Title: Tunable $φ$-Josephson junction with a quantum anomalous Hall insulator,
Abstract: 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 $\varphi$
appealing in the current-phase relationship $J\propto \sin(\theta-\varphi$) is
proportional to the amplitude of Zeeman fields and depends on the direction of
Zeeman fields. A phenomenological analysis of the Andreev reflection processes
explains the physical origin of $\varphi$. A quantum anomalous Hall insulator
breaks time-reversal symmetry and mirror reflection symmetry simultaneously.
However it preserves magnetic mirror reflection symmetry. Such characteristic
symmetry property enable us to have a tunable $\varphi$-junction with a quantum
Hall insulator.