Graphene Tuned Terahertz Lasers

Thomas Folland (left) and Subhasish Chakraborty

Authors: Subhasish Chakraborty¹, Owen Marshall^1,2, Thomas Folland¹, Yong-Jin Kim², Alexander Grigorenko², Konstantin Novoselov²

Affiliation:
¹School of Electrical and Electronic Engineering, University of Manchester, UK.
²School of Physics and Astronomy, University of Manchester, UK.

Terahertz light falls between microwave and the infrared in the electromagnetic spectrum, and has the useful property that it can pass through many non-metallic materials, including packaging and clothing. Furthermore, a wealth of material information can be obtained using terahertz waves. As such practical terahertz sources and detectors could be used for security scanning, quality control and wireless communication [1]. High power terahertz waves can be generated by using quantum cascade lasers. These semiconductor chips contain multiple stacked quantum wells, carefully designed so that the conduction band is split into multiple energy levels in which terahertz light is generated [2].

Controlling quantum cascade lasers so that they produce tuneable, single frequency light is particularly difficult. In our earlier work we achieved all-electrical tuning in a terahertz laser over a discrete set of frequencies [3]. We did this by integrating a specially designed photonic lattice into the gold waveguide of the laser, which we dubbed an ‘aperiodic lattice laser’. Such lasers are compact (~1 cm²), powerful (~10 mW of power), and capable of working at a range of terahertz frequencies. However, to be a practical THz source, these lasers need to show continuous tuning over a wide range of THz frequencies.

Figure 1. Graphene integrated laser, showing (from bottom to top) the QCL (Quantum Cascade Laser) chip, the gold grating, the graphene layer, the polymer electrolyte and the top gate.

Enters graphene, a single atomic layer of carbon atoms. Graphene interacts strongly with terahertz waves [4] forming surface plasmons, coupled oscillations between light and the electrons in a material. In graphene the properties of these surface plasmons can be controlled by applying a gate potential to the surface of the device (similar to field effect transistors). This allows graphene to control the properties of a range of optical devices, such as modulators [5]. In our article [6] we integrate graphene into a terahertz quantum cascade laser, allowing us to use tuneable surface plasmons to control the frequency of laser light. We did this by depositing graphene and a polymer electrolyte gate on top of an aperiodic lattice laser (see figure 1). The aperiodic lattice consists of a series sub-wavelength slits, inside which graphene surface plasmons could be excited. When no gate potential was applied to the graphene, a surface plasmon formed inside the slit to suppress light scattering from the lattice. Conversely when a gate potential was applied to the graphene, the surface plasmon wavelength became larger than the slit width, and scattering was enhanced from the lattice. The effect of this change in scattering strength is to change the laser emission frequency, as defined by the properties of the lattice (see figure 2).

Figure 2. Tuning laser emission using a graphene. The figure shows the simulated electric field in each lattice site, and the laser emission spectrum before and after the introduction of a gate potential.

This result shows that graphene plasmons can be excited and used to tune terahertz lasers. Although currently a proof of concept, it is in principle possible to individually gate each slit, allowing us to engineer the laser output. Such control would make terahertz lasers significantly more appealing for real world applications. Furthermore, although the design approach used in our work is most suitable for terahertz lasers, they could in principle be applied to more conventional lasers in the infrared. This would offer an entirely different way of controlling the properties of laser systems.

References:
[1] A. Giles Davies, Andrew D. Burnett, Wenhui Fan, Edmund H. Linfield, John E. Cunningham, "Terahertz spectroscopy of explosives and drugs", Materials Today, 11, 18–26 (2008). Full PDF.
[2] Rüdeger Köhler, Alessandro Tredicucci, Fabio Beltram, Harvey E. Beere, Edmund H. Linfield, A. Giles Davies, David A. Ritchie, Rita C. Iotti, Fausto Rossi, "Terahertz semiconductor-heterostructure laser", Nature, 417, 156–9 (2002). Abstract.
[3] Subhasish Chakraborty, Owen Marshall, Chen Wei Hsin, Md. Khairuzzaman, Harvey Beere, David Ritchie, "Discrete mode tuning in terahertz quantum cascade lasers", Optics Express, 20, B306–14 (2012). Abstract.
[4] Alessandro Tredicucci, Miriam Serena Vitiello, "Device Concepts for Graphene-Based Terahertz Photonics", IEEE Journal for Selected Topics in Quantum Electronics, 20, 130–138 (2014). Full Article.
[5] A. N. Grigorenko, M. Polini, K. S. Novoselov, "Graphene plasmonics", Nature Photonics, 6, 749–758 (2012). Abstract.
[6] S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, K. S. Novoselov, "Gain modulation by graphene plasmons in aperiodic lattice lasers", Science, 351, 246–248 (2016). Abstract.

Optomechanical Coupling between a Multilayer Graphene Mechanical Resonator and a Superconducting Microwave Cavity

Left to Right: (top row) V. Singh, S. J. Bosman, B. H. Schneider, (bottom row) Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele.

Authors: 
V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, 
G. A. Steele

Affiliation:
Kavli Institute of NanoScience, Delft University of Technology, The Netherlands.

Introduction:

Mechanical resonators made from two dimensional exfoliated crystals offer very low mass, low stress, and high quality factor due to their crystalline structure [1]. These properties make them very attractive for application in mass sensing, force sensing, and exploring the quantum regime of motion by providing large quantum zero-point fluctuations over a small bandwidth. The most studied exfoliated crystal so far is graphene, where a considerable progress has been made in exploring its properties for mass sensing, study of nonlinear mechanics, and voltage tunable oscillators [2-9]. These properties also make graphene attractive for exploring the quantum regime of motion.

Past 2Physics articles by Andres Castellanos-Gomez and Gary A. Steele:

July 20, 2014: "Few-layer Black Phosphorus Phototransistors for Fast and Broadband Photodetection" by Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, Gary A. Steele, Herre S.J. van der Zant, Andres Castellanos-Gomez.

