Quartet formation at (100)/(110) interfaces of d-wave superconductors

Across a faceted (100)/(110) interface between two $d_{x^2-y^2}$-superconductors the structure of the superconducting order parameter leads to an alternating sign of the local Josephson coupling. Describing the Cooper pair motion along and across the interface by a one-dimensional boson lattice model, we show that a small attractive interaction between the bosons strongly enhances their binding at the interface. As a consequence we propose that electrons tunnel in quartets across an interface with a staggered sequence of 0- and $\pi$-junction contacts. We connect this finding to the recently observed $h/4e$ oscillations in bicrystalline (100)/(110) SQUIDs of cuprate superconductors.