Importance of Electron-Electron Interactions in Graphene

Michael Crommie [Photo by Roy Kaltschmidt, Courtesy: Lawrence Berkeley National Laboratory]

 Perhaps no other material is generating as much excitement in the electronics world as graphene, sheets of pure carbon just one atom thick through which electrons can race at nearly the speed of light – 100 times faster than they move through silicon. Superthin, superstrong, superflexible and superfast as an electrical conductor, graphene has been touted as a potential wonder material for a host of electronic applications, starting with ultrafast transistors. For the vast potential of graphene to be fully realized, however, scientists must first learn more about what makes graphene so super. The latest step in this direction has been taken by researchers with the U.S. Department of Energy (DOE)’s Lawrence Berkeley National Laboratory (Berkeley Lab) and the University of California (UC) Berkeley.

Michael Crommie, a physicist who holds joint appointments with Berkeley Lab’s Materials Sciences Division and UC Berkeley’s Physics Department, led a study in which the first direct observations at microscopic lengths were recorded of how electrons and holes respond to a charged impurity – a single Coulomb potential – placed on a gated graphene device. The results provide experimental support to the theory that interactions between electrons are critical to graphene’s extraordinary properties. This work has been published online on July 29th in the journal 'Nature Physics'[1].

“We’ve shown that electrons in graphene behave very differently around charged impurities than electrons in other materials,” Crommie says. “Some researchers have held that electron-electron interactions are not important to intrinsic graphene properties while others have argued they are. Our first-time-ever pictures of how ultra-relativistic electrons re-arrange themselves in response to a Coulomb potential come down on the side of electron-electron interactions being an important factor.”

Graphene sheets are composed of carbon atoms arranged in a two-dimensional hexagonally patterned lattice, like a honeycomb. Electrons moving through this honeycomb lattice perfectly mimic the behavior expected of highly relativistic charged particles with no mass: think of a ray of light that is electrically charged. Because this is the same behavior displayed by highly relativistic free electrons, charge-carriers in graphene are referred to as “Dirac quasiparticles,” after Paul Dirac, the scientist who first described the behavior of relativistic fermions in 1928.

“In graphene, electrons behave as massless Dirac fermions,” Crommie says. “As such, the response of these electrons to a Coulomb potential is predicted to differ significantly from how non-relativistic electrons behave in traditional atomic and impurity systems. However, until now, many key theoretical predictions for this ultra-relativistic system had not been tested.”

Image 1: This zoom-in STM topograph shows one of the cobalt trimers placed on graphene for the creation of Coulomb potentials – charged impurities – to which electrons and holes could respond. (Image courtesy of Crommie group)

Working with a specially equipped scanning tunneling microscope (STM)in ultra-high vacuum, Crommie and his colleagues probed gated devices consisting of a graphene layer deposited atop boron nitride flakes which were themselves placed on a silicon dioxide substrate, the most common of semiconductor substrates.

“The use of boron-nitride significantly reduced the charge inhomogeneity of graphene, thereby allowing us to probe the intrinsic graphene electronic response to individual charged impurities,” Crommie says. In this study, the charged impurities were cobalt trimers constructed on graphene by atomically manipulating cobalt monomers with the tip of an STM.”

Image 2: The response of ultrarelativistic electrons in graphene to Coulomb potentials created by cobalt trimers was observed to be signficantly different the response of non-relativistic electrons in traditional atomic and impurity systems. (Image courtesy of Crommie group)

The STM used to fabricate the cobalt trimers was also used to map (through spatial variation in the electronic structure of the graphene) the response of Dirac quasiparticles – both electron-like and hole-like – to the Coulomb potential created by the trimers. Comparing the observed electron–hole asymmetry to theoretical simulations allowed the research team to not only test theoretical predictions for how Dirac fermions behave near a Coulomb potential, but also to extract graphene’s dielectric constant.

“Theorists have predicted that compared with other materials, electrons in graphene are pulled into a positively-charged impurity either too weakly, the subcritical regime; or too strongly, the supercritical regime,” Crommie says. “In our study, we verified the predictions for the subcritical regime and found the value for the dielectric to be small enough to indicate that electron–electron interactions contribute significantly to graphene properties. This information is fundamental to our understanding of how electrons move through graphene.”

Reference:
[1] Yang Wang, Victor W. Brar, Andrey V. Shytov, Qiong Wu, William Regan, Hsin-Zon Tsai, Alex Zettl, Leonid S. Levitov, Michael F. Crommie, "Mapping Dirac quasiparticles near a single Coulomb impurity on graphene", Nature Physics, doi:10.1038/nphys2379 (Published online July 29, 2012). Abstract.

[This article is written by Lynn Yarris of Lawrence Berkeley National Laboratory]

Capturing, Tuning and Controlling Light with a Single Sheet of Carbon Atoms

Group Leaders: (From Left to Right) Javier Garcia de Abajo, Rainer Hillenbrand, Frank Koppens  







Authors: Jianing Chen^1,2, Michela Badioli³, Pablo Alonso-González¹, Susokin Thongrattanasiri⁴, Florian Huth^1,5, Johann Osmond³, Marko Spasenović³, Alba Centeno⁶, Amaia Pesquera⁶, Philippe Godignon⁷, Amaia Zurutuza⁶, Nicolas Camara⁸, Javier García de Abajo⁴, Rainer Hillenbrand^1,9, Frank Koppens³

