Fresnel aperture diffraction: A phase-sensitive probe of the pairing symmetry of a superconductor

Abstract

Fresnel single aperture diffraction (FSAD) is proposed as a phase-sensitive probe for pairing symmetry and Fermi surface of a superconductor. We consider electrons injected, through a small aperture, into a thin superconducting (SC) layer. It is shown that in case of SC gap symmetry $\ensuremath{\Delta}(\ensuremath{-}{k}_{x},{\mathbf{k}}_{\ensuremath{\parallel}})=\ensuremath{\Delta}({k}_{x},{\mathbf{k}}_{\ensuremath{\parallel}})$ with ${k}_{x}$ and ${\mathbf{k}}_{\ensuremath{\parallel}}$ respectively the normal and parallel components of the electron Fermi wave vector, the quasiparticle FSAD pattern developed at the image plane is zeroth-order minimum if ${k}_{x}x=n\ensuremath{\pi}$ ($n$ is an integer and $x$ is SC layer thickness). In contrast, if $\ensuremath{\Delta}(\ensuremath{-}{k}_{x},{\mathbf{k}}_{\ensuremath{\parallel}})=\ensuremath{-}\ensuremath{\Delta}({k}_{x},{\mathbf{k}}_{\ensuremath{\parallel}})$, the corresponding FSAD pattern is zeroth-order maximum. Observable consequences are discussed for iron-based superconductors of complex multiband pairings.