Second-Order Josephson Effect in Excitonic Insulators

We show that in electron-hole bilayers with excitonic order arising from conduction and valence bands formed by atomic orbitals have different parities, nonzero interlayer tunneling leads to a second Josephson effect. This means the electrical current is related phase of parameter as $J = J_c \sin2\theta$ instead \sin \theta$, system has two degenerate ground states at $\theta=0, \pi$ can be switched an voltage pulse. When generalized three dimensional stack alternating planes or chains, AC effect implies electric field pulses perpendicular layers chains steer between states, making these devices ultrafast memories. The steering also applies insulator candidate Ta$_2$NiSe$_5$.