Affiliation:
¹CIC nanoGUNE Consolider, 20018 Donostia-San Sebastián, Spain
²Centro de Fisica de Materiales (CSIC-UPV/EHU) and Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
³ICFO-Institut de Ciéncies Fotoniques, Barcelona, Spain
⁴IQFR-CSIC, Madrid, Spain
⁵Neaspec GmbH, Munich, Germany
⁶Graphenea SA, 20018 Donostia-San Sebastián, Spain
⁷CNM-IMB-CSIC–Campus UAB, Barcelona, Spain
⁸GREMAN, UMR 7347, Université de Tours/CNRS, France
⁹IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

Graphene, a remarkable one-atom-thick material consisting of a lattice of carbon atoms possesses extraordinary and gate-tunable optical properties. Interestingly, graphene can also carry strongly confined optical fields that travel along the surface of the sheet. These surface waves, based on the coupling between optical fields and charge carrier oscillations, are also called plasmons. For graphene, these plasmons have unique properties, as they can be tuned by electric fields, they propagate with speeds more than 100 times below the velocity of light, and they have a wavelength that is more than 100 times below the wavelength of light in free space. This makes it possible to confine light to extremely small volumes and to guide light along nanometer scale waveguides.

Since graphene was discovered, many theoretical physicists predicted the existence of graphene plasmons, but no experimental observations of propagating plasmons in graphene were reported so far. Due to the large mismatch in momentum between photons and graphene plasmons, it is not trivial to excite graphene plasmons by just shining light on a graphene sheet. This work has overcome this problem by focusing light on a sharp tip which is placed close to the graphene sheet. Because the tip acts as a nanoantenna, it can provide the extra momentum needed for the plasmons to be created (also called scattering near-field microscopy, s-SNOM). Moreover, the same tip can be used to probe the plasmons, which are reflected at the edges, and propagate back to the tip.

Interestingly, due to the interference between the plasmon waves that propagate away from the tip and towards the tip, it was possible to make real-space images of the plasmon waves with nanometer scale resolution (see Figure). For this experiment, a tapered graphene sheet was used where the variable width allowed for the observation of plasmon resonances defined by the standing plasmon wave between the edges. Similar to what happens with the standing waves on strings, only waves with appropriate characteristics can appear for a certain width.

Tuning the plasmon properties is a novel and unique aspect of graphene. This work, along with the work by Fei et al [2] (see 2Physics article of last week), shows not only the plasmon wavelength can be tuned over a wide range, it’s also possible to completely switch on and off the existence of the plasmons. In this way, it’s possible to electrically control light in a similar fashion as is traditionally achieved with electrons in a transistor. These capabilities, which until now were impossible with other existing plasmonic materials, enable new highly efficient nano-scale optical switches, which can perform calculations using light instead of electricity. In addition, the capability of trapping light in very small volumes could give rise to a new generation of nano-sensors, with applications in diverse areas such as medicine and bio-molecules, solar cells and light detectors, as well as quantum information processing.

Reference:
[1]  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, "Optical nano-imaging of gate-tunable graphene plasmons", Nature, DOI: 10.1038/nature1125 (Published online June 20, 2012). Abstract. 
[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, DOI:10.1038/nature11253 (published online June 20, 2012). Abstract. 2Physics Article.

Contributions and institutes:
• Optical nano-imaging: CIC nanoGUNE Consolider (San Sebastian, Spain), CFM-CSIC-UPV/EHU (San Sebastian, Spain), Neaspec GmbH (Martinsried, Germany), Ikerbasque (Bilbao, Spain)
• Graphene nano-photonics and optoelectronics: ICFO (Barcelona, Spain)
• Theory: IQFR-CSIC (Madrid, Spain)
• Graphene synthesis: Graphenea (San Sebastian, Spain) University of Tours (Tours, France), and CNM-IMB-CSIC (Barcelona, Spain)

Direct Imaging of Plasmons in Graphene

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

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

Affiliation:
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.

References
[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.

Unusual ‘Quasiparticles’ in Tri-Layer Graphene

Liyuan Zhang and Igor Zaliznyak at the Center for Functional Nanomaterials, Brookhaven National Laboratory, USA

By studying three layers of graphene — sheets of honeycomb-arrayed carbon atoms — stacked in a particular way, scientists at the U.S. Department of Energy’s Brookhaven National Laboratory have discovered a “little universe” populated by a new kind of “quasiparticles” — particle-like excitations of electric charge. Unlike massless photon-like quasiparticles in single-layer graphene, these new quasiparticles have mass, which depends on their energy (or velocity), and would become infinitely massive at rest.

That accumulation of mass at low energies means this trilayer graphene system, if magnetized by incorporating it into a heterostructure with magnetic material, could potentially generate a much larger density of spin-polarized charge carriers than single-layer graphene — making it very attractive for a new class of devices based on controlling not just electric charge but also spin, commonly known as spintronics.

“Our research shows that these very unusual quasiparticles, predicted by theory, actually exist in three-layer graphene, and that they govern properties such as how the material behaves in a magnetic field — a property that could be used to control graphene-based electronic devices,” said Brookhaven physicist Igor Zaliznyak, who led the research team. Their work measuring properties of tri-layer graphene as a first step toward engineering such devices was published online in Nature Physics [1].

Graphene has been the subject of intense research since its discovery in 2004, in particular because of the unusual behavior of its electrons, which flow freely across flat, single-layer sheets of the substance. Stacking layers changes the way electrons flow: Stacking two layers, for example, provides a “tunable” break in the energy levels the electrons can occupy, thus giving scientists a way to turn the current on and off. That opens the possibility of incorporating the inexpensive substance into new types of electronics.

With three layers, the situation gets more complicated, scientists have found, but also potentially more powerful.

