Tunable dynamics of a flake on graphene: Libration frequency

O. Üzengi Aktürk, E. Aktürk, H. H. Gürel, and S. Ciraci

Phys. Rev. B 95, 125413 – Published 9 March 2017

Abstract

In this paper we investigated the interaction between a graphene nanoflake anchored to the 2D graphene monolayer. This interaction is attractive but weak and is capable of setting a well defined registry in equilibrium. Rotational and linear displacements from equilibrium registry generate restoring forces, which can be controlled by external agents. Similar flakes can be self-assembled and can also execute simple harmonic motion as if a physical pendulum. Oscillation of a nanoflake about their equilibrium registries resulting in a characteristic libration frequency is predicted. This frequency depends on the size and geometry of the flake. Moreover, the libration frequency, as well as the electronic and magnetic properties of the flake+monolayer systems, can be tuned by a foreign molecule anchored to the flake, by electric charging and applied parallel and perpendicular electric and magnetic fields. When the sliding of the flake is combined with rotation, the friction force can be reduced dramatically. It is surprising that weak interaction can offer such features at nanoscale, which may offer potential applications. Our predictions are obtained by first-principles calculations based on density functional theory.

Received 7 April 2016
Revised 13 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.125413

Physics Subject Headings (PhySH)

Friction

Graphene

Density functional theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

O. Üzengi Aktürk^1,2,3, E. Aktürk^1,2,4,*, H. H. Gürel⁵, and S. Ciraci^2,†

¹Nanotechnology Application and Research Center, Adnan Menderes University, Aydın 09010, Turkey
²Department of Physics, Bilkent University, 06800 Ankara, Turkey
³Department of Electric and Electronic Engineering, Adnan Menderes University, 09100, Aydın, Turkey
⁴Department of Physics, Adnan Menderes University, 09100, Aydın, Turkey
⁵Department of Information Systems Engineering, Kocaeli University, 41380 Kocaeli, Turkey

^*ethem.akturk@adu.edu.tr
^†ciraci@fen.bilkent.edu.tr

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Vol. 95, Iss. 12 — 15 March 2017

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Images

Figure 1
(a) and (b) Atomic configurations of AA and AB registries of a graphene bilayer with the primitive unit cell and lattice translation vectors, $R_{1}$ and $R_{2}$ . Three translation vectors between these two registries are $r_{i}$ $(i = 1$ –3). (c) and (d) Top and tilted views of the atomic configuration of the graphene flake+monolayer system in AA and AB registries. Their calculated characteristic frequencies are also given. (e) The variation of interaction energy $E_{i} (z, θ)$ (in eV) having the barrier of $Q_{R_{A A}} = 180$ meV between two adjacent minima, torque $τ (z, θ)$ (in eV/rad) and angular force constant $κ (z, θ)$ (in eV/ ${rad}^{2})$ for $- π / 6 < θ < π / 6$ at the AA registry. (f) The variation of $E_{i} (z, θ)$ with $Q_{R_{A B}} = 75$ meV between two adjacent minima, $τ (z, θ)$ and $κ (z, θ)$ for $- π / 6 < θ < π / 6$ at the AB registry. The harmonic parts of $E_{i}$ corresponding to small angular displacement, linear restoring torque $τ$ , and constant $κ$ are shown by insets for both registries.
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Figure 2
Tuning the dynamics of rotational motion of a graphene flake on the graphene ML: (a) Calculated characteristic frequency of simple harmonic motion (SHM) of glycine $C_{2} H_{5} {NO}_{2}$ anchored to the flake. (b) Isosurfaces of $Δ ρ$ (see text) of the flake+monolayer graphene system charged by three electrons per supercell and its calculated frequency. (c) Top and side views of SHM of the flake under the perpendicular electric field $E_{⊥}$ of 1 V/Å along the $z$ direction and its calculated characteristic frequency. Isosurfaces of $Δ ρ$ indicates polarization induced by $E_{⊥}$ . Turquoise regions indicate electron depletion. Angular frequency $ω$ or frequency $f$ of the bare flake has changed in (a), (b), and (c).
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Figure 3
Tuning of the electronic structure of the flake+monolayer system by perpendicular $E_{⊥}$ , and lateral $E_{∥}$ , electric field: (a) The electronic structure of the flake+monolayer corresponding to $θ = 0$ and $E = 0$ . (b) The electronic structure in (a) is tuned by applying $E_{⊥} = 1.0$ V/Å at $θ = 0$ . (c) The electronic structure of the flake on an armchair nanoribbon for $θ = 0$ and $E = 0$ . (d) The electronic structure (c) is tuned at $θ = 0$ by applying $E_{∥} = 1.0$ V/Å. Bands are calculated by using the local basis set.
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Figure 4
Translation of a graphene flake on the graphene ML: Atomic configuration of the flake translating (sliding) from the minimum energy AB configuration to a maximum energy configuration AA (shown in the background). Variation of the total energy (shown by solid line) in the course of sliding from AB $\to$ AA $\to$ AB. The energy barrier is $Q_{T} = 163$ meV. Variation of the lateral force, $F_{L}$ (shown by dashed line) in the course of translation of the flake.
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