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2Physics Quote:
"Today’s most precise time measurements are performed with optical atomic clocks, which achieve a precision of about 10-18, corresponding to 1 second uncertainty in more than 15 billion years, a time span which is longer than the age of the universe... Despite such stunning precision, these clocks could be outperformed by a different type of clock, the so called “nuclear clock”... The expected factor of improvement in precision of such a new type of clock has been estimated to be up to 100, in this way pushing the ability of time measurement to the next level."
-- Lars von der Wense, Benedict Seiferle, Mustapha Laatiaoui, Jürgen B. Neumayr, Hans-Jörg Maier, Hans-Friedrich Wirth, Christoph Mokry, Jörg Runke, Klaus Eberhardt, Christoph E. Düllmann, Norbert G. Trautmann, Peter G. Thirolf
(Read Full Article: "Direct Detection of the 229Th Nuclear Clock Transition"

Sunday, July 15, 2012

Direct Imaging of Plasmons in Graphene

(From Left to Right) Zhe Fei, Aleksandr S. Rodin, Michael M. Fogler, Dimitri N. Basov

Zhe Fei1, Aleksandr S. Rodin2, Michael M. Fogler1, Dimitri N. Basov1,

1Department of Physics, University of California, San Diego, USA
2Physics Department of Boston University, Boston, USA

Plasmonics is an emerging field, stemming from electronics and nanophotonics. At its heart lies plasmons—collective electronic oscillations where electrons in the system bunch up and spread out as a group. This rapidly developing technology enables localization and manipulation of electromagnetic energy at the nanometer length scale [1,2]. Applications of plasmonics are numerous and include such diverse examples as stained glass coloring, imaging nanoscopy, photovoltaics, metamaterials, optoelectronic devices, medical sensing and so on [3,4]. In addition, plasmonic technology holds promise for future applications in ultrafast information processing and transformation optics [5,6].

Plasmonic materials with high tunability and nano-scale confinement are required to fabricate high-speed devices with functionalities mimicking current state-of-the-art electronics. However, presently used plasmonic materials—noble metals and doped semiconductors—are not easily tunable. In fact, only limited plasmon tunablilties were reported before in sophisticated metal nanostructures or metamaterials. Graphene, on the other hand, is predicted to be capable of carrying gate-tunable surface plasmons in a wide frequency range with high confinement and low losses [7]. Recently, spectroscopic studies of graphene nanostructures verified the existence of plasmon resonances and their gate tunablilties in the terahertz and infrared frequencies [8,9]. Nevertheless, all the other essential properties of plasmons, such as confinement, damping, reflection, and interference, were still unknown.

Figure 1 Schematics of tip-launched plasmon waves close to the edge of graphene.

Our recent work [10], along with a similar one by Chen et al. [11], presents infrared nano-imaging results of graphene plasmons. In our experiments, we launched plasmons using a metalized tip illuminated by infrared light (Figure 1). The light polarizes the tip and this enables strong confined field close to the tip apex— the so-called “lighting-rod effect”. This electric field drives the electrons inside graphene back and forth, forming collective electronic oscillations known as plasmons. The plasmon waves propagate away like water ripples after throwing a stone into a pond [12].

Interestingly, we are able to detect plasmons using the same tip that produces them. While the tip launches plasmons, the plasmonic energy also enhances the polarization of the tip. The polarized tip is basically an antenna, so any enhancement in polarization of the tip will increase its far-field radiation that will be collected by a detector. Therefore, the signal we obtained is a direct measure of the plasmonic energy underneath the tip.

When the tip is close to the edge of graphene, the plasmons are able to travel to the edge, reflect from it, and, eventually, return back to the tip. In this case, the plasmonic energy underneath the tip is governed by both launched and reflected plasmon waves, which add up constructively when they are in phase or destructively when they are out of phase. Since their phase difference is solely determined by the distance between the tip and the edge of graphene, one would expect plasmonic energy underneath the tip to oscillate as the tip scans towards the edge. Final outcomes are images like Figure 2, where plasmon fringes parallel to the edge (or line defect) of graphene are observed. The distance between these fringes is well defined—exactly half the plasmon wavelength.

Figure 2: Imaging data that shows plasmonic fringe pattern close to the edge or line defect of graphene. The blue dashed line marks the edge of graphene. The green dashed line marks a line defect inside graphene. Scale bar, 100nm.