One important variable is the way the layers are stacked: In “ABA” systems, the carbon atoms making up the honeycomb rings are directly aligned in the top and bottom layers (A) while those in the middle layer (B) are offset; in “ABC” variants, the honeycombs in each stacked layer are offset, stepping upwards layer by layer like a staircase. So far, ABC stacking appears to give rise to more interesting behaviors — such as those that are the subject of the current study.

ABC trilayer graphene, where the three layers are offset from one another like stair steps [Image courtesy: Brookhaven National Laboratory]

For this study, the scientists created the tri-layer graphene at the Center for Functional Nanomaterials (CFN) at Brookhaven Lab, peeling it from graphite, the form of carbon found in pencil lead. They used microRaman microscopy to map the samples and identify those with three layers stacked in the ABC arrangement. Then they used the CFN’s nanolithography tools, including ion-beam milling, to shape the samples in a particular way so they could be connected to electrodes for measurements.

At the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, Florida, the scientists then studied the material’s electronic properties — specifically the effect of an external magnetic field on the transport of electronic charge as a function of charge carrier density, magnetic field strength, and temperature.

“Ultimately, the success of this project relied on hard work and rare experimental prowess of talented young researchers with whom we engaged in these studies, in particular, Liyuan Zhang, who at the time was research associate at Brookhaven, and Yan Zhang, then a graduate student from Stony Brook University,” said Igor Zaliznyak.

The measurements provide the first experimental evidence for the existence of a particular type of quasiparticle, or electronic excitation that acts like a particle and serves as a charge carrier in the tri-layer graphene system. These particular quasiparticles, which were predicted by theoretical studies, have ill-defined mass — that is, they behave as if they have a range of masses — and those masses diverge as the energy level decreases with quasiparticles becoming infinitely massive.

Ordinarily such particles would be unstable and couldn’t exist due to interactions with virtual particle-hole pairs — similar to virtual pairs of oppositely charged electrons and positrons, which annihilate when they interact. But a property of the quasiparticles called chirality, which is related to a special flavor of spin in graphene sytems, keeps the quasiparticles from being destroyed by these interactions. So these exotic infinitively massive particles can exist.

“These results provide experimental validation for the large body of recent theoretical work on graphene, and uncover new exciting possibilities for future studies aimed at using the exotic properties of these quasiparticles,” Zaliznyak said.

For example, combining magnetic materials with tri-layer graphene could align the spins of the charge-carrier quasiparticles. “We believe that such graphene-magnet heterostructures with spin-polarized charge carriers could lead to real breakthroughs in the field of spintronics,” Zaliznyak said.

Reference
[1] Liyuan Zhang, Yan Zhang, Jorge Camacho, Maxim Khodas, Igor Zaliznyak, "The experimental observation of quantum Hall effect of l=3 chiral quasiparticles in trilayer graphene", Nature Physics, doi:10.1038/nphys2104 (Published online September 25, 2011). Abstract.

Measurements of the 'Edge States' of Graphene Nanoribbons

Michael Crommie [photo courtesy: Lawrence Berkeley National Laboratory]

As far back as the 1990s, long before anyone had actually isolated graphene – a honeycomb lattice of carbon just one atom thick – theorists were predicting extraordinary properties at the edges of graphene nanoribbons. Now physicists at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), and their colleagues at the University of California at Berkeley, Stanford University, and other institutions, have made the first precise measurements of the “edge states” of well-ordered nanoribbons.

A graphene nanoribbon is a strip of graphene that may be only a few nanometers wide. Theorists have envisioned that nanoribbons, depending on their width and the angle at which they are cut, would have unique electronic, magnetic, and optical features, including band gaps like those in semiconductors, which sheet graphene doesn’t have.

“Until now no one has been able to test theoretical predictions regarding nanoribbon edge-states, because no one could figure out how to see the atomic-scale structure at the edge of a well-ordered graphene nanoribbon and how, at the same time, to measure its electronic properties within nanometers of the edge,” says Michael Crommie of Berkeley Lab’s Materials Sciences Division (MSD) and UC Berkeley’s Physics Division, who led the research. “We were able to achieve this by studying specially made nanoribbons with a scanning tunneling microscope.”

Graphene nanoribbons are narrow sheets of carbon atoms only one layer thick. Their width, and the angles at which the edges are cut, produce a variety of electronic states, which have been studied with precision for the first time using scanning tunneling microscopy and scanning tunneling spectroscopy. [image courtesy: Lawrence Berkeley National Laboratory]

The team’s research not only confirms theoretical predictions but opens the prospect of building quick-acting, energy-efficient nanoscale devices from graphene-nanoribbon switches, spin-valves, and detectors, based on either electron charge or electron spin. Farther down the road, graphene nanoribbon edge states open the possibility of devices with tunable giant magnetoresistance and other magnetic and optical effects.

Crommie and his colleagues have published their research in Nature Physics, available May 8, 2011 in advanced online publication [1].

The well-tempered nanoribbon

“Making flakes and sheets of graphene has become commonplace,” Crommie says, “but until now, nanoribbons produced by different techniques have exhibited, at best, a high degree of inhomogeneity” – typically resulting in disordered ribbon structures with only short stretches of straight edges appearing at random. The essential first step in detecting nanoribbon edge states is access to uniform nanoribbons with straight edges, well-ordered on the atomic scale.

Hongjie Dai of Stanford University’s Department of Chemistry and Laboratory for Advanced Materials, a member of the research team, solved this problem with a novel method of “unzipping” carbon nanotubes chemically. Graphene rolled into a cylinder makes a nanotube, and when nanotubes are unzipped in this way the slice runs straight down the length of the tube, leaving well-ordered, straight edges.

