2021/08/18 by Faraei, Zahra, Jafari, S. A.
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #Superconductivity (cond-mat.supr-con)
paper · doi:10.48550/arxiv.2108.08182
We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions is of the Δs+iγ5Δ5 where Δs is the usual order parameter and Δ5 is the pseudo-scalar order parameter. After factoring out the U(1) phase eiϕ, this form of superconductivity admits yet additional complex structure in the plane of (Δs,Δ5). The polar angle χ in this plane dubbed chiral angle will be locked to the U(1) phase ϕ. We propose a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes ±Φ leads to Δ5=Δ0 sin(χ), where Δ0 is the superconducting order parameter of the SC layers, and the chiral angle χ=Φ/Φ0 is directly given by the flux Φ in units of the flux quantum Φ0=h/(2e). This can be used as a building block to construct a two-dimensional Josephson array. In this setup χ will be a background field defining a pseudoscalar Δ5 that can be tuned to desired configuration. While in a uniform background field Δ5 the dynamics of ϕ is given by standard XY model and its associated vortices, a \em staggered background ±Δ5 (or equivalently χ and χ+π in alternating lattice sites) creates a new set of minima for the ϕ field that will support half-vortex excitations. An isolated single synthetic "half-vortex" in the χ field in an otherwise uniform background will bind a ϕ-half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.