Molecular Wires Acting as Coherent Quantum Ratchets

Lehmann, Jörg; Kohler, Sigmund; Hänggi, Peter; Nitzan, Abraham

doi:10.1103/physrevlett.88.228305

Cited by 159 publications

(208 citation statements)

References 25 publications

(39 reference statements)

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“…On the other hand, the continuous system considered is essentially different from the tight-binding molecular wire investigated in Ref. [6], and may thus apply to different experimental situations. Weak dissipation is even a favorable situation in our approach.…”

Section: Discussionmentioning

confidence: 99%

“…The interest has recently grown with the transfer of the problem in the quantum regime. There, the description of dissipative tunneling [2] presents a theoretical challenge which was tackled in relatively few works [3,4,5,6,7,8], while first experimental realizations were reported [9,10]. After the semiclassical work [3], further progress towards the theoretical description of quantum ratchets involved modeling in terms of tight-binding systems [4,5] or in terms of a molecular wire [6].…”

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confidence: 99%

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Quantum Brownian motion in ratchet potentials: Duality relation and its consequences

Peguiron

Grifoni

2006

Chemical Physics

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Quantum Brownian motion in ratchet potentials is investigated by means of an approach based on a duality relation. This relation links the long-time dynamics in a tilted ratchet potential in the presence of dissipation with the one in a driven dissipative tight-binding model. The application to quantum ratchets yields a simple expression for the ratchet current in terms of the transition rates in the tight-binding system.Keywords: Quantum dissipative systems; Quantum ratchets; Path inegrals methods Brownian motion in ratchet potentials [1] has attracted a lot of interest. One reason is the fact that ratchet systems, i.e. periodic structures with broken spatial symmetry, present the property of allowing transport under the influence of unbiased forces. The interest has recently grown with the transfer of the problem in the quantum regime. There, the description of dissipative tunneling [2] presents a theoretical challenge which was tackled in relatively few works [3,4,5,6,7,8], while first experimental realizations were reported [9,10]. After the semiclassical work [3], further progress towards the theoretical description of quantum ratchets involved modeling in terms of tight-binding systems [4,5] or in terms of a molecular wire [6]. Other available methods include perturbation theory [7] or a quantum Smoluchowski equation [8]. Most of these methods [3,4,5,8] are restricted to the regime of moderate-tostrong friction.The approach discussed in this article originates from works [11,12,13,14,15] on quantum Brownian motion in a tilted sinusoidal potential, which led to a duality relation for the mobility of the system considered with the one of a driven dissipative tight-binding model. This idea emerged first in Ref. [11], where the linear dc mobility at zero temperature was considered. In that work the interest was focused on the occurrence of a diffusion-to-localization transition in the system with increasing dissipation. These results were corroborated by means of renormalizationgroup methods [12]. The duality relation was extended to the nonlinear dc mobility at finite temperatures in Ref. [13], where an extensive physical discussion as well as important milestones of the proof were given. It was subsequently applied to the investigation of the current-voltage characteristic of small Josephson junctions [14]. Later, an identical duality relation for the linear ac mobility was obtained by a different approach in the frame of linear response [15]. In particular, that work went beyond the case of a strictly Ohmic dissipative bath considered in Ref. [13], and included the case of an Ohmic bath with finite cutoff frequency as well as sub and super-Ohmic baths. In Ref.[16], the formalism of Ref.[13] was generalized to arbitrary ratchet potentials, i.e., periodic potentials of arbitrary shape. Moreover, the duality relation was extended to the average position of the quantum particle at long time. In the present article, we give detailed proofs and discussion of these last results. The duality relation is obtained i...