By "unzipping" carbon nanotubes, regular edges with differing chiralities can be produced between the extremes of the zigzag configuration and, at a 30-degree angle to it, the armchair configuration. [image courtesy: Lawrence Berkeley National Laboratory]


Graphene can be wrapped at almost any angle to make a nanotube. The way the nanotube is wrapped determines the pitch, or “chiral vector,” of the nanoribbon edge when the tube is unzipped. A cut straight along the outer atoms of a row of hexagons produces a zigzag edge. A cut made at a 30-degree angle from a zigzag edge goes through the middle of the hexagons and yields scalloped edges, known as “armchair” edges. Between these two extremes are a variety of chiral vectors describing edges stepped on the nanoscale, in which, for example, after every few hexagons a zigzag segment is added at an angle.

These subtle differences in edge structure have been predicted to produce measurably different physical properties, which potentially could be exploited in new graphene applications. Steven Louie of UC Berkeley and Berkeley Lab’s MSD was the research team’s theorist; with the help of postdoc Oleg Yazyev, Louie calculated the expected outcomes, which were then tested against experiment.

Chenggang Tao of MSD and UCB led a team of graduate students in performing scanning tunneling microscopy (STM) of the nanoribbons on a gold substrate, which resolved the positions of individual atoms in the graphene nanoribbons. The team looked at more than 150 high-quality nanoribbons with different chiralities, all of which showed an unexpected feature, a regular raised border near their edges forming a hump or bevel. Once this was established as a real edge feature – not the artifact of a folded ribbon or a flattened nanotube – the chirality and electronic properties of well-ordered nanoribbon edges could be measured with confidence, and the edge regions theoretically modeled.

Electronics at the edge

“Two-dimensional graphene sheets are remarkable in how freely electrons move through them, including the fact that there’s no band gap,” Crommie says. “Nanoribbons are different: electrons can become trapped in narrow channels along the nanoribbon edges. These edge-states are one-dimensional, but the electrons on one edge can still interact with the edge electrons on the other side, which causes an energy gap to open up.”

A scanning tunneling microscope determines the topography and orientation of the graphene nanoribbons on the atomic scale. In spectroscopy mode, it determines changes in the density of electronic states, from the nanoribbon's interior to its edge. [image courtesy: Lawrence Berkeley National Laboratory]

Using an STM in spectroscopy mode (STS), the team measured electronic density changes as an STM tip was moved from a nanoribbon edge inward toward its interior. Nanoribbons of different widths were examined in this way. The researchers discovered that electrons are confined to the edge of the nanoribbons, and that these nanoribbon-edge electrons exhibit a pronounced splitting in their energy levels.

“In the quantum world, electrons can be described as waves in addition to being particles,” Crommie notes. He says one way to picture how different edge states arise is to imagine an electron wave that fills the length of the ribbon and diffracts off the atoms near its edge. The diffraction patterns resemble water waves coming through slits in a barrier.

For nanoribbons with an armchair edge, the diffraction pattern spans the full width of the nanoribbon; the resulting electron states are quantized in energy and extend spatially throughout the entire nanoribbon. For nanoribbons with a zigzag edge, however, the situation is different. Here diffraction from edge atoms leads to destructive interference, causing the electron states to localize near the nanoribbon edges. Their amplitude is greatly reduced in the interior.

The energy of the electron, the width of the nanoribbon, and the chirality of its edges all naturally affect the nature and strength of these nanoribbon electronic states, an indication of the many ways the electronic properties of nanoribbons can be tuned and modified.

Says Crommie, “The optimist says, ‘Wow, look at all the ways we can control these states – this might allow a whole new technology!’ The pessimist says, ‘Uh-oh, look at all the things that can disturb a nanoribbon’s behavior – how are we ever going to achieve reproducibility on the atomic scale?’”

Crommie himself declares that “meeting this challenge is a big reason for why we do research. Nanoribbons have the potential to form exciting new electronic, magnetic, and optical devices at the nanoscale. We might imagine photovoltaic applications, where absorbed light leads to useful charge separation at nanoribbon edges. We might also imagine spintronics applications, where using a side-gate geometry would allow control of the spin polarization of electrons at a nanoribbon’s edge.”

Although getting there won’t be simple — “The edges have to be controlled,” Crommie emphasizes — “what we’ve shown is that it’s possible to make nanoribbons with good edges and that they do, indeed, have characteristic edge states similar to what theorists had expected. This opens a whole new area of future research involving the control and characterization of graphene edges in different nanoscale geometries.”

Reference
[1] Chenggang Tao, Liying Jiao, Oleg V. Yazyev, Yen-Chia Chen, Juanjuan Feng, Xiaowei Zhang, Rodrigo B. Capaz, James M. Tour, Alex Zettl, Steven G. Louie, Hongjie Dai, and Michael F. Crommie, “Spatially resolving edge states of chiral graphene nanoribbons,” Nature Physics, Published online on May 8th, 2011. doi:10.1038/nphys1991. Abstract.

[The text is written by Paul Preuss of Lawrence Berkeley National Laboratory]

Controlling Quantum Pathways for Raman Scattering in Graphene

Feng Wang beside a diagram showing how lowering the Fermi energy eliminates quantum pathways in graphene (lower left). The upper plot reveals that when destructively interfering quantum pathways are blocked, Raman scattering intensity is strongly enhanced (pale blue vertical, labeled G). At the same scattering, and at specific values of the Fermi energy, the plot reveals “hot electron luminescence” (labeled H.L.). (Click on image for best resolution.)


Scientists at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) and the University of California at Berkeley have learned to control the quantum pathways determining how light scatters in graphene. Controlled scattering provides a new tool for the study of this unique material – graphene is a single sheet of carbon just one atom thick – and may point to practical applications for controlling light and electronic states in graphene nanodevices.

