Sup. Mat. contains two video files showning motion of Wigner crystal to the left (wignerdiode1.mp4 diode flow) and to the right (wignerdiode2.mp4 practically no flow) The system parameters are (see also Appendix of the paper): Edc=-0.03 (force moves crystal left for wignerdiode1.mp4) and Edc=0.03 (force moves crystal right for wignerdiode2.mp4); other system parameters are: size 5x21 periodic cells in y and x axes, charge density $\nu=34/21$ (34 charges in 21 periods of x-axis, 5 charges in 5 periods in y-axis, it total 170 chardes with periodic boundary conditions), temperature $T/K_c=0.1$, $K_c=0.0462$ (critical amplitude for the Aubry transition in 1S), potential amplitude is $K=0.05$.