A possible route towards exploring the quantum regime of graphene motion is cavity optomechanics [10]. It has shown exquisite position sensitivity, enabled the preparation and detection of mechanical systems in the quantum ground state with conventional top-down superconducting mechanical resonators [11-18]. Therefore, a natural candidate for implementing cavity optomechanics with graphene resonator is to couple it to a high Q superconducting microwave cavity. However, coupling graphene resonators with superconducting cavities in such a way that both retain their excellent properties (such as their high quality factors) is technologically challenging. Using a deterministic dry transfer technique [19], we combine a multilayer graphene resonator to a high quality factor microwave cavity [20]. Although multilayer graphene has a higher mass than a mono-layer, it could be advantageous for coupling to a superconducting cavity because of its lower electrical resistance.

Results:

Device

To fabricate the superconducting cavities in coplanar waveguide geometry, we use an alloy of molybdenum and rhenium with superconducting transition temperature of 8.1 K. Using the dry transfer technique, we place a few layer thick graphene mechanical resonator near the coupler forming coupling capacitor for the cavity. Figure 1(a) shows a false color scanning electron microscope image of a device with a 10 nm thick multilayer graphene resonator coupled to a superconducting cavity. Figure 1(b) shows an equivalent schematic diagram with graphene resonator acting as a capacitor (C_g ) between the superconducting cavity (formed by L_sc and C_sc ) and the external microwave source. By cooling these cavities to very low temperatures (14 mK), we measured internal quality factor as high as 107,000.

FIG. 1: Coupling of a multilayer graphene mechanical resonator to a superconducting cavity. (a) A tilted angle scanning electron micrograph (false color) near the coupler showing 4 μm diameter multilayer (10 nm thick) graphene resonator (cyan) suspended 150 nm above the gate. (b) Schematic lumped element representation of the device with the equivalent lumped parameters as C_sc ≈ 415 fF and L_sc ≈ 1.75 nH.

Mechanical motion readout sensitivity

To the first order, the superconducting microwave cavity can be thought simply as motional transducer for the graphene resonator. To readout the motion of the graphene resonator, we inject a microwave near the cavity frequency given by

                                       
The motion of graphene resonator modulates the cavity frequency and hence its displacement gets imprinted on the phase of the reflected microwave signal from the cavity. By measuring the phase of the reflected signal (technically known as the homodyne detection), one can directly read the mechanical motion of the resonator [11]. The large quality factor of our cavity and its ability to sustain superconductivity with large number of the microwave photons enable us to measure the thermo-mechanical motion of the graphene resonator down to temperatures of 96 mK and a displacement sensitivity as low as 17 fm/√Hz.

Optomechanical coupling

In addition to detecting the motion of the graphene drum, we can also exert a force on the mechanical drum by using the radiation pressure of microwave photons trapped in the superconducting cavity. This force comes from the fact that light carries momentum: shining light from a flashlight at a piece of paper would in principle apply a force to it, pushing it away from the light source. The radiation pressure force that light exerts, however, is usually far too small to detect. Due to the tiny mass of the graphene sheet and the ability to detect small displacement, we could see the graphene sheet shaking in response to a "beat" set by the microwave light sent into the cavity.

By sending two microwave signals, a probe signal ω_p (near the cavity resonance frequency ω_c ) and another signal at ω_d (detuned by mechanical frequency ω_m , such that ω_d = ω_c +ω_m ), one can apply a a radiation pressure force on the mechanical resonator. This radiation pressure force beats at the mechanical resonance frequency, leading to coherent driven motion of the mechanical resonator, as shown schematically by process 1 in Figure 2(a). In presence of the significant optomechanical coupling, this coherent drive of the mechanical resonator down-converts the detuned drive photons exactly at the probe frequency (pink arrow) shown by process 2 in Figure 2(a). These two signals at probe frequency interfere with each other leading to a transmission window, appearing as a sharp peak in the cavity response, shown in Figure 2(b). This phenomena is known as "optomechanically induced transparency" (OMIT) and is a signature of the optomechanical coupling between the graphene mechanical resonator and the superconducting cavity [21-23]. As this effect rely on the coherent driven motion of the graphene mechanical resonator, the width of the transparency window is set by the mechanical resonator's linewidth as shown in the inset of Figure 2(b). Using the radiation pressure force driving, we measure the quality factor of the graphene resonator as high as 220,000.

FIG. 2: Optomechanically induced transparency (OMIT). (a) Schematic illustrate OMIT features in terms of the interference of the probe field (black arrow) with the microwave photons that are cyclically down- and then up- converted by the optomechanical interaction (pink arrow). (b) Measurement of the cavity reflection |S₁₁| in presence of sideband detuned drive tone. A detuned drive at ω_c+ω_m results in a window of optomechanically induced reflection (OMIR) in the cavity response. Inset: Zoom of the OMIR window. (c) Measurement of the cavity reflection |S₁₁| with a stronger detuned drive. At the center of the cavity response, the reflection coefficient exceeds 1, corresponding to mechanical microwave amplification of 17 dB by the graphene resonator.

By increasing the drive signal amplitude further, one can increase the strength of the optomechanical coupling. Using this, we make an amplifier in which microwave signals are amplified by the mechanical motion of the graphene resonator [16]. With a stronger detuned drive, we observed a microwave gain of 17 dB (equivalent to a photon gain of 50) as shown in Figure 2(c), before the nonlinear effects from the mechanical resonators come into play. Similarly, a different "beat" of the microwave photons (having ω_d = ω_c - ω_m ) allows one to store microwave photons into the mechanical motion of the resonator [24]. To this end we show a storage time up to 10 millisecond, which is equivalent to delay from a few hundreds of kilometer long coaxial cable.

The phenomena of OMIT also allow one to directly extract a quantity called "cooperativity" C without any fi t parameters. The quantity C is an important fi gure of merit in characterizing the optomechanical systems. For example, in sideband resolved limit (when mechanical frequency exceeds the cavity linewidth), the criteria for quantum-coherent regime can be simply written as C + 1 > n_th , where n_th is the average number of thermal phonon in the mechanical resonator. In our experiment, we have been able to achieve C = 8 close to the expected number of thermal phonon in the mechanical resonator at 14 mK, bringing this system close to the quantum coherent regime.

