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arXiv:1909.05671 · Physical review. B./Physical review. B

Critical exponents and fine-grid vortex model of the dynamic vortex Mott transition in superconducting arrays

Enzo Granato

Published Sep 16, 2019• 3 citations
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Abstract

We study the dynamic vortex Mott transition in two-dimensional superconducting arrays in a magnetic field with $f$ flux quantum per plaquette. The transition is induced by external driving current and thermal fluctuations near rational vortex densities set by the value of $f$ and has been observed experimentally from the scaling behavior of the differential resistivity. Recently, numerical simulations of interacting vortex models have demonstrated this behavior only near fractional $f$. A fine-grid vortex model is introduced, which allows us to consider both the cases of fractional and integer $f$. The critical behavior is determined from a scaling analysis of the current-voltage relation and voltage correlations near the transition and by Monte Carlo simulations. The critical exponents for the transition near $f=1/2$ are consistent with the experimental observations and previous numerical results from a standard vortex model. The same scaling behavior is obtained for $f=1$, in agreement with experiments. However, the estimated correlation-length exponent indicates that even at integer $f$, the critical behavior is not of mean-field type.

DOI
10.1103/physrevb.100.104517

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We study the dynamic vortex Mott transition in two-dimensional superconducting arrays in a magnetic field with fff flux quantum per plaquette. The transition is induced by external driving current and thermal fluctuations near rational vortex densities set by the value of fff and has been observed experimentally from the scaling behavior of the differential resistivity. Recently, numerical simulations of interacting vortex models have demonstrated this behavior only near fractional fff. A fine-grid vortex model is introduced, which allows us to consider both the cases of fractional and integer fff. The critical behavior is determined from a scaling analysis of the current-voltage relation and voltage correlations near the transition and by Monte Carlo simulations. The critical exponents for the transition near f=1/2f=1/2f=1/2 are consistent with the experimental observations and previous numerical results from a standard vortex model. The same scaling behavior is obtained for f=1f=1f=1, in agreement with experiments. However, the estimated correlation-length exponent indicates that even at integer fff, the critical behavior is not of mean-field type.
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to fff flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of fff. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near f=1/2f=1/2f=1/2 are consistent with the experimental observations. The same scaling behavior is observed near f=1/3f=1/3f=1/3. For a honeycomb array, although similar results are obtained for f=1/3f=1/3f=1/3, the transition is absent for f=1/2f=1/2f=1/2, consistent with an incommensurate vortex phase.
Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration ppp are considered, where pc{p}_{c}pc​ is the percolation threshold. For p>pcp>{p}_{c}p>pc​ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At pc{p}_{c}pc​ and finite temperature T,T,T, the results show the scaling behavior of a T=0T=0T=0 superconducting transition. The resistance is linear but vanishes for decreasing TTT with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted XY\mathrm{XY}XY model at pc.{p}_{c}.pc​.
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 (PT\mathcal{P}TPT) 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.
We calculate analytically the dynamic critical exponent zMC{z}_{\mathrm{MC}}zMC​, measured in Monte Carlo simulations for a vortex loop model of the superconducting transition, and account for the simulation results. In the weak screening limit, where magnetic fluctuations are neglected, the dynamic exponent is found to be zMC=3/2{z}_{\mathrm{MC}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2zMC​=3/2. In the perfect screening limit, zMC=5/2{z}_{\mathrm{MC}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2zMC​=5/2. We relate zMC{z}_{\mathrm{MC}}zMC​ to the actual value of zzz observable in experiments and find that $z\ensuremath{\sim}2$, consistent with some experimental results.
We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic fields. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below Tc{T}_{c}Tc​, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field, or system size is varied, and find a strong multiplicative logarithmic correction near Tc{T}_{c}Tc​, all of which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large-scale numerical simulations, and calculate the dynamic critical exponent zzz, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.
We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below TcT_cTc​, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field or system size is varied, and find a strong multiplicative logarithmic correction near TcT_cTc​, all which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large scale numerical simulations, and calculate the dynamic critical exponent zzz, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.