Andreev Bound States at the Interface of Antiferromagnets and d-wave Superconductors

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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-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.