Fig. 2: Doubled magnetoelectric current in DAI.
From: Doubled Shapiro steps in a dynamic axion insulator Josephson junction
a Schematic for the instant charge polarization induced by a static magnetic field B along \(\hat{z}\)-direction at t1 = 0 and t2 = 2π/5ω, respectively. The charge polarization driven by AFMR oscillates between these two values in a doubled harmonic mode. The yellow and lime spheres represent positive and negative charges, respectively. b Unbalanced charge distribution Q(z) at t1 = 0 for a system with size Lz = 10 and Ly = 16. We use periodic boundary conditions along \(\hat{x}\)-direction. Here, Ax = 0.1 and the magnetic flux inside one unit cell is \({\Phi }_{0}=B{a}_{0}^{2}=0.005{\phi }_{0}\) with ϕ0 = h/e the magnetic flux quanta. c Increment of the charge distribution δQ(z) = Q(z, t)−Q(z, t = 0) at different times ranging from t = 0 to t = 0.5π. ω with an interval of 0.1π/ω at the same parameters as the system in (b). d Temporal evolutions of the increment of the charge polarization δP = [Q(1/2)−Q(−1/2)]/2 obtained in the adiabatic limit from the equilibrium Green’s functions provided in the “Methods” section (red inverted triangle) and the ensuing dynamic magnetoelectric current calculated from the time derivative of δP (blue triangle). The black dashed line shows the anticipated magnetoelectric current obtained from the time derivative of instant charge polarization given by Eq. (2). e Stem plot of the Fourier coefficients In.
