Master equation approach to transient quantum transport in nanostructures incorporating initial correlations

Yang, Pei; Lin, Chuan Yu; Zhang, Wei Min

doi:10.1103/physrevb.92.165403

Cited by 38 publications

(65 citation statements)

References 43 publications

(78 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, so far, the Heisenberg EOM approach has been only applied to simple noninteracting electronic systems, since it requires the inverse Laplace transform in order to calculate the dynamics of observables, typically a tedious and prohibitive task in molecular systems. Langevin equation techniques discussed in the literature for quantum transport are formulated for density matrix elements within the scope of the QME 63,131 . In contrast, the GIOM formulates the dynamics at the level of operators, rather than states, and it is nonperturbative.…”

Section: B Input-output Equations Of Motionmentioning

confidence: 99%

Generalized input-output method to quantum transport junctions. II. Applications

Liu

Segal

2020

Phys. Rev. B

View full text Add to dashboard Cite

The interaction of electrons with atomic motion critically influences charge transport properties in molecular conducting junctions and quantum dot systems, and it is responsible for a plethora of transport phenomena. Nevertheless, theoretical tools are still limited to treat simple model junctions in specific parameter regimes. In this work, we put forward a generalized input-output method (GIOM) for studying charge transport in molecular junctions accounting for strong electron-vibration interactions and including electronic and phononic environments. The method radically expands the scope of the input-output theory, which was originally put forward to treat quantum optic problems. Based on the GIOM we derive a Langevin-type equation of motion for molecular operators, which posses a great generality and accuracy, and permits the derivation of a stationary charge current expression involving only two types of transfer rates. Furthermore, we devise the so-called "Polaron Transport in Electronic Resonance" (PoTER) approximation, which allows to feasibly simulate electron dynamics in generic tight-binding models with strong electron-vibration interactions. To illustrate the breadth of applications of the GIOM-PoTER technique, we analyze prototype molecular junction models with primary and secondary vibrational modes. For short chains, the charge current reduces to known limits and reasonably agrees with exact numerical simulations (when available). For extended junctions the current displays a turnover from phonon-assisted to phonon-suppressed transport. Nevertheless, the onset of ohmic behavior requires extensions beyond the PoTER approximation. As an additional application, we consider a cavity-coupled molecule junction. Here we identify a cavity-induced suppression of charge current in the single-site case, and observe signatures of polariton formation in the current-voltage characteristics in the strong light-matter coupling regime. A critical understanding gained from the GIOM-PoTER scheme is that the single-site vibrationally-coupled model is deceptively simpler, and amenable to approximations than multi-site models. Therefore, benchmarking of methods should not be concluded with the single-site case. The work manifests that the input-output framework, which is normally employed in quantum optics, can serve as a powerful and feasible tool in the realm of electron transport junctions.

show abstract

Section: B Input-output Equations Of Motionmentioning

confidence: 99%

Generalized input-output method to quantum transport junctions. II. Applications

Liu

Segal

2020

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The Hamiltonian in Eq. (1) is quadratic, so it can be solved using many different methods; such as Heisenberg equations of motion, 9,12,[22][23][24]26,27,29,31,40,47,49 Feynman-Vernon path integrals, 37 extended quantum Langevin equations, 38 Green's functions, 8 and Keldysh Green's functions. 27,34,36,39,50 Here we use the Heisenberg equations of motion, which consist of a set of linear first-order differential equation, 9,12,[22][23][24]26,27,29,31,40,47,49 solved using a Laplace transform.…”

Section: Solution Via Laplace Transform Of Equations Of Motionmentioning

confidence: 99%

“…[27][28][29][30][31] It stops an atom's excited state fully decaying into the continuum, as recently observed in an NV centre in a waveguide, 32 and is predicted to lead to perfect subradiance. 33 The bound state (or localized mode) was extensively studied in the context of a quantum dot coupled to finite temperature fermionic reservoirs, 27,29,[34][35][36][37][38][39][40][41] exhibiting the same absence of decay, and even infinite-time oscillations. It also induces Landau-Zener-Stueckelberg physics in a slowly pumped dot.…”

Section: Introductionmentioning

confidence: 99%

Signature of the transition to a bound state in thermoelectric quantum transport

2019

View full text Add to dashboard Cite

We study a quantum dot coupled to two semiconducting reservoirs, when the dot level and the electrochemical potential are both close to a band edge in the reservoirs. This is modelled with an exactly solvable Hamiltonian without interactions (the Fano-Anderson model). The model is known to show an abrupt transition as the dot-reservoir coupling is increased into the strong-coupling regime for a broad class of band structures. This transition involves an infinite-lifetime bound state appearing in the band gap. We find a signature of this transition in the continuum states of the model, visible as a discontinuous behaviour of the dot's transmission function. This can result in the steady-state DC electric and thermoelectric responses having a very strong dependence on coupling close to critical coupling. We give examples where the conductances and the thermoelectric power factor exhibit huge peaks at critical coupling, while the thermoelectric figure of merit ZT grows as the coupling approaches critical coupling, with a small dip at critical coupling. The critical coupling is thus a sweet spot for such thermoelectric devices, as the power output is maximal at this point without a significant change of efficiency.

show abstract

“…The red data points are the inverse time for the dot occupation to decay to threshold (using the method reviewed in Refs. 35 and 36) that we set at 2% of its initial value, i.e. we plot the 1/t r that satisfies…”

Section: Adiabaticity and Band Gapsmentioning

confidence: 99%

Adiabatic almost-topological pumping of fractional charges in noninteracting quantum dots

2019

View full text Add to dashboard Cite

We use exact techniques to demonstrate theoretically the pumping of fractional charges in a single-level non-interacting quantum dot, when the dot-reservoir coupling is adiabatically driven from weak to strong coupling. The pumped charge averaged over many cycles is quantized at a fraction of an electron per cycle, determined by the ratio of Lamb shift to level-broadening; this ratio is imposed by the reservoir band-structure. For uniform density of states, half an electron is pumped per cycle. We call this adiabatic almost-topological pumping, because the pumping's Berry curvature is sharply peaked in the parameter space. Hence, so long as the pumping contour does not touch the peak, the pumped charge depends only on how many times the contour winds around the peak (up to exponentially small corrections). However, the topology does not protect against non-adiabatic corrections, which grow linearly with pump speed. In one limit the peak becomes a delta-function, so the adiabatic pumping of fractional charges becomes entirely topological. Our results show that quantization of the adiabatic pumped charge at a fraction of an electron does not require fractional particles or other exotic physics.

show abstract

Master equation approach to transient quantum transport in nanostructures incorporating initial correlations

Cited by 38 publications

References 43 publications

Generalized input-output method to quantum transport junctions. II. Applications

Generalized input-output method to quantum transport junctions. II. Applications

Signature of the transition to a bound state in thermoelectric quantum transport

Adiabatic almost-topological pumping of fractional charges in noninteracting quantum dots

Contact Info

Product

Resources

About