The research team, led by Feng Wang of Berkeley Lab’s Materials Sciences Division, made the first direct observation, in graphene, of so-called quantum interference in Raman scattering. Raman scattering is a form of “inelastic” light scattering. Unlike elastic scattering, in which the scattered light has the same color (the same energy) as the incident light, inelastically scattered light either loses energy or gains it.

Raman scattering occurs in graphene and other crystals when an incoming photon, a particle of light, excites an electron, which in turn generates a phonon together with a lower-energy photon. Phonons are vibrations of the crystal lattice, which are also treated as particles by quantum mechanics.

Quantum particles are as much waves as particles, so they can interfere with one another and even with themselves. The researchers showed that light emission can be controlled by controlling these interference pathways. They present their results in a forthcoming issue of the journal Nature [1].

Fig.1: The quantum pathways in Raman scattering are optically stimulated electronic excitations only possible if the initial electronic state is filled and the final state is empty (top). As pathways are removed by doping the graphene and lowering the Fermi energy (bottom), light from scattering may increase or decrease, depending on whether the removed pathways interfere constructively or destructively with the remaining pathways.

Manipulating quantum interference, in life and in the lab

“A familiar example of quantum interference in everyday life is antireflective coating on eyeglasses,” says Wang, who is also an assistant professor of physics at UC Berkeley. “A photon can follow two pathways, scattering from the coating or from the glass. Because of its quantum nature it actually follows both, and the coating is designed so that the two pathways interfere with each other and cancel light that would otherwise cause reflection.”

Wang adds, “The hallmark of quantum mechanics is that if different paths are nondistinguishable, they must always interfere with each other. We can manipulate the interference among the quantum pathways that are responsible for Raman scattering in graphene because of graphene’s peculiar electronic structure.”

In Raman scattering, the quantum pathways are electronic excitations, which are optically stimulated by the incoming photons. These excitations can only happen when the initial electronic state is filled (by a charged particle such as an electron), and the final electronic state is empty.

Quantum mechanics describes electrons filling a material’s available electronic states much as water fills the space in a glass: the “water surface” is called the Fermi level. All the electronic states below it are filled and all the states above it are empty. The filled states can be reduced by “doping” the material in order to shift the Fermi energy lower. As the Fermi energy is lowered, the electronic states just above it are removed, and the excitation pathways originating from these states are also removed.

“We were able to control the excitation pathways in graphene by electrostatically doping it – applying voltage to drive down the Fermi energy and eliminate selected states,” Wang says. “An amazing thing about graphene is that its Fermi energy can be shifted by orders of magnitude larger than conventional materials. This is ultimately due to graphene’s two-dimensionality and its unusual electronic bands.”

The Fermi energy of undoped graphene is located at a single point, where its electronically filled bands, graphically represented as an upward-pointing cone, meet its electronically empty bands, represented as a downward-pointing cone. To move the Fermi energy appreciably requires a strong electric field.

Fig.2: A flake of graphene was grown on copper and transferred onto an insulating substrate of silicon dioxide. The Fermi energy in the graphene was adjusted by varying the gate voltage on the overlying ion gel, which confines a strongly conducting liquid in a polymer matrix.

Team member Rachel Segalman, an associate professor of chemical engineering at UC Berkeley and a faculty scientist in Berkeley Lab’s Materials Sciences Division, provided the ion gel that was key to the experimental device. An ion gel confines a strongly conducting liquid in a polymer matrix. The gel was laid over a flake of graphene, grown on copper and transferred onto an insulating substrate. The charge in the graphene was adjusted by the gate voltage on the ion gel.

“So by cranking up the voltage we lowered the graphene’s Fermi energy, sequentially getting rid of the higher energy electrons,” says Wang. Eliminating electrons, from the highest energies on down, effectively eliminated the pathways that, when impinged upon by incoming photons, could absorb them and then emit Raman-scattered photons.

What comes of interference, constructive and destructive

“People have always known that quantum interference is important in Raman scattering, but it’s been hard to see,” says Wang. “Here it’s really easy to see the contribution of each state.”

Removing quantum pathways one by one alters the ways they can interfere. The changes are visible in the Raman-scattering intensity emitted by the experimental device when it was illuminated by a beam of near-infrared laser light. Although the glow from scattering is much fainter than the near-infrared excitation, changes in its brightness can be measured precisely.

“In classical physics, you’d expect to see the scattered light get dimmer as you remove excitation pathways,” says Wang, but the results of the experimenter came as a surprise to everyone. “Instead the signal got stronger!”

The scattered light grew brighter as the excitation pathways were reduced – what Wang calls “a canonical signature of destructive quantum interference.”

Why “destructively?” Because phonons and scattered photons can be excited by many different, nondistinguishable pathways that interfere with one another, blocking one path can either decrease or increase the light from scattering, depending on whether that pathway was interfering constructively or destructively with the others. In graphene, the lower and higher-energy pathways interfered destructively. Removing one of them thus increased the brightness of the emission.

“What we’ve demonstrated is the quantum-interference nature of Raman scattering,” Wang says. “It was always there, but it was so hard to see that it was often overlooked.”

In a second observation, the researchers found yet another unexpected example of inelastic light scattering. This one, “hot electron luminescence,” didn’t result from blocked quantum pathways, however.

When a strong voltage is applied and the graphene’s Fermi energy is lowered, higher-energy electron states are emptied from the filled band. Electrons that are highly excited by incoming photons, enough to jump to the unfilled band, thus find additional chances to fall back to the now-vacant states in what was the filled band. But these “hot” electrons can only fall back if they emit a photon of the right frequency. The hot electron luminescence observed by the researchers has an integrated intensity a hundred times stronger than the Raman scattering.

