Plasmonic excitations in tight-binding nanostructures

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Plasmonic excitations in tight-binding nanostructures

Rodrigo A. Muniz, Stephan Haas, A. F. J. Levi, and Ilya Grigorenko

Phys. Rev. B 80, 045413 – Published 15 July 2009

Abstract

We explore the collective electromagnetic response in atomic clusters of various sizes and geometries. Our aim is to understand, and hence to control, their dielectric response based on a fully quantum-mechanical description which captures accurately their relevant collective modes. The electronic energy levels and wave functions, calculated within the tight-binding model, are used to determine the nonlocal dielectric response function. It is found that the system shape, the electron filling, and the driving frequency of the external electric field strongly control the resonance properties of the collective excitations in the frequency and spatial domains. Furthermore, it is shown that one can design spatially localized collective excitations by properly tailoring the nanostructure geometry.

Received 20 March 2009

DOI:https://doi.org/10.1103/PhysRevB.80.045413

Authors & Affiliations

Rodrigo A. Muniz^* and Stephan Haas

Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484, USA

A. F. J. Levi

Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089-0082, USA

Ilya Grigorenko

Theoretical Division T-11, Center for Nonlinear Studies and Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^*rmuniz@usc.edu

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Vol. 80, Iss. 4 — 15 July 2009

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Images

Figure 1
(Color online) Longitudinal modes in atomic chains. (a) Decimal logarithm of the total induced energy (artificially offset) as a function of the frequency of an external electric field which is applied along the direction of the chain. The resonance peaks correspond to different modes. The arrows indicate the peaks for which the corresponding charge density profiles are shown in (b) and (c). (b) Induced charge density distribution for the lowest-energy mode at $ω = 0.73 t$ in the five-atom chain. (c) Induced charge density distribution for the highest-energy mode at $ω = 3.56 t$ in the six-atom chain. In (b) and (c) the arrows indicate the direction of the external applied electric field.Reuse & Permissions
Figure 2
(Color online) Transverse modes in coupled chain structures. (a) Logarithm of the total induced energy (artificially offset) as a function of the frequency of an external electric field applied transversely to the chain. The low-energy mode is central, the analog of a bulk plasmon, and the high-energy mode is located at the surface, the analog of a surface plasmon. The arrows indicate the peaks for which the corresponding charge density profiles are shown in the other insets. (b) Induced charge density distribution for the mode at $ω = 4.91 t$ in the three-atom double chain. (c) Induced charge density distribution for $ω = 5.41 t$ in the five-atom double chain. (d) Induced charge density distribution for $ω = 1.93 t$ in the six-atom double chain. In (b)–(d) the arrow indicates the direction of the external applied electric field.Reuse & Permissions
Figure 3
(Color online) Dependence on the direction of the applied electric field. (a) Logarithm of the total induced energy (artificially offset) as a function of frequency of external electric fields applied to a $4 \times 6$ rectangle at different incident angles. $θ = 0 °$ when the field is parallel to the four-atom edge and $θ = 90 °$ when it is parallel to the six-atom edge. The arrows indicate the peaks for which the corresponding charge density profiles are shown in the other insets. (b) Induced charge distribution for $θ = 0 °$ and $ω = 3.15 t$ . (c) Induced charge density distribution for $θ = 90 °$ and $ω = 2.15 t$ . In (b) and (c) the arrow indicates the direction of the external applied electric field.Reuse & Permissions
Figure 4
(Color online) Variation in the number of electrons. (a) Logarithm of the total induced energy as a function of the external electric field frequency. The number of electrons $N_{e l}$ in a nine-atom chain is varied. The arrows indicate the modes whose charge density profiles are shown in the other insets. (b) Induced charge density distribution for $N_{e l} = 1$ at $ω = 0.36 t$ . (c) Induced charge density distribution for $N_{e l} = 9$ at $ω = 0.53 t$ . In (b) and (c) the arrow indicates the direction of the external applied electric field.Reuse & Permissions
Figure 5
(Color online) Connection between two chains, $N_{e l} = 1$ . (a) Logarithm of the total induced energy as a function of the frequency of an external electric field applied to two eight-atom chains with an extra atom connecting them at the center. The arrows indicate the peaks for which the corresponding charge density profiles are shown in the other insets. (b) Induced charge density distribution for $ω = 0.28 t$ . (c) Induced charge density distribution for $ω = 4.36 t$ . In (b) and (c) the arrow indicates the direction of the external applied electric field.Reuse & Permissions
Figure 6
(Color online) Variation in the distance between neighbor atoms $a$ . Logarithm of the total induced energy as a function of the frequency of an external electric field applied to seven-atom chains with different spacings between atoms $a$ in units of the Bohr radius $r_{B}$ . The damping constant $γ$ is kept constant for all the different atomic spacings. In this figure the frequency unit is $t_{3}$ , the tight-binding hopping parameter for $a = 3 r_{B}$ . The thin red lines connect corresponding peaks for systems with different interatom spacings, indicating that the oscillator strength of the dominant low-energy mode decreases with decreasing spacing, whereas the peaks of the higher-energy modes increase.Reuse & Permissions

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