Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

doi:10.1103/physrevlett.120.157701

Cited by 26 publications

(31 citation statements)

References 49 publications

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“…Notably, we found an example of a 'Markov-only' semigroup approximation that is non-perturbative in all parameters, yet simultaneously completely positive (CP) and trace-preserving (TP). It should be noted that this approximation relies only on the exact value of the stationary occupation n(∞) = 144,145 that are based on a mapping to the noninteracting limit studied here.…”

Section: Discussionmentioning

confidence: 99%

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

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To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.

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Section: Discussionmentioning

confidence: 99%

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

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“…As a testbed to benchmark the performance of a recently proposed non-adiabatic exchange-correlation potential, 11 we consider a single impurity Anderson model at finite temperature, as depicted in Fig 1(a). The Hamiltonian is given by…”

Section: A Modelmentioning

confidence: 99%

“…8,10 To improve the performance of TDDFT, recently, a non-adiabatic approximation for the Hartree-exchangecorrelation potential of the single-impurity Anderson model was derived by exploiting analogies to quantum transport theory. 11 The derivation is based on a firstorder perturbative treatment in the tunnel coupling between the impurity and the reservoir and uses a Markov approximation for the time propagation in the rate equation approach. It was shown that the resulting nonadiabatic functional improves over its adiabatic counterpart and yields the correct exponential decay of the density after a quench in the gate voltage, see Fig.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Anderson impurity model: Benchmarking a nonadiabatic exchange-correlation potential in time-dependent density-functional theory

2019

Self Cite

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In this comparative study we benchmark a recently developed non-adiabatic exchange-correlation potential within time-dependent density functional theory (TDDFT) (Phys. Rev. Lett. 120, 157701 (2018)) by (a) validating the transient dynamics using a numerically exact density matrix renormalization group approach as well as by (b) comparing the RC-time, a typical linear response quantity, to upto second order perturbation theory results. As a testbed we use the dynamics of the single impurity Anderson model. These benchmarks show that the non-adiabatic functional yields quantitatively accurate results for the transient dynamics for temperatures of the order of the hybridization strength while the TDDFT RC-times quantitatively agree with those from second-order perturbation theory for temperatures which are large compared to the hybridization strength. Both results are particularly intriguing given the relatively low numerical cost of a TDDFT calculation (at least compared to exact approaches).

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“…but smaller than γ L/R , the interacting spectral function is well approximated by [31,38] In particular for Θ = 0 the Friedel sum rule implies that the zero-bias interacting and KS conductances G αβ = ∂I α /∂V β and G s,αβ = ∂I α /∂V s,β are identical [39]. Since (repeated indices are summed over) (17) the zero-temperature xc voltages must fulfill ∂V µ,xc /∂I ν = 0 at zero currents.…”

Section: I-dft Potentials For the Anderson Modelmentioning

confidence: 99%

Nonequilibrium spectral functions from multiterminal steady-state density functional theory

et al. 2019

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Multi-terminal transport setups allow to realize more complex measurements and functionalities (e.g., transistors) of nanoscale systems than the simple two-terminal arrangement. Here the steady-state density functional formalism (i-DFT) for the description of transport through nanoscale junctions with an arbitrary number of leads is developed. In a three-terminal setup and in the ideal STM limit where one of the electrodes (the "STM tip") is effectively decoupled from the junction, the formalism allows to extract its non-equilibrium spectral function (at arbitrary temperature) while a bias is applied between the other two electrodes. Multi-terminal i-DFT is shown to be capable of describing the splitting of the Kondo resonance in an Anderson impurity in the presence of an applied bias voltage, as predicted by numerically exact many-body approaches. arXiv:1905.13070v1 [cond-mat.mes-hall]

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Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

Cited by 26 publications

References 49 publications

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Dynamics of the Anderson impurity model: Benchmarking a nonadiabatic exchange-correlation potential in time-dependent density-functional theory

Nonequilibrium spectral functions from multiterminal steady-state density functional theory

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