The road taken

The poet Robert Frost wrote of coming upon two roads that diverged in a wood, and was sorry he could not travel both. Not only can quantum processes take both roads at once, they can interfere with themselves in doing so.

The research team, working at UC Berkeley and at Berkeley Lab’s Advanced Light Source, has shown that inelastic light scattering can be controlled by controlling interference between the intermediate states between photon absorption and emission. Manipulating that interference has enabled new kinds of quantum control of chemical reactions, as well as of “spintronic” states, in which not charge but the quantum spins of electrons are affected. Strongly enhanced Raman scattering can be a boon to nanoscale materials research. Hot luminescence is potentially attractive for optoelectronics and biological research, in which near-infrared tags – even weak ones – could be very useful.

“Likewise the phenomenon of hot electron luminescence, because it immediately follows excitation by a probe laser, could become a valuable research tool,” says Wang, “particularly for studying ultrafast electron dynamics, one of the chief unusual characteristics of graphene.”

Reference
[1] Chi-Fan Chen, Cheol-Hwan Park, Bryan W. Boudouris, Jason Horng, Baisong Geng, Caglar Girit, Alex Zettl, Michael F. Crommie, Rachel A. Segalman, Steven G. Louie, and Feng Wang, “Controlling Inelastic Light Scattering Quantum Pathways in Graphene,” Nature, (Published online March 16, 2011). Abstract.

[The report is written by Paul Preuss of Lawrence Berkeley National Laboratory]

Quantum Dot Bumps in the Graphene Electronic Highway

Suyong Jung (left) and Gregory Rutter (right), the leading authors of the Nature Physics paper[1] describing quantum dot formation in graphene when placed on insulating substrates.

Electronics researchers love graphene. A two-dimensional sheet of carbon one atom thick, graphene is like a superhighway for electrons, which rocket through the material 100 times faster than they normally do in silicon. But creating graphene-based devices with a full realization of this ultrafast electron transport will be challenging, say researchers at the National Institute of Standards and Technology (NIST), because new measurements show that placing graphene on a substrate, which is essential for graphene transistor operations, transforms its bustling speedway into hills and valleys that make it harder for electrons to get around. These hills and valleys can further localize the electrons into quantum dots when then graphene is exposed to an applied magnetic field, as reported in a new article in Nature Physics [1].

According to NIST Fellow Joseph Stroscio, graphene’s ideal properties are only realized when graphene is isolated from the environment. “To get the most benefit from graphene, we have to understand fully how graphene’s properties change when put in real-world conditions, such as part of device where it is in contact with other kinds of materials like semiconductors and insulators,” Stroscio says.

To see how graphene’s ideal properties are altered when placed on a substrate, NIST postdoctoral researcher Suyong Jung made a graphene device by exfoliating a single layer of graphene onto an insulating SiO2 substrate, using the so-called “scotch tape” method. The SiO2 substrate has a highly doped Si region on the back, which serves as a back gate conductor. When the bottom conductor is charged, an equal and opposite charge is induced in the graphene. This allows the researchers to study the electronic properties of graphene with different types of carriers, electrons versus holes, and with different densities by changing the potential on the back gate conductor. This extra experimental knob allowed the NIST researchers to develop a novel “gate-mapping” spectroscopy, when combined with scanning tunneling spectroscopy.

The researchers used a home-built scanning tunneling microscope operating at 4 K to measure the electron density of states in the graphene as a function of applied magnetic field and carrier density. The researchers first identified the disorder potential hills and valleys in the graphene sheet due to the presence of the substrate by tracking the location of the so-called “Dirac point,” which is the energy location where the conduction and valence bands in graphene come to a point. At this point “ideal” graphene has no carriers, but when placed on a substrate graphene’s potential “hills” and “valleys” fill up with electrons and holes, which leads to puddles, like potholes filling up with water on a damaged highway.

The electron and hole puddles reduce the mobility of electrons in graphene and even cause them to weakly localize in space. The effect of puddles, however, is more pronounced when electrons in graphene are exposed to high magnetic fields. In a magnetic field the electrons undergo cyclotron motion, where the carriers move in circular orbits. These orbits are not random, but take on only certain radii, which are quantized in terms of Landau levels, due to the laws of quantum mechanics. The electrons -- already made sluggish by the substrate interaction -- lack the energy to scale the mountains of resistance, and settle into isolated pockets of “quantum dots,” nanometer-scale regions that confine electrical charges in all directions.

The NIST researchers were able to see the effects of the graphene quantum dots in their measurements in a number of ways. The electrons require a certain energy (charging energy) to tunnel into and out of the quantum dot, which gives rise to a pattern of Coulomb diamonds in the spectroscopic sample bias-gate voltage maps. A series of Coulomb diamonds indicate the sequential addition of single electrons to the graphene quantum dots. Interestingly, the diamonds occur in groups of four reflecting the four-fold degeneracies of electron and valley degrees of freedom in graphene. The spatial location of quantum dots was directly obtained by mapping the compressible (metallic) regions of the Landau levels at the Fermi-energy.

Motivated by the current measurements, a somewhat unique application of graphene can be considered where information on insulating substrates can be obtained by first covering them with graphene, says NIST researcher Nikolai Zhitenev. Usually insulators cannot be studied at the atomic scale with the STM, since the closed loop servo requires a tunneling current to a conducting surface to maintain a constant tip-sample distance. On an insulator, no current is available. Placing the conducting graphene on an insulator lets researchers get close enough to these substrate materials to study their electrical properties, but not so close that the substrate and probe tip are damaged.