Figure 2 contains rich information about plasmon propagation, reflection, and interference. One can extract essential parameters, such as plasmon wavelength and damping rate, directly from it. We found that the plasmon wavelength of graphene is about 200 nm which is less than 2% of wavelength of incident light. Such strong confinement of electromagnetic energy hasn’t been achieved yet in infrared frequencies. The plasmon damping rate determined from Figure 2 is about 3 times higher than theoretical prediction. Detailed analysis of this observation sheds light to many-body effects in graphene.

Amazingly, the plasmon fringe pattern in Figure 2 evolves systematically when we tune the carrier density of graphene via gating. Instead of displaying all the images at different carrier densities, we show line profiles taken perpendicular to the plasmon fringes in these images as shown in Figure 3. One can see both the fringe width and amplitude increase with carrier density of graphene indicating that the plasmon wavelength and energy are tunable by gating.

Figure 3 A line profile taken perpendicular to the fringes in Figure 2 and its evolution with carrier density of graphene. Graphene is present at L>0 while SiO2 is present at L<0.

Our work, together with the work by Chen et al., shows for the first time to the world vivid images of graphene plasmons, which give us comprehensive understanding of graphene plasmons in both fundamental and application aspects. Two open questions come up after this work: (1) How far can graphene plasmons propagate? Is there any fundamental limit? (2) What is the potential application of tip-launched plasmons? The authors will try to answer these questions in their future work.

[1] Harry A. Atwater, "The promise of plasmonics". Scientific American, 296, 56–62 (2007). Abstract.
[2] Jon. A. Schuller, Edward S. Barnard, Wenshan Cai, Young Chul Jun, Justin S. White, Mark L. Brongersma, "Plasmonics for extreme light concentration and manipulation". Nature Materials, 9, 193–204 (2010). Abstract.
[3] Mark I. Stockman, "Nanoplasmonics: the physics behind the applications". Physics Today, 64, 39–44 (2011). Abstract.
[4] S.A. Maier,  "Plasmonics: Fundamentals and Applications", Ch. 4 (Springer, 2007).
[5] Prashant Nagpal, Nathan C. Lindquist, Sang-Hyun Oh and David J. Norris, "Ultrasmooth patterned metals for plasmonics and metamaterials". Science 325, 594–597 (2009). Abstract.
[6] Surbhi Lal, Stephan Link, Naomi J. Halas, "Nano-optics from sensing to waveguiding". Nature Photonics, 1, 641–648 (2007). Abstract.
[7] Marinko Jablan, Hrvoje Buljan, Marin Soljačić, "Plasmonics in graphene at infrared frequencies". Physical Review B, 80, 245435 (2009). Abstract.
[8] Zhe Fei, Gregory O. Andreev, Wenzhong Bao, Lingfeng M. Zhang, Alexander S. McLeod, Chen Wang, Margaret K. Stewart, Zeng Zhao, Gerardo Dominguez, Mark Thiemens, Michael M. Fogler, Michael J. Tauber, Antonio H. Castro-Neto, Chun Ning Lau, Fritz Keilmann, Dimitri N. Basov, "Infrared nanoscopy of Dirac plasmons at the graphene-SiO2 interface". Nano Letters, 11, 4701–4705 (2011). Abstract.
[9] Long Ju, Baisong Geng, Jason Horng, Caglar Girit, Michael Martin, Zhao Hao, Hans A. Bechtel, Xiaogan Liang, Alex Zettl, Y. Ron Shen, Feng Wang, "Graphene plasmonics for tunable terahertz metamaterials". Nature Nanotechnology, 6, 630–634 (2011). Abstract.
[10] Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, "Gate-tuning of graphene plasmons revealed by infrared nano-imaging", Nature, doi:10.1038/nature11253 (published online June 20, 2012). Abstract.
[11] Jianing Chen, Michela Badioli, Pablo Alonso-González, Sukosin Thongrattanasiri, Florian Huth, Johann Osmond, Marko Spasenović, Alba Centeno, Amaia Pesquera, Philippe Godignon, Amaia Zurutuza Elorza, Nicolas Camara, F. Javier García de Abajo, Rainer Hillenbrand, Frank H. L. Koppens, "Optical nano-imaging of gate-tunable graphene plasmons". Nature, doi:10.1038/nature11254 (published online June 20, 2012). Abstract.
[12] Michael Dyakonov and Michael Shur, "Shallow water analogy for a ballistic field effect transistor: New mechanism of plasma wave generation by dc current". Physical Review Letters, 71, 2465–2468 (1993). Abstract.

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