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Quantum Brownian motion in ratchet potentials: Duality relation and its consequences

Peguiron

Grifoni

2006

Chemical Physics

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“…The laser irradiation induces a large current enhancement of several orders of magnitude and also can reduce the current noise level. The observation of these resonances could serve as an experimental starting point for the more challenging attempt of measuring quantum ratchet effects [7,8] or current switching by laser fields [9,10].…”

Section: Discussionmentioning

confidence: 99%

“…It is for example possible to induce by the laser field an oscillating current in the molecule which under certain asymmetry conditions is rectified by the molecule. This results in a directed electron transport even in the absence of any applied voltage [7,8]. Another theoretically predicted effect is the current suppression by the laser field [9,10] which offers the possibility to control both the average current and the current noise.…”

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confidence: 99%

Molecular Wires in Electromagnetic Fields

Kohler

Lehmann

Strass

et al. 2004

Advances in Solid State Physics 44

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Abstract. We investigate the role of external electromagnetic fields on the conduction properties of bridged molecular wires. In particular, it is analyzed quantitatively how resonant excitations of electrons enhance the dc current and, simultaneously, lower the noise level of the current. The results from an exact numerical treatment are in good agreement with those obtained within an approximation scheme applicable at resonances.Thirty years ago, Aviram and Ratner proposed in a seminal work [1] to build elements of electronic circuits-in their case a rectifier-with single molecules. In the present days their vision starts to become reality and the experimental and theoretical study of such systems enjoys a vivid activity [2][3][4]. Recent experimental progress has enabled reproducible measurements [5,6] of weak tunneling currents through molecules which are coupled by chemisorbed thiol groups to the gold surface of external leads.Typical energy scales in molecules are in the optical and the infrared regime, where basically all of the today's lasers operate. Hence, lasers represent a natural possibility to control atoms or molecules and also currents through them. It is for example possible to induce by the laser field an oscillating current in the molecule which under certain asymmetry conditions is rectified by the molecule. This results in a directed electron transport even in the absence of any applied voltage [7,8]. Another theoretically predicted effect is the current suppression by the laser field [9,10] which offers the possibility to control both the average current and the current noise.Since the considered frequencies lie below typical plasma frequencies of metals, the laser light will be reflected at the metal surface, i.e., it does not penetrate the leads. Consequently, we assume that the leads' bulk properties are essentially unaffected by the laser field-in particular each lead remains close to equilibrium. Thus, it is sufficient to consider the influence of the driving solely in the molecule Hamiltonian. In addition, the energy of infrared light quanta is by far smaller than the work function of a common metal, which is of the order of 5 eV. This prevents the generation of a photo current, which otherwise would dominate the effects discussed below. For a quantitative description of an experiment, it might be necessary to take into account also the influence of the laser on the leads.Most theoretical descriptions of the molecular conductivity in static situations are based on a scattering approach [11][12][13], or assume that the un-

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“…For a system for which the ac potential is spatially uniform in the driven region, the average current and the noise strength follow in the weak tunnelling limit already from the static conduction properties [21]. Especially for long wires, the master equation approach presented in [22,23] allows a more efficient numerical computation. The central idea behind this approach is to solve the coherent dynamics by means of a transformation into the basis given by the coherent Floquet states, i.e.…”

Section: Floquet Transport Theorymentioning

confidence: 99%

Controlling currents through molecular wires

Kohler

Lehmann

Hänggi

2003

Superlattices and Microstructures

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We investigate the possibility of controlling by means of external laser fields both the current through molecular wires and the corresponding noise properties. It is found that an appropriate off-resonant driving field reduces the coherent transport across the molecule resulting in a strong current suppression. The relative level of transport noise, characterized by a Fano factor, exhibits characteristic maxima and minima near regimes of current suppression. In a three-terminal configuration, the field allows one to steer the current selectively towards one terminal.

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Molecular Wires Acting as Coherent Quantum Ratchets

Cited by 159 publications

References 25 publications

Quantum Brownian motion in ratchet potentials: Duality relation and its consequences

Quantum Brownian motion in ratchet potentials: Duality relation and its consequences

Molecular Wires in Electromagnetic Fields

Controlling currents through molecular wires

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