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arXiv:1708.00273 · Physical review. B./Physical review. B

Scaling universality at the dynamic vortex Mott transition

Martijn H. R. Lankhorst, Nicola Poccia, Martin Stehno, Alexey Galda, Himadri Barman, Francesco Coneri, Hans Hilgenkamp, A. Brinkman, Alexander A. Golubov, Vikram Tripathi, T. I. Baturina, V. M. Vinokur

Published Jan 17, 2018• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.97.020504

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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 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.
We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.
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 describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P)(\mathcal{P})(P) and time-reversal (T)(\mathcal{T})(T) operations. The dynamic Mott transition is identified as a PT\mathcal{PT}PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT\mathcal{PT}PT symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.
Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.
We present the first-ever multi-scale dynamical simulation of the temperature-controlled Mott metal-insulator transition in the Hubbard model. By integrating advanced electronic structure method and an efficient Gutzwiller/slave-boson solver into molecular dynamics simulations, we demonstrate that the transformation from a correlated metal to the Mott insulating phase proceeds via the nucleation and growth of the Mott droplets. Moreover, the time evolution of the Mott volume fraction is found to follow a universal transformation kinetics. We show that after an initial incubation period, the early stage of the phase transformation is characterized by a constant nucleation rate and an interface-controlled cluster growth mechanism, consistent with the classical theory developed by Kolmogorov, Johnson, Mehl, and Avrami. This is followed by a novel intermediate stage of accelerated phase transformation that is significantly different from the prediction of the classical theory. Moreover, the cluster-growth dynamics in this intermediate stage exhibits an unexpected avalanche behavior, similar to the Barkhausen noise in magnetization dynamics, even in the absence of quenched disorder. Detailed structural characterization further uncovers a universal correlation function for the transient mixed-phase states of the Mott transition. We also discuss implications of our findings for spatially resolved measurements of Mott metal-insulator transition obtained in recent nano-imaging experiments.