Observing Majorana bound states of Josephson vortices in topological superconductors

Abstract

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain nonconventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.

Microwave transitions as a signature of coherent parity mixing effects in the Majorana-transmon qubit

“…The operators satisfy g y i ¼ g i and {g i ,g j } ¼ d ij . The properties of the device are determined by the interplay of the Josephson coupling E J , the charging energy E C , the coupling E M between the Majorana excitations and the superconducting phase difference j 18,20,[35][36][37][38][39][40] . The Hamiltonian for the hybrid junction is…”

Quantum information sharing between topologically distinct platforms

“…Hence, the accumulated phase can be adjusted to ∆θ = π/2 (mod π). With the estimated value of the bare coupling strength m 0 ∼ 0.025 meV and the typical edge velocity v m ∼ 10 5 m/s, [35] the accumulated phase is estimated to be ∆θ ∼ ∆x × 10 6 µm −1 . This implies that ∆x should be of order 1 − 2 µm in order to have ∆θ = π/2.…”

“…1, is a direct consequence of the fact that p x ± ip y superconductors are in two distinct topological superconducting phases. As both p x ± ip y superconductor are fully gapped in the bulk, these chiral Majorana edge states are the lowest energy degrees of freedom at the domain wall and are described by the Hamiltonian [35] …”

Majorana Fermions and Topology in Superconductors

“…A simple example is a class D topological superconductor attached to a single metallic lead (Fig.6). A more sophisticated approach proposed by Grosfeld and Stern 182) is to utilize the interplay between the Aharonov-Bohm effect and Aharonov-Casher effect.…”