Nonequilibrium current-induced forces caused by quantum localization: Anderson adiabatic quantum motors

Lucas J. Fernández-Alcázar, Horacio M. Pastawski, and Raúl A. Bustos-Marún

Phys. Rev. B 99, 045403 – Published 2 January 2019

Abstract

In recent years, there has been an increasing interest in nanomachines. Among them, current-driven ones deserve special attention as quantum effects can play a significant role there. Examples of the latter are the so-called adiabatic quantum motors. In this paper, we propose using Anderson's localization to induce nonequilibrium forces in adiabatic quantum motors. We study the nonequilibrium current-induced forces and the maximum efficiency of these nanomotors in terms of their respective probability distribution functions. Expressions for these distribution functions are obtained in two characteristic regimes: the steady-state and the short-time regimes. Even though both regimes have distinctive expressions for their efficiencies, we find that, under certain conditions, the probability distribution functions of their maximum efficiency are approximately the same. Finally, we provide a simple relation to estimate the minimal disorder strength that should ensure efficient nanomotors.

Received 24 April 2018
Revised 12 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.045403

Physics Subject Headings (PhySH)

Anderson localization Quantum interference effects Quantum transport

1-dimensional systems Nanomechanical devices Nanostructures Nanowires

S-matrix method in transport Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Lucas J. Fernández-Alcázar¹, Horacio M. Pastawski¹, and Raúl A. Bustos-Marún^1,2,*

¹Instituto de Física Enrique Gaviola and Facultad de Matemática Astronomía, Física y Computación, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina
²Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina

^*Corresponding author: rbustos@famaf.unc.edu.ar

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Vol. 99, Iss. 4 — 15 January 2019

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Images

Figure 1
(a), (b) Examples of AAQMs. Panel (a) stands for a conductive wire coiled around a rotating piece with randomly placed charges. Panel (b) represents a multiwall nanotube where the inner nanotube is longer and the outer one has random impurities. The outer nanotube is supposed to be free to move along the guide given by the inner nanotube. Panel (c) schematizes the changes of the potential energy (characterized by $a$ and $Δ E$ ) sensed by the electrons inside the conductive wire of example (a) or the inner nanotube of example (b). There, a displacement of the potential by $δ x$ produces a phase change of $2 k δ x$ on the reflection coefficient.
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Figure 2
Probability distribution function $P (\tilde{ξ} | {\tilde{ξ}}_{0})$ of the reduced localization length, $\tilde{ξ} = ξ / L$ , calculated analytically (Analyt.) from Eq. (17) and numerically (Num.) from the Anderson's model with $ɛ / V = - 1.9, L = 10^{4} a$ , and $Δ E / V$ equal to 0.15 and 0.20, for $1 / ξ_{0} = 24$ and $1 / ξ_{0} = 43$ , respectively.
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Figure 3
CIFs in arbitrary units, $F$ , calculated numerical for the Anderson's model, Eqs. (14, 15, 16), as function of the Fermi energy $ɛ$ . The value $(ɛ - 2 V) / V = 0$ corresponds to the lower band-edge given by Eq. (16) (close to this region the system is expected to behave as a continuum). The red dashed line corresponds to the theoretical maximum value of nonequilibrium CIFs, $F = δ μ k_{F} / π$ . Grey solid lines show the force for different disorder realizations. The black solid line gives the average of the grey solid lines for $N = 20$ realizations. In the calculations, we used $L = 10^{4} a$ and $Δ E / V = 0.2$ .
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Figure 4
(a) Probability distribution function of the optimal efficiency $P (η_{op} | ν_{0})$ as function of the optimal efficiency $η_{op}$ and the parameter $ν_{0}$ [see discussion above Eq. (32)]. (b) Horizontal cuts of panel (a). (c) Probability of achieving a given interval of optimum efficiency, between $η_{op}$ and $η_{op} + δ η_{op}$ ( $δ η_{op} = 0.1$ ).
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Figure 5
Example of the potential experienced by the electron in a wire coiled around a rotor with a fixed charge. (a) Geometry considered. $R_{int}$ is the radius of the rotor, $R_{ext} - R_{int}$ is the minimum separation between the wire and the rotor, $θ$ is the angle that sets the position of the rotor, and $x^{*}$ is the coordinate along the wire. The example assumes a potential of the form $U \propto 1 / d$ , where $d$ is the distance between the fixed charge and the point along the wire (set by $x^{*}$ ). (b) Potential in arbitrary units as a function of the position along the wire ( $x^{*}$ ) and the position of the rotor ( $θ$ ). In the figure, we set $R_{int} = 0.99 R_{ext}$ .
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Figure 6
Comparison between $P ({〈T〉}_{x})$ and $P (T)$ . In the numerical simulations, we used $Δ E / V = 0.2, L = 10^{3} a$ , and $ɛ / V = 1.9$ . The vertical line is $- log [〈T〉] / 2$ , where $〈T〉$ is the average value of $T$ .
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