Superconducting phase interference effect in momentum space

Detecting the phases of the superconducting order parameter is pivotal for unraveling the pairing symmetry of superconducting electrons. Conventional methods for probing these phases have focused on macroscopic interference effects, such as the Josephson effect. However, at the microscopic level, phase interference effects within momentum space have remained elusive due to the inherent difficulty of extracting phase information from individual momentum points. By introducing the hybridization effect between a primary band and its replica bands arising from density wave orders or other interactions, we uncover a novel superconducting phase interference effect at the intersection points on the Fermi surfaces of these bands. This effect elucidates the remarkable anomalies recently observed in the single-particle spectral function through angle-resolved photoemission spectroscopy (ARPES) in $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi2212) superconductors. It can also emerge in twisted junctions of superconductors with coherent tunneling, offering an alternative framework for probing the relative superconducting phase through twisted superstructures.