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

Fresnel single aperture diffraction is proposed as a phase-sensitive probe for studying the pairing symmetry of a superconductor. It is shown that in case of gap symmetry $\Delta(-\mathbf{k})=\Delta(\mathbf{k})$ with wavevector ${\bf k}$ normal to the tunnelling junction of a superconducting film, the quasiparticle diffraction pattern developed at the image plane is zeroth-order minimum. In contrast, the corresponding diffraction pattern is zeroth-order maximum for the case of $\Delta(-\mathbf{k})=-\Delta(\mathbf{k})$. Observable consequences are discussed and proposed for studying the iron- arsenic based superconductor to which gap symmetry may be complicated as a result of multiple Fermi surface pairings.