Reference
[1] S. Jung, G. Rutter, N. Klimov, D. Newell, I. Calizo, A. Hight-Walker, N. Zhitenev and J. Stroscio, "Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots", Nature Physics. Published online Jan. 9, 2010, DOI:10.1038/nphys1866. Abstract.

A Large Faraday Effect Observed in An Atomically Thin Material

(From L to R): Dirk van der Marel, Alexey Kuzmenko, Julien Levallois and Iris Crassee of University of Geneva

A team of physicists from the University of Geneva (Switzerland) -- in collaboration with researchers in the University of Erlangen-Nuremberg (Germany) and Berkeley Advanced Light Source (USA) -- has recently measured the magnetically induced rotation of the polarization of light (Faraday rotation) [1] in graphene in the far-infrared range.

In contradiction to the common logics, the rotation angle, which is usually proportional to sample thickness, appears to be very strong – up to a few degrees in a single atomic layer. Such a large effect, which is due to the cyclotron resonance of ‘relativistic’ electrons in graphene, does not only provide a useful contact free tool to study the dynamics of the charge carriers in graphene, but also suggests that graphene can be used to manipulate the state of the optical polarization. This work is published in a recent issue of Nature Physics [2].

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice. Electrons in graphene behave like massless relativistic particles moving with a velocity of about 300 times smaller than the speed of light [3]. A high mobility of charge carriers makes graphene potentially useful for electronics. Moreover, graphene shows unique optical properties such as the universal transparency [4], which in combination with excellent electrical conductivity favor its use in important optical applications, such as solar cells, infrared detection, computer screens and ultra fast lasers [5].

On the left: A schematic representation of the Faraday rotation. On the right: the Faraday rotation as a function of the photon energy and the magnetic field (This figure is reproduced from Reference [2]. We thank authors of the paper and 'Nature Physics' for their permission. -- 2Physics.com)

When an external magnetic field is applied over a medium it becomes magnetically polarized and the state of the optical polarization of light passing through the medium is affected: linearly polarized light is rotating gradually during its passage due to a difference in velocity and absorption of left- and right-handed polarized light. The rotation angle, also known as the Faraday angle, is proportional to the optical path length, to the applied magnetic field and a material specific parameter, the Verdet constant, which depends on the wavelength of the passing light. The ‘thickness’ of graphene is given by the inter atomic distance of graphite – stacked graphene layers; therefore an intriguing question is what happens to the optical polarization state if the optical path is as short as only one atom.

Iris Crassee, Julien Levallois, Dirk van der Marel and Alexey Kuzmenko at the University of Geneva have studied the Faraday rotation in the far-infrared range by graphene, epitaxially grown on SiC and characterized in the University of Erlangen-Nuremberg and Berkeley Advanced Light Source [2]. The experiments showed that even for such an extremely thin layer the Faraday rotation can reach 6 degrees in a moderate magnetic field of 7 Tesla (see the figure). If one could be able to stack several graphene layers at distances similar to interlayer spacing in graphite (about 0.35 nm) without changing their individual properties then the effective Verdet constant of such a material can in principle attain a few times of 10⁷ radian/(meter∙Tesla). For comparison, the Verdet constants of the magneto-optical materials used in the visible range, such as rare-earth garnets, are only of the order of 10²-10³ radian/(meter∙Tesla). A more appropriate, though, would be to compare the Faraday rotation in graphene and in the semiconductor-based two-dimensional electron gases (2DEGs) in the same spectral range (far-infrared and teraherz). The fact is that the effective Verdet constant in graphene is still at least one to two orders of magnitude larger!

The origin of the observed Faraday rotation is in a peculiar cyclotron orbital motion of nearly massless electrons in graphene in a magnetic field. A similar effect can also be observed in 2DEGs. However, the cyclotron mass and therefore the cyclotron frequency (at a given magnetic field) in 2DEGs are fixed. In graphene they can be varied with doping. Moreover, since graphene can be doped both positively and negatively either electrostatically or chemically, the cyclotron frequency, and therefore the direction of the Faraday rotation, can be inverted without changing the magnetic field.

The Faraday effect and the associated magneto-optical Kerr effect are already widely used in such vital applications as optical communications, data storage and laser systems, largely in the visible range. Although the Faraday rotation in graphene was shown to be strong in the by far less exploited far-infrared part of the electromagnetic spectrum, one can nevertheless think of using graphene for example, in ultrathin and ultra fast tunable ‘Faraday isolators’, in which light can travel in one direction, but is blocked in the other. In contrast to the existing devices, one should be able to tune the spectral range and also change the sign of the Faraday rotation in graphene by simply adjusting the gate voltage.

References
[1] M. Faraday, “On the magnetization of light and the illumination of magnetic lines of force”, Phil. Trans. R. Soc. 136, 104 (1846).
[2] I. Crassee, J. Levallois, A.L.Walter, M. Ostler, A. Bostwick, E. Rotenberg, Th. Seyller, D. van der Marel and A. B. Kuzmenko, “Giant Faraday rotation in single- and multi ayer graphene”, Nature Physics, 7, 48-51 (2011). Abstract.
[3] A. K. Geim and K. S. Novoselov, “The rise of graphene: Nature Materials, 6, 183 (2007). Abstract.
[4] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres and A.K. Geim, “Fine structure constant defines visual transparancy of graphene”, Science 320, 1308 (2008). Abstract.
[5] F. Bonaccorso, Z. Sun, T. Hasan and A. C. Ferrari, “Graphene photonics and optoelectronics”, Nature Photonics, 4, 611 (2010). Abstract.

