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arXiv:2001.11669 · Physical review. B./Physical review. B

Superconductor-like effects in an ac-driven normal Mott-insulating quantum dot array

Sanjeev Kumar, Vikram Tripathi

Published Dec 22, 2020• 1 citation
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Abstract

We study the current response of an ac-driven dissipative Mott-insulator system, a normal quantum dot array, using an analytical Keldysh field-theory approach. Deep in the Mott-insulator regime, the nonequilibrium steady state (NESS) response resembles a resistively shunted Josephson array with a nonequilibrium Mott-insulating to conductor transition as the drive frequency $\mathrm{\ensuremath{\Omega}}$ is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the $\ensuremath{\eta}$-pairing phase of a Josephson array with negative phase stiffness. However, in the presence of an additional dc field the signature of supercurrent---Shapiro steps---is completely absent. We interpret these properties as number-phase fluctuation effects shared with Josephson systems rather than superconductivity.

DOI
10.1103/physrevb.102.235147

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Journal of Physics Condensed Matter•Apr 7, 2021•0 citations
We study the current response of an ac-driven dissipative Mott-insulator system, a normal quantum dot array, using an analytical Keldysh field-theory approach. Deep in the Mott-insulator regime, the nonequilibrium steady state (NESS) response resembles a resistively shunted Josephson array with a nonequilibrium Mott-insulating to conductor transition as the drive frequency \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the \ensuremathη\ensuremath{\eta}\ensuremathη-pairing phase of a Josephson array with negative phase stiffness. However, in the presence of an additional dc field the signature of supercurrent---Shapiro steps---is completely absent. We interpret these properties as number-phase fluctuation effects shared with Josephson systems rather than superconductivity.
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-N\mathcal{N}N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with N.\mathcal{N}.N. Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.
The combined action of a dc bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent nonequilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U(1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak-coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the ac Josephson effect and an ac voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net dc current, the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport, we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net dc current flowing against the applied dc bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied dc bias.
The combined action of a DC bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent non-equilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U (1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the AC Josephson effect and an AC voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net DC current the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net DC current flowing against the applied DC bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied DC bias.
We present a systematic study of the nonequilibrium steady states (NESS) in Mott insulators driven by dc or ac electric fields, based on the Floquet dynamical mean-field theory. The results are analyzed using a generalized tunneling formula for the current, which is reminiscent of the Meir-Wingreen formula and provides insights into the relevant physical processes. In the dc case, the spectrum of the NESSs exhibits Wannier-Stark (WS) states associated with the lower and upper Hubbard bands. In addition, there emerge WS sidebands from many-body states. Using the tunneling formula, we demonstrate that the tunneling between these WS states leads to peaks or humps in the induced dc current. In the ac case, we cover a wide parameter range of excitation frequencies and field strengths to clarify the crossover from field-induced tunneling behavior in the dc limit to nonequilibrium states dominated by multiphoton absorption in the ac limit. In the crossover regime, the single-particle spectrum is characterized by a coexistence of Floquet sidebands and WS peaks, and the current and double occupation exhibit a nontrivial dependence on the field strength. The tunneling formula works quantitatively well even in the ac case, and we use it to discuss the potential cooperation of tunneling and multiphoton processes in the crossover regime. The tunneling formula and its simplified versions also provide physical insights into the high-harmonic generation in Mott insulators.
In order to investigate photoinduced insulator-metal transitions observed in correlated electron systems, we propose a new theoretical method, where we combine a Floquet-matrix method for AC-driven systems with the dynamical mean-field theory. The method can treat nonequilibrium steady states exactly beyond the linear-response regime. We have applied the method to the Falicov-Kimball model coupled to AC electric fields, and numerically obtained the spectral function, the nonequilibrium distribution function and the current-voltage characteristic. The results show that intense AC fields indeed drive Mott-like insulating states into photoinduced metallic states in a nonlinear way.
Abstract The scrambling rate λ s , a measure of the early growth of decoherence in an interacting quantum system, has been conjectured to have a universal saturation bound, λ s ⩽ 2 πk B T / ℏ , where T is the temperature. This decoherence arises from the spread of quantum information over a large number of untracked degrees of freedom. The commonly studied indicator of scrambling is the out of time-ordered correlator (OTOC) of noncommuting quantum operators, in-turn related to generalized uncertainty relations, and reminiscent of the Lyapunov exponent of classically chaotic systems. From a practical measurement point of view, other quantities besides OTOCs, that are also sensitive to these generalized uncertainty relations, may capture the scrambling behavior. Here, using a large- N Keldysh field theory approach, we show that the nonequilibrium current response of a Mott insulator system consisting of a mesoscopic quantum dot array, when subjected to an electric field quench, reveals this phenomenon on account of number-phase uncertainty. Both ac and dc field quenches are considered. The passage from the initial Mott insulator phase with well-defined charge excitations, to the final nonequilibrium steady current state, is revealed in the transient current response that has Bloch-like oscillations. We find that the amplitude of these oscillations decreases at the universal rate, 2 πk B T / ℏ , associated with fast scramblers. Our Mott insulator model provides a new example of a fast scrambler in addition to the known ones such as extremal black holes and the Sachdev–Ye–Kitaev (SYK) model.