Field-free Josephson diode effect in a d-wave superconductor heterostructure

We study the superconductor/normal region/superconductor (S|N|S) Josephson junction formed using superconductors with d, d + id ', and d + is superconducting pairings. We show that the quality factor of the Josephson diode effect and its sign can be substantially tuned by the external magnetic field, the gate voltage, and the length of the junction for all three types of pairings. We also identify the conditions under which the anomalous Josephson and Josephson diode effects can appear in the junction by analyzing appropriate symmetries. In particular, by breaking a pi-rotation symmetry, we show how a large field-free Josephson diode effect can be realized even in the absence of spin-orbit coupling. We also study the role of edge states appearing in the case of chiral superconductor with d + id ' pairing. Our results demonstrate that the Josephson diode effect in a planar geometry can be used as a signature of unconventional superconducting pairings.