Summary and outlook:

In our work, we demonstrated the potential of exfoliated graphene crystal applied to form an optomechanical device, which so far have been realized using top-down technology. This opens up a new dimension to explore exfoliated two-dimensional crystals in optomechanical systems, and harnessing their unique properties such as extremely low mass and high quality factors. For future devices, two-dimensional superconducting exfoliated flakes could be of great interest for such applications. Superconducting cavity in our work is a very good detector for mechanical displacement with a bandwidth three orders of magnitude larger than the mechanical line-width. This would provide a new tool to study nonlinear restoring forces, nonlinear damping, and mode coupling in mechanical resonators from twodimensional crystals. The characterization of our device shows that in future by making little larger area mechanical resonators, devices operating in quantum regime can be easily realized, which can possibly be used as a memory element in a quantum computer. As many of the 2D crystals can be grown by chemical processes in large areas, they also hold the promise of scalability.

References:
[1] Andres Castellanos-Gomez, Vibhor Singh, Herre S.J. van der Zant, Gary A. Steele, "Mechanics of freely-suspended ultrathin layered materials". arXiv:1409.1173 [cond-mat] (2014).
[2] J. Scott Bunch, Arend M. van der Zande, Scott S. Verbridge, Ian W. Frank, David M. Tanenbaum, Jeevak M. Parpia, Harold G. Craighead, Paul L. McEuen, "Electromechanical resonators from graphene sheets". Science, 315, 490-493 (2007). Abstract.
[3] Changyao Chen, Sami Rosenblatt, Kirill I. Bolotin, William Kalb, Philip Kim, Ioannis Kymissis, Horst L. Stormer, Tony F. Heinz, James Hone, "Performance of monolayer graphene nanomechanical resonators with electrical readout". Nature Nanotechnology, 4, 861-867 (2009). Abstract.
[4] Vibhor Singh, Shamashis Sengupta, Hari S Solanki, Rohan Dhall, Adrien Allain, Sajal Dhara, Prita Pant, Mandar M Deshmukh, "Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators". Nanotechnology, 21, 165204 (2010). Abstract.
[5] Robert A. Barton, B. Ilic, Arend M. van der Zande, William S. Whitney, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "High, size-dependent quality factor in an array of graphene mechanical resonators". Nano Letters, 11, 1232{1236 (2011). Abstract.
[6] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson-Rae, A. Bachtold, "Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene". Nature Nanotechnology, 6, 339-342 (2011). Abstract.
[7] Xuefeng Song, Mika Oksanen, Mika A. Sillanpää, H. G. Craighead, J. M. Parpia, Pertti J. Hakonen, "Stamp transferred suspended graphene mechanical resonators for radio frequency electrical readout". Nano Letters, 12, 198-202 (2012). Abstract.
[8] Robert A. Barton, Isaac R. Storch, Vivekananda P. Adiga, Reyu Sakakibara, Benjamin R. Cipriany, B. Ilic, Si Ping Wang, Peijie Ong, Paul L. McEuen, Jeevak M. Parpia, Harold G. Craighead, "Photothermal self-oscillation and laser cooling of graphene optomechanical systems". Nano Letters, 12, 4681-4686 (2012). Abstract.
[9] Changyao Chen, Sunwoo Lee, Vikram V. Deshpande, Gwan-Hyoung Lee, Michael Lekas, Kenneth Shepard, James Hone, "Graphene mechanical oscillators with tunable frequency". Nature Nanotechnology 8, 923{927 (2013). Abstract.
[10] Markus Aspelmeyer, Tobias J. Kippenberg, Florian Marquardt, "Cavity optomechanics". arXiv:1303.0733 [cond-mat.mes-hall] (2013).
[11] C. A. Regal, J. D. Teufel, K. W. Lehnert, "Measuring nanomechanical motion with a mi- crowave cavity interferometer". Nature Physics, 4, 555-560 (2008). Abstract.
[12] J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, K. W. Lehnert, "Nanomechanical motion measured with an imprecision below that at the standard quantum limit". Nature Nanotechnology 4, 820-823 (2009). Abstract.
[13] T. Rocheleau, T. Ndukum, C. Macklin, J. B. Hertzberg, A. A. Clerk, K. C. Schwab, "Preparation and detection of a mechanical resonator near the ground state of motion". Nature, 463, 72-75 (2010). Abstract.
[14] J. D. Teufel, Dale Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, R. W. Simmonds, "Circuit cavity electromechanics in the strong-coupling regime". Nature, 471, 204-208 (2011). Abstract.
[15] J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, R. W. Simmonds, "Sideband cooling of micromechanical motion to the quantum ground state". Nature, 475, 359-363 (2011). Abstract.
[16] F. Massel, T.T. Heikkilä, J.-M. Pirkkalainen, S.U. Cho, H. Saloniemi, P.J. Hakonen, M.A. Sillanpää, "Microwave ampli fication with nanomechanical resonators". Nature, 480, 351-354 (2011). Abstract.
[17] Fredrik Hocke, Xiaoqing Zhou, Albert Schliesser, Tobias J Kippenberg, Hans Huebl, Rudolf Gross, "Electromechanically induced absorption in a circuit nano-electromechanical system". New Journal of Physics, 14, 123037 (2012). Abstract.
[18] T. A. Palomaki, J. D. Teufel, R. W. Simmonds, K. W. Lehnert, "Entangling mechanical motion with microwave fields". Science, 342, 710-713 (2013). Abstract.
[19] Andres Castellanos-Gomez, Michele Buscema, Rianda Molenaar, Vibhor Singh, Laurens Janssen, Herre S J van der Zant, Gary A Steele, "Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping". 2D Materials, 1, 011002 (2014). Abstract.
[20] V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, G. A. Steele, "Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity". Nature Nanotechnology 9, 820–824 (2014). Abstract.
[21] G. S. Agarwal, Sumei Huang, "Electromagnetically induced transparency in mechanical eff ects of light". Physical Review A, 81, 041803 (2010). Abstract.
[22] Stefan Weis, Rémi Rivière, Samuel Deléglise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, Tobias J. Kippenberg, "Optomechanically induced transparency". Science, 330, 1520-1523 (2010). Abstract.
[23] A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, O. Painter, "Electromagnetically induced transparency and slow light with optomechanics". Nature, 472, 69-73 (2011). Abstract.
[24] X. Zhou, F. Hocke, A. Schliesser, A. Marx, H. Huebl, R. Gross, T. J. Kippenberg, "Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics". Nature Physics, 9, 179-184 (2013). Abstract.

