Josephson diodes induced by the loop current states

We study the diode effect of the supercurrent in the Josephson junctions with the loop current states as the tunneling barrier. The loop current states are realized by the Haldane model which preserves the inversion symmetry and thus forbids the diode effect. We demonstrate how the inversion symmetry can be broken in the monolayer and bilayer systems. In the monolayer system, inversion symmetry can be broken by either introducing a sublattice staggered potential for the Haldane model or introducing a modified Haldane model, and in the bilayer system, it can be broken by either staking the two layers with opposite current directions or by directly applying an electric field perpendicular to the layers. We further show that the diode efficiency can be tuned by the interlayer coupling and the strength of the electric field or interlayer voltage. Our results provide another route to realize the Josephson diode effect by breaking the time-reversal symmetry through the loop-current states.