Driven disordered periodic media with an underlying structural phase transition

We study the nonequilibrium steady states of a crystal whose ground state can be tuned through a square-triangular transition. Driving such a system across a quenched random background yields a complex sequence of dynamical states. These include plastic flow states, anisotropic hexatics, dynamically stabilized triangle and square phases, and intermediate regimes of phase coexistence with anomalously slow dynamics. Such states should be observable in transport experiments on the mixed phase of several superconductors which exhibit related structural transitions. They may also be accessible in similar experiments on adsorbed monolayer colloids with tunable interactions.

Figure 1

Dynamical phase diagram in the $v_3\text{−}{F}_x$ plane. The phases are $A$, pinned triangle, $B$, pinned square, $C$, plastic flow or isotropic liquid, $D$, driven hexatic glass, $E$, moving triangle, $F$, moving square, and $G$, dynamical square-triangle coexistence. Two points with error bars show the boundary of $G$ for $v_3=6$, obtained by averaging over 24 disorder realizations, as an example. The boundaries for all other transitions are considerably sharper. The inset shows the center of mass velocity $v_{\mathit{c.m.}}$ as a function of the driving force $F_x$ as the force is increased (bold) and then decreased across the depinning transition. The right panel shows $S\left(\mathbf{q}\right)$ for the plastic flow state (i), driven hexatic glass (ii), moving triangle (iii), and moving square solid phases (iv) at $v_3=6.0$ and $F_x=10$, 20, 60, and 140, respectively. To obtain $S\left(\mathbf{q}\right)$, 50 independent configurations were used. The structure in (iv) reflects the presence of two mutually misoriented square crystallites.

Figure 2

(a) Shaking temperatures for a system with $v_3=6$ as a function of $F_x$ in the drive $\left(x\right)$ and transverse $\left(y\right)$ directions. These are obtained by averaging over 100 independent configurations as well as over 25 separate disorder realizations. For $F_x$ in the coexistence region, there is a significant enhancement of the shaking temperature in excess of the prediction of KV (Ref. 9). The lines represent fits to the KV form. (b) Hexatic correlation function $g_6\left(r\right)$ for $F_x=8$, 22, 25, and 40, each averaged over 50 independent configurations of a 10 000-particle system at $v_3=6$. The solid line indicates the universal behavior $g_6\left(r\right)\sim r^{-1∕4}$ at the liquid to hexatic transition. (c) $P\left(n\right)$ for $n=4,5,6,7$ (see text) vs $F_x$ averaged as in (a).

Figure 3

(Color online) Single particle configuration showing square-triangle coexistence at $F_x=107$. The particles are colored according to the number of neighbors computed from the Delaunay mesh $n=4$ [magenta (open) circle], 5 [green (filled gray) circle with white spot], 6 [blue (filled gray) circle], and 7 [orange (open) circle with black spot]. Particles with coordination 5 are present mainly in the interfacial region while those with 7 are associated with isolated dislocations.

Figure 4

(a) Power spectrum ${\tilde{P}}_{\varphi }\left(f\right)$ of current fluctuations in the moving triangle phase (thin line, $F_x=55$) and in the coexistence region (bold line, $F_x=100$), logarithmically binned and plotted for a range of frequencies below the washboard frequency. Current fluctuations in the coexistence region are enhanced, also showing a $1∕f$ decay at intermediate frequencies. (b) ${\tilde{P}}_n\left(f\right)$ for the fluctuations of the numbers of four-(◻), five-(엯), and six-(▵) coordinated particles in the coexistence region. The number of seven-coordinated particles (not shown) is vanishingly small. The straight line in both figures represents the $1∕f$ law.