Few-layer Black Phosphorus Phototransistors for Fast and Broadband Photodetection

From Left to Right: (Top) Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, (Bottom) Gary A. Steele, Herre S.J. van der Zant and Andres Castellanos-Gomez

Authors:
Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, Gary A. Steele, Herre S.J. van der Zant, Andres Castellanos-Gomez.

Affiliation:
Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands.

Introduction

The isolation of graphene has opened the door for the studying of the large family of layered two-dimensional (2D) materials, driven by the extraordinary properties that these materials show in their single and few-layer form [1-4]. Graphene, a one-atom thick layer of carbon atoms, has shown excellent electrical properties (e.g. mobility in the order of 170 000 cm²/Vs at room temperature) and large breaking strength [5,6]. However, its applicability in low-power field effect transistors (FETs) and optoelectronic devices (e.g. photodetectors) is hampered by its zero bandgap.

This absence of a bandgap has intensified the current research in other 2D materials with an intrinsic bandgap [7]. For instance, silicene, a single layer of silicon atoms, represents a semiconducting analogue to graphene but so far it has only been realized in an ultra-high-vacuum environment, a severe limitation for further studies and applications [8]. Other promising candidates for optoelectronic applications are the members of the transition metal dichalcogenides (TMDCs) material class [9-13]. The large and direct bandgap of their single-layer form provides strong light absorption – a necessary condition for large photoresponse – but operation is limited to part of the visible spectrum. A material with a direct and small bandgap is needed to extend the detection range accessible with 2D materials.

Black phosphorus

Few-layer black phosphorus is a new member of the 2D-materials family. Black phosphorus is a layered allotrope of the element phosphorus and, in bulk, it is a semiconductor with a direct bandgap of 0.35 eV [14]. In its few-layer form, the bandgap is predicted to strongly depend on the number of layers, from 0.35 eV (bulk) to 2.0 eV (single-layer). Moreover, FETs based on few-layer black-phosphorus show promising electrical properties [15-18], making them an appealing candidate for tunable photodetection from the visible to the infrared part of the spectrum.

Main Results

In our recently published work [19], we characterized the response to light excitation of FETs based on few-layer black phosphorus (thickness ranging from 3nm to 8nm). Figure 1a shows a schematic of the device and of the measurement circuit. Without illumination, the black-phosphorus FETs show ambipolar behavior, as both holes and electrons can be induced in the conducting channel by the gate electric field. The measured mobilities are in the order of 100 cm²/Vs and current on/off ratio in the order of 10³, demonstrating good electrical behavior. Under illumination, we measure a sizable photoresponse to excitation wavelengths from the visible up to 940 nm (see Figure 1b). Figure 1c shows the photocurrent measured for a single pulse of light excitation from which we estimate a rise time of 1 ms, demonstrating broadband and fast photodetection. For comparison, photodetectors based on single-layer molybdenum disulphide (MoS₂) can reach higher responsivities (~ 880 X 10³ mA/W) but their response time is limited to 0.6 sec [20].

Figure 1: (a) Device schematics (b) Source-drain current vs. gate voltage in dark (black solid line), with λ = 940 nm illumination (purple solid line), λ = 640 nm illumination (red solid line) and λ = 532 nm illumination (green solid line). The total incident optical power is 750 μW for all wavelengths. (c) Source-drain current vs. time for a single period of light modulation with a mechanical chopper (different device from panel b).

Future trends and outlook

Taking advantage of the ambipolarity, one could think of electrostatically defining a PN junction in a few-layer black phosphorus flake, as already pioneered in single-layer tungsten diselenide (WSe₂) [9-11]. A PN junction could be used to boost the photoresponse and generate electrical power via the photovoltaic effect. Given the small and direct bandgap of few-layer black-phosphorus, it would be possible to harvest photons also in the near-infrared part of the spectrum.

