Tunable-φ Josephson junction with a quantum anomalous Hall insulator

We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current J flows without a phase difference across the junction theta. The phase shift phi appearing in the current-phase relationship J alpha sin(theta - phi) is proportional to the amplitude of Zeeman fields and depends on the direction ofZeeman fields. Aphenomenological analysis of the Andreev reflection processes explains the physical origin of phi. In a quantum anomalous Hall insulator, time-reversal symmetry and mirror-reflection symmetry are broken simultaneously. However, magnetic mirror-reflection symmetry is preserved. Such characteristic symmetry properties enable us to have a tunable phi junction with a quantum Hall insulator.