Andreev bound states at the interface of antiferromagnets and d-wave superconductors

We set up a simple transfer matrix formalism to study the existence of bound states at interfaces and in junctions between antiferromagnets and d-wave superconductors. The well-studied zero energy mode at the $\{110\}$ interface between an insulator and a $d_{x^2-y^2}$ wave superconductor is spin split when the insulator is an antiferromagnet. This has, as a consequence, that any competing interface induced superconducting order parameter that breaks the time reversal symmetry needs to exceed a critical value before a charge current is induced along the interface.