References:
[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene". Nature, 438, 197-200 (2005). Abstract.
[2] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, "Two-dimensional atomic crystals". Proceedings of the National Academy of Sciences of the United States of America, 102, 10451(2005). Full Article.
[3] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A. A. Firsov, "Electric Field Effect in Atomically Thin Carbon Films". Science, 306, 666 (2004). Abstract.
[4] Qing Hua Wang, Kourosh Kalantar-Zadeh, Andras Kis, Jonathan N. Coleman, Michael S. Strano, "Electronics and optoelectronics of two-dimensional transition metal dichalcogenides". Nature nanotechnology, 7, 699–712 (2012). Abstract.
[5] L. Wang, I. Meric, P.Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D.A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, C. R. Dean, "One-Dimensional Electrical Contact to a Two-Dimensional Material". Science, 342, 614-617 (2013). Abstract.
[6] Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, James Hone, "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene". Science, 321, 385-388 (2008). Abstract.
[7] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, "Single-layer MoS₂ transistors". Nature Nanotechnology, 6, 147-150 (2011). Abstract.
[8] Patrick Vogt, Paola De Padova, Claudio Quaresima, Jose Avila, Emmanouil Frantzeskakis, Maria Carmen Asensio, Andrea Resta, Bénédicte Ealet, Guy Le Lay, "Silicene: Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon". Physical Review Letters, 108, 155501 (2012). Abstract.
[9] Britton W. H. Baugher, Hugh O. H. Churchill, Yafang Yang, Pablo Jarillo-Herrero, "Optoelectronic devices based on electrically tunable p–n diodes in a monolayer dichalcogenide". Nature Nanotechnology, 9, 262-267 (2014). Abstract.
[10] Andreas Pospischil, Marco M. Furchi, Thomas Mueller, "Solar-energy conversion and light emission in an atomic monolayer p–n diode". Nature Nanotechnology, 9, 257-261 (2014). Abstract.
[11] Jason S. Ross, Philip Klement, Aaron M. Jones, Nirmal J. Ghimire, Jiaqiang Yan, D. G. Mandrus, Takashi Taniguchi, Kenji Watanabe, Kenji Kitamura, Wang Yao, David H. Cobden, Xiaodong Xu, "Electrically tunable excitonic light-emitting diodes based on monolayer WSe₂ p–n junctions". Nature Nanotechnology, 9, 268-272 (2014). Abstract.
[12] Zongyou Yin, Hai Li, Hong Li, Lin Jiang, Yumeng Shi, Yinghui Sun, Gang Lu, Qing Zhang, Xiaodong Chen, Hua Zhang, "Single-Layer MoS₂ Phototransistors". ACS Nano, 6, 74-80 (2012). Abstract.
[13] Néstor Perea-López, Ana Laura Elías, Ayse Berkdemir, Andres Castro-Beltran, Humberto R. Gutiérrez, Simin Feng, Ruitao Lv, Takuya Hayashi, Florentino López-Urías, Sujoy Ghosh, Baleeswaraiah Muchharla, Saikat Talapatra, Humberto Terrones, Mauricio Terrones, "Photosensor Device Based on Few-Layered WS₂ Films". Advanced Functional Materials, 23, 5511-5517 (2013). Abstract.
[14] Yuichi Akahama, Shoichi Endo, Shin-ichiro Narita, "Electrical Properties of Black Phosphorus Single Crystals". Journal of the Physical Society of Japan, 52, 2148-2155 (1983). Abstract.
[15] Han Liu, Adam T. Neal, Zhen Zhu, David Tomanek, Peide D. Ye, "Phosphorene: A New 2D Material with High Carrier Mobility". arXiv:1401.4133 [cond-mat.mes-hall] (2014).
[16] Likai Li, Yijun Yu, Guo Jun Ye, Qingqin Ge, Xuedong Ou, Hua Wu, Donglai Feng, Xian Hui Chen, Yuanbo Zhang, "Black phosphorus field-effect transistors". Nature Nanotechnology, 9, 372–377 (2014). Abstract.
[17] Steven P. Koenig, Rostislav A. Doganov, Hennrik Schmidt, A. H. Castro Neto, Barbaros Özyilmaz, "Electric field effect in ultrathin black phosphorus". Applied Physics Letters, 104, 103106 (2014). Abstract.
[18] Han Liu, Adam T. Neal, Zhen Zhu, Zhe Luo, Xianfan Xu, David Tománek, Peide D. Ye, "Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility". ACS Nano, 8, 4033-4041 (2014). Abstract.
[19] Michele Buscema, Dirk J. Groenendijk, Sofya I. Blanter, Gary A. Steele, Herre S. J. van der Zant, Andres Castellanos-Gomez, "Fast and Broadband Photoresponse of Few-Layer Black Phosphorus Field-Effect Transistors". Nano letters, 14, 3347-3352 (2014). Abstract.
[20] Oriol Lopez-Sanchez, Dominik Lembke, Metin Kayci, Aleksandra Radenovic, Andras Kis, "Ultrasensitive photodetectors based on monolayer MoS₂" Nature Nanotechnology, 8, 497-501 (2013). Abstract.

Realizing Two-Dimensional Optics with Metal Antennas and Graphene Plasmons

(From Left to Right) Pablo Alonso-González, Alexey Nikitin and Rainer Hillenbrand.

Authors: 
Pablo Alonso-González¹, Alexey Nikitin^1,2, Federico Golmar^1,3, Alba Centeno⁴, Amaia Pesquera⁴, Saül Vélez¹, Jianing Chen¹, Gabriele Navickaite⁵, Frank Koppens⁵, Amaia Zurutuza⁴, Félix Casanova^1,2, Luis E. Hueso^1,2, Rainer Hillenbrand^1,2.

Affiliation:
¹CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain.
²IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain.
³I.N.T.I-CONICET and ECyT-UNSAM, San Martín, Bs. As., Argentina.
⁴Graphenea SA, 20018 Donostia-San Sebastián, Spain.
⁵ICFO-Institut de Ciéncies Fotoniques, Mediterranean Technology Park, Barcelona, Spain.

Optical circuits and devices could make signal processing and computing much faster. However, although light is very fast, it needs too much space. In fact, propagating light needs at least the space of half its wavelength, which is much larger than state-of-the-art electronic building blocks in our computers. For that reason, a quest for squeezing light to propagate it through nanoscale materials arises.

Graphene, a single layer of carbon atoms with extraordinary properties, has been proposed as one solution. The wavelength of light captured by a graphene layer can be strongly shortened by a factor of 10 to 100 compared to light propagating in free space [1, 2]. As a consequence, this light propagating along the graphene layer - called graphene plasmon - requires much less space and promises ultra-compact photonic devices [3,4].

Past 2Physics articles by this Group:
July 22, 2012: "Capturing, Tuning and Controlling Light with a Single Sheet of Carbon Atoms"
by Jianing Chen, Michela Badioli, Pablo Alonso-González, Susokin Thongrattanasiri, Florian Huth, Johann Osmond, Marko Spasenović, Alba Centeno, Amaia Pesquera, Philippe Godignon, Amaia Zurutuza, Nicolas Camara, Javier García de Abajo, Rainer Hillenbrand, Frank Koppens

Converting light efficiently into graphene plasmons, however, has been a major challenge. In our recent work [5], we demonstrate that the antenna concept of radio wave technology could be a promising solution. We show that a nanoscale metal rod on graphene (acting as an antenna for light) can capture infrared light and convert it into graphene plasmons, analogous to a radio antenna converting radio waves into electromagnetic waves in a metal cable. The excitation of graphene plasmons is purely optical, the device is compact and the phase and wavefronts of the graphene plasmons can be directly controlled by geometrically tailoring the antennas. The latter is essential for the development of applications that require focusing and guiding of graphene plasmons.

Fig. 1: Launching graphene plasmons with a gold antenna. The oscillations of the calculated electromagnetic field around the antenna reveal the graphene plasmons.

Based on calculations (Fig. 1), we fabricated gold nanoantennas on graphene provided by Graphenea. We then used the Neaspec near-field microscope to image how infrared graphene plasmons are launched and propagate along the graphene layer. In the experimental near-field images, we observed that indeed electromagnetic waves on the graphene propagate away from the antenna, with a wavelength that is about 30 times smaller than that of the incident light (Fig. 2).

Fig. 2: Top: Topography of a gold nanoantenna on graphene. Bottom: Near-field image showing the fields of the antenna and the graphene plasmons around the antenna. The image was taken at an illumination wavelength of 11.06 μm and shows the real part of the imaged field. The distance between fringes of the same color reveals the graphene plasmon wavelength.

