0 is calculated . We find within the Bogoliubov-deGennes approach that there exists a pair of precisely zero energy states when 2k ⊥ (R e − R i ) /π is integer (here k ⊥ is the momentum component in the disk plane while k ⊥ ξ > 1 ). They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon.

Zero-bias anomaly in p-wave superconductor

“…It was shown that a magnetic field can be used to tune the Andreev state energy precisely to zero. The ZES are not topologically protected, but is "quenched" there [30]. They can be further manipulated by pinning of the skyrmions on columnar defects and nanoholes.…”

Size constraints on a Majorana beam-splitter interferometer: Majorana coupling and surface-bulk scattering

“…The Corbino geometry has been studied for small disk size, in which case the same zero energy criterion is found in the limit 2mv 2 F µ ∆ 2 0 by imposing Dirichlet boundary conditions on the wavefunctions directly. 63 direction ϕ. The resulting scattering rates display an average absolute deviation |ε| (averaged over the Fermi energy range in Fig.…”

“…The Corbino geometry has been studied for small disk size, in which case the same zero energy criterion is found in the limit 2mv 2 F µ ∆ 2 0 by imposing Dirichlet boundary conditions on the wavefunctions directly. 63 Appendix D: Surface-Bulk Scattering with Screened Disorder…”

Tuning pairing amplitude and spin-triplet texture by curving superconducting nanostructures

“…Although the investigation of Majorana modes primarily focuses on single semiconducting wires, the path for Majorana detection and braiding often requires to employ more complex networks [16][17][18] or suggests alternative curved geometries, e.g. circular [19][20][21][22] and elliptical quantum rings [23].…”