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Plasmons in One and Two Dimensions

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Springer Handbook of Surface Science

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter will provide an overview of the properties of low-dimensional plasmons, discussing particularly characteristic examples. We will start with two-dimensional sheet plasmons (Sect. 19.1), concentrating on the plasmonic properties of the system most widely investigated in the recent past, graphene. Further emphasis will be given to low-dimensional plasmons coupled to other electron gases, which leads to linearization in the form of acoustic surface plasmons, but also to crossover of dimensionality, depending on plasmonic wavelengths. Finally we turn to quasi-one-dimensional systems and their corresponding plasmons, and try at the end to solve the puzzle of broad loss peaks but still fairly large plasmonic lifetimes.

Plasmons in low-dimensional systems represent an important tool for coupling energy into nanostructures and the localization of energy on the scale of only a few nanometers. Contrary to ordinary surface plasmons of metallic bulk materials, the dispersion of low-dimensional plasmons goes to zero in the long wavelength limit, thus covering a broad range of energies from terahertz to near-infrared, and from mesoscopic wavelengths down to those of just a few nanometers. Using specific, characteristic examples, we first review the properties of plasmons in two-dimensional (2-D) metallic layers from an experimental point of view. As demonstrated, tuning of their dispersion is possible by changes in charge carrier concentration in the partially filled 2-D conduction bands, but for a relativistic electron gas such as in graphene, only in the long wavelength limit. For short wavelengths, on the other hand, the dispersion turns out to be independent of the position of the Fermi level with respect to the Dirac point. A linear dispersion, seen under the latter conditions in graphene, can also be obtained in nonrelativistic electron gases by coupling between 2-D and 3-D (three-dimensional) electronic systems. As a well-investigated example, we discuss the acoustic surface plasmons in Shockley surface states, coupled with the bulk electronic system. Also, the introduction of anisotropy, e. g., by regular arrays of steps, seems to result in linearization (and to partial localization of the plasmons normal to the steps, depending on wavelengths). In quasi-one-dimensional (1-D) systems, such as arrays of gold chains on regularly stepped Si surfaces, only the dispersion is 1-D, whereas the shape and slope of the dispersion curves are dependent on the 2-D distribution of charge within each terrace and on coupling between wires on different terraces. In other words, the form of the confining quasi-1-D potential enters directly into the 1-D plasmon dispersion and offers new opportunities for tuning.

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Acknowledgements

It is a pleasure to acknowledge the experimental contributions of the groups in Hannover and in Genova to several parts of this work, in particular by T. Block, U. Krieg, T. Lichtenstein, L. Savio, M. Smerieri and M. Rocca. We also strongly benefited from collaborations and discussions with the theory group at DIPC, San Sebastian, Spain, in particular by the collaboration with V.M. Silkin. Financial support for this work by the Deutsche Forschungsgemeinschaft, mainly through FOR1700 and project Pf238/28, is gratefully acknowledged.

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Authors and Affiliations

  1. Festkörperphysik (Solid State Physics), ATMOS, Leibniz Universität Hannover, Hannover, Germany

    Herbert Pfnür

  2. Institut für Physik, Technische Universität Chemnitz, Chemnitz, Germany

    Christoph Tegenkamp

  3. Dipt. di Fisica, Università di Genova and IMEM-CNR Unità di Genova, Genova, Italy

    Luca Vattuone

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  1. Herbert Pfnür
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  2. Christoph Tegenkamp
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Correspondence to Herbert Pfnür .

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Editors and Affiliations

  1. Dipt. di Fisica, Università di Genova, Genova, Italy

    Mario Rocca

  2. Department of Physics, University of Central Florida, Orlando, FL, USA

    Talat S. Rahman

  3. Dipt. di Fisica, Università di Genova and IMEM-CNR Unità di Genova, Genova, Italy

    Luca Vattuone

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Pfnür, H., Tegenkamp, C., Vattuone, L. (2020). Plasmons in One and Two Dimensions. In: Rocca, M., Rahman, T.S., Vattuone, L. (eds) Springer Handbook of Surface Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-46906-1_19

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