Moving smectic phase and transverse mode locking in driven vortex matter

Abstract

Out-of-equilibrium systems exhibit various dynamic phases with different degrees of order. A moving smectic phase with transverse periodicity is one of the ordered states, which is theoretically expected to be generic to driven two-dimensional systems. However, a comprehensive dynamic phase diagram, including the moving smectic phase, has not been obtained because of lack of suitable experimental methods. Here we study dynamic phases of driven vortex matter in an amorphous ${\mathrm{Mo}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ film by using two-step measurements of transient voltage in response to mutually perpendicular driving currents. We find dynamic orderings from the plastic flow to the anisotropic smectic flow and from the anisotropic smectic flow to the isotropic moving Bragg glass as a function of the current. Convincing evidence of the moving smectic phase is obtained from the first transverse mode locking (ML) with signals larger than those of longitudinal ML, indicating the higher transverse order than the longitudinal one. Transverse ML developed here is useful to detect the anisotropic periodicity in driven media.