In order to test whether the two-dimensional propagation of light waves along a one-atom-thick carbon layer follow the laws of conventional optics, we tried to focus and refract the waves. For the focusing experiment, we curved the antenna. The images then showed that the graphene plasmons focus away from the antenna, similar to the light beam that is concentrated with a lens or concave mirror.

We also observed that graphene plasmons refract (bend) when they pass through a prism-shaped graphene bilayer (Fig. 3), analogous to the bending of a light beam passing through a glass prism. The big difference is that the graphene prism is only two atoms thick. By measuring the graphene plasmon wavelengths in the bi- and monolayer, λ₁ and λ₂, as well as the propagation angles α₁ and α₂, we could demonstrate that the refraction of graphene plasmons qualitatively follows the fundamental law of refraction (Snell´s law): sin(α₁)/sin(α₂) = λ₁/λ₁.

Fig. 3: (a) Illustration of a graphene bilayer prism next to a gold antenna. (b) Near-field image (taken at an illumination wavelength of 10.20 μm) of graphene plasmons refracting at a graphene bilayer prism. The yellow lines and arrows illustrate the plasmon wavefronts and their refraction.

Intriguingly, the graphene plasmons are refracted because the conductivity in the two-atom-thick prism is larger than in the surrounding one-atom-thick layer. In the future, local conductivity changes in graphene could be generated by simple electronic means, such as gating, allowing for highly efficient electrical control of refraction, among others for steering applications.

Altogether, the experiments show that the fundamental and most important principles of conventional optics also apply for graphene plasmons, in other words, squeezed light propagating along a one-atom-thick layer of carbon atoms. Future developments based on these results could lead to extremely miniaturized optical circuits and devices that could be useful for sensing and computing, among other applications.

References:
[1] 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, 487, 77-81 (2012). Abstract. 2Physics Article.
[2] 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, 487, 82-85 (2012). Abstract. 2Physics Article.
[3] Ashkan Vakil, Nader Engheta, “Transformation optics using graphene”. Science, 332, 1291-1294 (2011). Abstract.
[4] A.N. Grigorenko, M. Polini, K.S. Novoselov, “Graphene plasmonics”, Nature Photonics, 6, 749-758 (2012). Abstract.
[5] P. Alonso-González, A.Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L.E. Hueso and R. Hillenbrand. “Controlling grapheme plasmons with resonant metal antennas and spatial conductivity patterns”. Science,  344, 1369-1373 (2014). Abstract.

Institutes:

CIC nanoGUNE
The nanoGUNE Cooperative Research Center, located in Donostia-San Sebastian, Basque Country, is a research centre set up with the mission to conduct excellence research into nanoscience and nanotechnology with the aim of increasing the Basque Country’s business competitiveness and economic and social development.

GRAPHENEA S.A.
Graphenea is a pioneer graphene production start-up company founded in 2010 by private investors and CIC nanoGUNE. The company produces and commercializes graphene films by Chemical Vapor Deposition technology and graphene powders by Chemical Exfoliation techniques.

ICFO
ICFO is a young research institution located in Barcelona that aims to advance the very limits of knowledge in Photonics, namely the science and technology of harnessing Light. Its research programs target the global forefront of photonics, and aim to tackle important challenges faced by society at large. ICFO is focused on current and future problems in Health, Energy, Information, Safety, Security and caring for the Environment.

Quantum Ratchet in Graphene: One-way Electron Traffic at Atomic Scale

S.D. Ganichev (Left) and S.A. Tarasenko (Right)

Authors: 
S.D. Ganichev¹ and S.A. Tarasenko²

Affiliation:
¹Terahertz Center, University of Regensburg, Germany
²Ioffe Physical-Technical Institute, St. Petersburg, Russia

A mechanical or electronic system driven by alternating force can exhibit a directed motion facilitated by thermal or quantum fluctuations. Such a ratchet effect occurs in systems with broken spatial inversion symmetry. Canonical examples are the ratchet-and-pawl mechanisms in watches, electric current rectifying diodes and transistors in electronics, and Brownian molecular motors in biology [1,2]. The ratchet suggests one-way traffic. One can pull it back and forth, but it moves predominantly in a certain direction. Therefore, the effect has fascinating ramifications in engineering and natural sciences.

Now an international consortium consisting of research groups from Germany, Russia, Sweden, and the U.S. has demonstrated that electronic ratchets can be successfully scaled down to one-atom thick layers [3]. Specifically, it has been shown that graphene layers support a ratchet motion of electrons when placed in a static magnetic field. The ac electric field of terahertz radiation [4] was applied to push the Dirac electrons back and forth, while the magnetic field acted as a valve letting the electrons move in one direction and suppressing the oppositely directed motion. The resulting magnetic quantum ratchet transforms the ac power into a dc current, extracting work from the out-of-equilibrium Dirac electrons driven by undirected periodic forces.

Graphene, a one-atom-thick layer of carbon with a honeycomb crystal lattice [5], is usually threated as a spatially symmetric structures, as far as its electric or optical properties are concerned. Driven by a periodic electric field, no directed electric current can be expected to flow. However, if the space inversion symmetry of the structure is broken due to the substrate or chemisorbed adatoms on the surface, an electronic ratchet motion can arise. In Ref.[3], we and our colleagues report on the observation and experimental and theoretical study of quantum ratchet effects in single-layer graphene samples, proving and quantifying the underlying spatial asymmetry.

Figure 1: Alternating electric field drives a ratchet current in graphene.

The physics behind the magnetic quantum ratchet effect in graphene is illustrated in Fig. 1. The alternating electric field E(t) drives Dirac electrons back and forth in the graphene plane. Due to the Lorentz force, the applied static magnetic field B deforms the electron orbitals such that the right-moving electrons have their centre of gravity shifted upwards, while the left-moving electrons are shifted downwards. (In quantum mechanical consideration, the shift is caused by the magnetic-field-induced coupling between σ- and π-band states). For spatial symmetric systems the net dc current would vanish. However, in a graphene layer with spatial asymmetry, e.g., caused by top adsorbates, the electrons shifted upwards feel more disorder and exhibit a lower mobility than the electrons shifted downwards and moving in the opposite direction. This difference in the effective mobility for the right- and left-moving carriers results in a net dc current. The current scales linearly with the magnetic field, changes a sign by switching the magnetic field polarity, and proportional to the square of the amplitude of the ac electric field. The linear dependence on B comes from the Lorentz force. The electric field appears twice: on the one hand, it causes the oscillating motion of carriers in the plane, and on the other, the Lorentz force itself is proportional to the electron velocity.

