Fresnel aperture diffraction: a phase-sensitive probe for superconducting pairing symmetry

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 $\mathrm{\Delta }(-k_x,{\mathbf{k}}_{\parallel })=\mathrm{\Delta }(k_x,{\mathbf{k}}_{\parallel })$ with $k_x$ and ${\mathbf{k}}_{\parallel }$ respectively the normal and parallel component of electron Fermi wavevector, quasiparticle FSAD pattern developed at the image plane is zeroth-order minimum if $k_{x}x=n\pi$ ($n$ is an integer and $x$ is SC layer thickness). In contrast, if $\mathrm{\Delta }(-k_x,{\mathbf{k}}_{\parallel })=-\mathrm{\Delta }(k_x,{\mathbf{k}}_{\parallel })$, the corresponding FSAD pattern is zeroth-order maximum. Observable consequences are discussed for iron-based superconductors of complex multi-band pairings.