Higher-Order Topological Josephson Junctions from Conventional Superconductors

Higher-order topological superconductivity (HOTSC) in two dimensions hosts localized Majorana quasiparticles at the geometric corners of a system, yet its experimental realization has remained elusive. We propose a pathway to realize time-reversal-invariant HOTSC in a Josephson junction formed from conventional three-dimensional s-wave superconductors. The phase bias across the junction can effectively mimic unconventional Cooper pairing for the Andreev bound states, thus enabling higher-order topology. Using a dimensional-reduction framework, we establish a correspondence between inversion- and rotation-symmetry indicators of three-dimensional class AII normal bands and those of two-dimensional class DIII Andreev bound states within the same junction geometry. Guided by these indicators, we demonstrate higher-order topological Josephson behavior in several model systems. Our work underscores the versatility of Josephson junctions as a platform for engineering exotic superconducting phases and points to a new route toward crystalline topology in superconductors.