The ratchet motion implies that the particle flow depends on the orientation of the ac force with respect to the direction of built-in spatial asymmetry. In the case of magnetic quantum ratchets, where the asymmetry stems from the magnetic field, the relevant parameter is the angle β between the ac electric field E(t) and the static magnetic field B. Shown in Fig. 2 is the measured dependence of the dc current on the angle β. The current reaches a maximum for the perpendicular electric and magnetic fields and remains finite for the co-linear fields. The whole angular dependence is well described by the equation

j_x(β) = j₁ Cos(2β) + j₂

with two contributions j₁ and j₂, which is in agreement with the developed theory [see Ref.3]. It has also been shown that the ratchet transport can be induced by a force rotating in space. By exciting the graphene samples with a clockwise or counterclockwise rotating in-plane electric field E(t), the dc current is detected. Interestingly, the current measured along the static magnetic field turns out to be sensitive to the radiation helicity being of the opposite sign for the clockwise and counterclockwise rotating fields.

Figure 2: Dependence of the ratchet current on the orientation of ac electric field. Experimental data (dots) are obtained for an epitaxial graphene on SiC at temperature 115K, magnetic field 7T, and electric field amplitude 10 kV/cm. Solid line is a theoretical fit.

Graphene may be the ultimate electronic material, possibly replacing silicon in electronic devices in the future. It has attracted worldwide attention from physicists, chemists, and engineers. The discovery of the ratchet motion in this purest possible two-dimensional system known in nature indicates that the orbital effects may appear and be substantial in other two-dimensional crystals such as boron nitride, molybdenum dichalcogenides and related heterostructures. The measurable orbital effects in the presence of an in-plane magnetic field provide strong evidence for the existence of structure inversion asymmetry in graphene.

References:
[1] R. P. Feynman, R. B. Leighton, and M. Sands, "The Feynman Lectures on Physics, Vol. 1" (Addison-Wesley, 1966).
[2] Peter Hänggi and Fabio Marchesoni, "Artificial Brownian motors: controlling transport on the nanoscale", Review of Modern Physics, 81, 387 (2009). Abstract.
[3] C. Drexler, S. Tarasenko, P. Olbrich, J. Karch, M. Hirmer, F. Müller, M. Gmitra, J. Fabian, R. Yakimova, S. Lara-Avila, S. Kubatkin, M. Wang, R. Vajtai, P. Ajayan, J. Kono, and S.D. Ganichev: "Magnetic quantum ratchet effect in graphene", Nature Nanotechnology 8, 104 (2013). Abstract.
[4] S.D. Ganichev and W. Prettl, "Intense Terahertz Excitation of Semiconductors" (Oxford Univ. Press, 2006).
[5] A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, "The electronic properties of graphene". Review of Modern Physics, 81, 109 (2009). Abstract.

Unconventional Fractional Quantum Hall Sequence in Graphene

Ben Feldman (left) and Amir Yacoby (right)
















Authors: Ben Feldman and Amir Yacoby

Affiliation: Department of Physics, Harvard University, USA

Graphene, a two-dimensional sheet of carbon that is one atom thick, has attracted considerable interest due to its unique and potentially useful physical properties. Like other two-dimensional materials, application of a perpendicular magnetic field leads to the formation of a sequence of flat energy bands called Landau levels (LLs). At high magnetic fields or when samples are very clean, interactions among electrons become important and produce additional energy gaps, even when the LLs are only partially filled. This phenomenon is known as the fractional quantum Hall effect (FQHE), and it leads to striking physical consequences such as excitations with a fraction of an electron charge [1-3].

Graphene provides an especially rich platform to study the FQHE. The low dielectric constant and unique band structure lead to FQH states with energy gaps that are larger than in GaAs at the same field. Moreover, charge carriers in graphene have an overall fourfold degeneracy that arises from their spin and valley degrees of freedom. This means that graphene can support FQH states that have no analogues in more conventional systems. Suspending samples above the substrate or depositing them on boron nitride minimizes disorder, and the FQHE was recently observed in such devices at all multiples of filling factor ν = 1/3 up to 13/3, except at ν = 5/3 [4-7]. The absence of a state at ν = 5/3 might result from low-lying excitations associated with the underlying symmetries in graphene, but alternate scenarios associated with disorder could not be ruled out in prior studies.

Figure 1: Picture of the scanning Single-Electron Transistor (SET) microscope setup

To further explore this behavior, we used a scanning single-electron transistor (SET) to probe a suspended graphene flake [8]. The SET is a unique local probe that is particularly non-invasive. It measures the presence of energy gaps in the electronic spectrum with sensitivity that no other technique can provide and therefore is very well adapted to the exploration of the FQHE. Moreover, we are able to study small regions of a graphene flake, and these local measurements reveal a dramatic improvement in sample quality relative to prior studies of larger-scale areas.

Our measurements show that electron-electron interactions in graphene produce different types and patterns of electronic states from what has been observed in more conventional materials. Although we observe the standard sequence of FQH states between ν = 0 and 1, states only occur at even-numerator fractions between ν = 1 and 2. This suggests that both spin and valley degeneracy are lifted below ν = 1, but one symmetry remains between ν = 1 and 2. The pattern of states that we observe and their corresponding energy gaps indicate an intriguing interplay between electron-electron interactions and the underlying symmetries of graphene.

Figure 2: Schematic of the measurement setup. The scanning single-electron transistor is held about 100 nm above a suspended graphene flake, and it measures the energy cost of adding additional electrons to the system.

Moreover, the scanning technique allows us to study variations in behavior as a function of position. Although all regions of the graphene flake show qualitatively similar behavior, local doping shifts the gate voltage required to observe each FQH state. Global measurements such as transport studies therefore require an especially homogenous sample to observe the delicate effects associated with interactions among electrons, whereas using a local probe allows us to observe especially clean regions and therefore observe more of the intrinsic physics.

Figure 3: Inverse compressibility of graphene as a function of carrier density and magnetic field. Incompressible behavior, which indicates the presence of an energy gap, is labeled at integer and certain fractional filling factors.

