Scaling universality at the dynamic vortex Mott transition

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the DMT based on the parity reflection-time reversal ($\mathcal{P}T$) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.

Figure 1

Experimental realization of charge-vortex duality for a Mott insulator. (a) A sketch of the device. The device consists of a square array of $270\times 270$ superconducting Nb islands on a conducting Au layer. On both sides of the array, a Nb bar is placed to ensure the current passes through the array homogeneously. The potential difference between the bars is measured as a function of the external current and an external magnetic field perpendicular to the plane of the array. (b) Scanning electron microscopy image of the sample.

Figure 2

Vortex dynamic Mott insulator-to-metal transition. (a) The temperature-current phase diagram of the vortex Mott states. The left and right panels present the transition line between the insulating and metallic states at $f<1$ and $f>1$, respectively. In the former, the elementary excitations are vortex holes, i.e., some of the traps lack vortices. In the latter, the elementary excitations are the excess vortices, i.e., some traps contain more than one vortex. (b) A set of differential resistance vs filling factor curves taken at different currents in the critical region at temperature $T=1.0\mathrm{K}$. The set corresponds to a currentwise crossing of the phase boundary. The currents increase from the bottom to the top; the range of currents is shown in the color legend. The black dotted line is the separatrix ${dV/dI|}_{I=I_0}, I_0=51.0\mu \mathrm{A}$, for $f>1$. The separatrix divides current ranges corresponding to the vortex Mott insulator (at $I<I_0, dV/dI$ bends down as $f\to 1$) and vortex Mott metal (at $I>I_0, dV/dI$ turning up as $f\to 1$). (c) A similar set of differential resistances vs filling factor curves, but taken at different temperatures and fixed current $I=50.5\mu \mathrm{A}$. The temperature increases from the bottom to the top and corresponds to the temperaturewise crossing of the phase boundary line. The black dotted line is the separatrix ${dV/dI|}_{T=T_0}, T_0=1.0\mathrm{K}$, for $f>1$. (d), (e) The differential magnetoresistances $dV/dI$ after subtracting the separatrices ${dV/dI|}_{I=I_0}$ and ${dV/dI|}_{T=T_0}$, respectively. The fanlike sets of curves visualize the dynamic Mott transition.

Figure 3

The critical region of the vortex dynamic Mott transition. The color plots of the measure of degree of nonlinearity $\mathcal{N}=dV/dI-V/I$ as a function of the filling factor $f$ and current at $T=1.0\mathrm{K}$ (a) and as function of $f$ and temperature at $I=90\mu \mathrm{A}$ (b). The color legend is the same for both plots.

Figure 4

Scaling analysis of the dynamic Mott transition. (a), (b) The log-log plots of ${[\partial (dV/dI)/\partial I]}_{I_0}$ and of ${[\partial (dV/dI)/\partial T]}_{T_0}$ vs $b$, both shown by symbols. The solid lines show the linear fits. (c) The semilog plot of the differential magnetoresistances $dV/dI$ after subtracting the separatrix ${dV/dI|}_{I=I_0}$ presents the same data as Fig. 2 as a function of the scaling variable $|I-I_0|/b^{2/3}$. The perfect collapse onto two generic scaling curves for $I<I_0$ and $I>I_0$ at ${\epsilon }_{\mathrm{I}}=2/3$ evidences the critical behavior of the current-driven vortex Mott transition. (d) The semilog plot of the differential magnetoresistances $dV/dI$ after subtracting the separatrix ${dV/dI|}_{T=T_0}$ presents the same data as Fig. 2 as a function of the scaling variable $|T-T_0|/b^{2/3}$. This illustrates the critical behavior of the temperature-driven crossing of the DMT transition line. (e) The plots from (c) (blue symbols) and (d) (red symbols) perfectly collapse on top of each other upon rescaling the abscissa of (d) by a factor $1/r$ with $r=1.5\times {10}^4\mathrm{K}/\mathrm{A}$, evidencing the identity of the ${\mathcal{F}}_{\mathrm{I}}$ and ${\mathcal{F}}_{\mathrm{T}}$ scaling functions defined by Eqs. (1) and (2). The inset shows the segment of the phase transition line. The blue and red arrows stand for current-driven and temperature-driven crossings of the transition line, respectively.