In the future, we are interested in continuing to explore the unusual FQH in graphene. In particular, we hope to better understand how the electrons are ordered in the various FQH states. We are also interested in learning more about the FQHE at higher filling factors and in related materials such as bilayer graphene.

References:
[1] D. C. Tsui, H. L. Stormer, A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit”, Physical Review Letters, 48, 1559 (1982). Abstract.
[2] R. B. Laughlin, “Anomalous quantum Hall-effect - an incompressible quantum fluid with fractionally charged excitations”, Physical Review Letters, 50, 1395 (1983). Abstract.
[3] J. K. Jain, “Composite-fermion approach for the fractional quantum Hall-effect”, Physical Review Letters, 63, 199 (1989). Abstract.
[4] Kirill I. Bolotin, Fereshte Ghahari, Michael D. Shulman, Horst L. Stormer, Philip Kim, “Observation of the fractional quantum Hall effect in graphene”, Nature, 462, 196 (2009). Abstract.
[5] Xu Du, Ivan Skachko, Fabian Duerr, Adina Luican, Eva Y. Andrei, “Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene”, Nature, 462, 192 (2009). Abstract.
[6] C. R. Dean, A. F. Young, P. Cadden-Zimansky, L. Wang, H. Ren, K. Watanabe, T. Taniguchi, P. Kim, J. Hone, K. L. Shepard, “Multicomponent fractional quantum Hall effect in graphene”, Nature Physics, 7, 693 (2011). Abstract.
[7] Dong Su Lee, Viera Skákalová, R. Thomas Weitz, Klaus von Klitzing, Jurgen H. Smet, “Transconductance fluctuations as a probe for interaction induced quantum Hall states in graphene”,  Physical Review Letters, 109, 056602 (2012). Abstract.
[8] Benjamin E. Feldman, Benjamin Krauss, Jurgen H. Smet, Amir Yacoby, “Unconventional sequence of fractional quantum Hall states in Suspended Graphene”, Science. 337, 1196 (2012). Abstract.

Graphene Can Be Used for Terahertz Hyperlens

From left to right: Andrei Andryieuski, Dmitry Chigrin, Andrei Lavrinenko








Author: Andrei Andryieuski
Affiliation: DTU Fotonik, Technical University of Denmark, Denmark

Andrei Andryieuski and Andrei Lavrinenko, the researchers from the Metamaterials group at Technical University of Denmark (DTU) -- in collaboration with Dmitry Chigrin from the University of Wuppertal (BUW) -- made the first theoretical description of graphene hyperlens, able to work in the terahertz range.

Terahertz radiation, which occupies the spectral range between infrared and microwaves, is harmless to humans and animals and passes easily through many dielectric materials. Terahertz waves, which are able to detect drugs even in sealed vessels, to reveal hidden weapon and to detect cancer tumors, may revolutionize spectroscopy, defense and medical analysis.

 Fig. 1. Artistic view of the graphene hyperlens in action. Multiple structured graphene layers resolve and magnify two subwavelength sources.

The wavelength of terahertz radiation is, however, relatively large (300 µm at 1 THz) so the image-quality is seriously limited by the natural diffraction limit. To overcome this limit, artificially structured metamaterial lenses or metallic funnels can be employed. The very fine details hindered in the evanescent waves, which rapidly decay from the radiating object, can be captured by negative index superlens or indefinite medium (hyperbolic dispersion) hyperlens. While negative index metamaterials are still very lossy and far from being employed for practical purposes, the hyperlens present a realistic approach to imaging.

To make the hyperlens a very special material is required. It should behave as a metal in one direction and as an insulator in another. To obtain such properties, thin multiple metal-dielectric layers are normally used in optics. The theoretical concept -- proposed by Evgenii Narimanov’s group from Princeton University (USA) in 2006 [1] -- was checked experimentally by Xiang Zhang’s group from UC Berkeley (USA) in 2007 [2]. To realize the hyperlens the researchers deposited many ultrathin (35 nm) layers of silver and alumina. Even though the metal based hyperlens shows a subwavelength resolution, it is prohibited in tunability; basically, once being fabricated, its properties cannot be changed.

Contrary to metals, graphene, an atomically thin layer of carbon atoms, easily changes its properties under the influence of electrostatic field, magnetic field or chemical doping. This is why the researchers from DTU and BUW decided to employ it for the hyperlens. They propose to construct the hyperlens from narrow (starting from 40 nm) tapered graphene wires embedded into polymer.

Fig. 2. The building block of the hyperlens is the narrow graphene wire embedded into polymer. Arranging such tapered wires radially gives the required material properties for the hyperlens, namely, negative dielectric permittivity in radial direction and positive in azimuthal direction.

Such structured graphene arranged into multiple layers has the very properties needed for hyperbolic dispersion: the wave feels it as metal along the wires and as dielectric perpendicular to the wires. The hyperlens showed subwavelength resolution at the wavelength 50 µm of two sources separated with 10 µm, thus giving the possibility to image the points as close as 1/5 of the wavelength. The resolution of the hyperlens depends on its radii, so with proper selection of geometrical parameter it is possible to separate the images far enough to be captured by the conventional terahertz camera. The hyperlens can be tuned by applying voltage to various graphene layers. It works reciprocally, thus being able not only to image, but also to concentrate terahertz radiation in small volumes.

Fig. 3. Electromagnetic waves emitted by two line sources are captured by the hyperlens and magnified to such extent that they can be resolved with a conventional imaging device.

DTU’s researchers are looking forward to realize and test the graphene hyperlens experimentally.

The paper presenting the above work was published last week in Physical Review B Rapid Communications [3].

References:
[1] Zubin Jacob, Leonid V. Alekseyev, and Evgenii Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit”, Optics Express, 14, 8247 (2006). Abstract.
[2] Zhaowei Liu, Hyesog Lee, Yi Xiong, Cheng Sun and Xiang Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects”, Science, 315,  1686 (2007). Abstract.
[3] Andrei Andryieuski, Andrei V. Lavrinenko, Dmitry N. Chigrin, "Graphene hyperlens for terahertz radiation", Physical Review B, 86, 121108(R) (2012). Abstract. Also available at: arXiv:1209.3951.