Physics Nobel Prize 2010: Graphene

Andre Geim (photo courtesy: Sergeom, Wikimedia Commons) and Konstantin Novoselov (photo courtesy: University of Manchester, UK)

The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov of the University of Manchester "for groundbreaking experiments regarding the two-dimensional material graphene"

Graphene is a form of carbon. As a material it is completely new – not only the thinnest ever but also the strongest. As a conductor of electricity it performs as well as copper. As a conductor of heat it outperforms all other known materials. It is almost completely transparent, yet so dense that not even helium, the smallest gas atom, can pass through it. Carbon, the basis of all known life on earth, has surprised us once again.

Homepage of Andre Geim >> Homepage of Konstantin Novoselov >>
Link to the Mesoscopic Physics Group, University of Manchester, UK >>

Geim and Novoselov extracted the graphene from a piece of graphite such as is found in ordinary pencils. Using regular adhesive tape they managed to obtain a flake of carbon with a thickness of just one atom. This at a time when many believed it was impossible for such thin crystalline materials to be stable.

However, with graphene, physicists can now study a new class of two-dimensional materials with unique properties. Graphene makes experiments possible that give new twists to the phenomena in quantum physics. Also a vast variety of practical applications now appear possible including the creation of new materials and the manufacture of innovative electronics. Graphene transistors are predicted to be substantially faster than today’s silicon transistors and result in more efficient computers.

Since it is practically transparent and a good conductor, graphene is suitable for producing transparent touch screens, light panels, and maybe even solar cells.

When mixed into plastics, graphene can turn them into conductors of electricity while making them more heat resistant and mechanically robust. This resilience can be utilised in new super strong materials, which are also thin, elastic and lightweight. In the future, satellites, airplanes, and cars could be manufactured out of the new composite materials.

This year’s Laureates have been working together for a long time now. Konstantin Novoselov, 36, first worked with Andre Geim, 51, as a PhD-student in the Netherlands. He subsequently followed Geim to the United Kingdom. Both of them originally studied and began their careers as physicists in Russia. Now they are both professors at the University of Manchester.

Playfulness is one of their hallmarks, one always learns something in the process and, who knows, you may even hit the jackpot. Like now when they, with graphene, write themselves into the annals of science.

New Physics from Graphene Quartet's Quantum Harmonies

Joseph Stroscio [Photo courtesy: Center for Nanoscale Science & Technology (CNST), Gaithersburg, MD, USA]

An international team of researchers from the National Institute of Standards and Technology (NIST), the University of Maryland, Seoul National University, the Georgia Institute of Technology, and the University of Texas at Austin, have "unveiled" a quartet of graphene's electron states and discovered that electrons in graphene can split up into an unexpected and tantalizing set of energy levels when exposed to extremely low temperatures and extremely high magnetic fields.

The team, led by Joseph Stroscio of the Electron Physics Group in the NIST Center for Nanoscale Science and Technology (CNST), published their results in Sept. 9, 2010, issue of Nature [1]. The new research raises several intriguing questions about the fundamental physics of this exciting material and reveals new effects that may make graphene even more powerful than previously expected for practical applications.

Graphene is one of the simplest materials—a single-atom-thick sheet of carbon atoms arranged in a honeycomb-like lattice—yet it has many remarkable and surprisingly complex properties. Measuring and understanding how electrons carry current through the sheet is important to realizing its technological promise in wide-ranging applications, including high speed electronics and sensors. For example, the electrons in graphene act as if they have no mass and are almost 100 times more mobile than in silicon. Moreover, the speed with which electrons move through graphene is not related to their energy, unlike materials such as silicon where more voltage must be applied to increase their speed, which creates heat that is detrimental to most applications.

To fully understand the behavior of graphene's electrons, scientists must study the material under an extreme environment of ultra-high vacuum, ultra-low temperatures and large magnetic fields. Under these conditions, the graphene sheet remains pristine for weeks, and the energy levels and interactions between the electrons can be observed with precision [2].

NIST recently constructed the world's most powerful and stable scanning-probe microscope, with an unprecedented combination of low temperature (as low as 10 millikelvin, or 10 thousandths of a degree above absolute zero), ultra-high vacuum and high magnetic field. In the first measurements made with this instrument, the team has used its power to resolve the finest differences in the electron energies in graphene, atom-by-atom.



















[Image credit: T. Schindler and K. Talbott/NIST] This artist's rendition illustrates the electron energy levels in graphene as revealed by a unique NIST instrument. Because of graphene's properties, an electron in any given energy level (the wide, purple band) comprises four quantum states (the four rings), called a "quartet." This quartet of levels split into different energies when immersed in a magnetic field. The two smaller bands on the outermost ring represent the further splitting of a graphene electronic state.

"Going to this resolution allows you to see new physics," said Young Jae Song, a postdoctoral researcher who helped develop the instrument at NIST and make these first measurements.

And the new physics the team saw raises a few more questions about how the electrons behave in graphene than it answers.

Because of the geometry and electromagnetic properties of graphene's structure, an electron in any given energy level populates four possible sublevels, called a "quartet." Theorists have predicted that this quartet of levels would split into different energies when immersed in a magnetic field, but until recently there had not been an instrument sensitive enough to resolve these differences.

"When we increased the magnetic field at extreme low temperatures, we observed unexpectedly complex quantum behavior of the electrons," said NIST Fellow Joseph Stroscio.

What is happening, according to Stroscio, appears to be a "many-body effect" in which electrons interact strongly with one another in ways that affect their energy levels.

One possible explanation for this behavior is that the electrons have formed a "condensate" in which they cease moving independently of one another and act as a single coordinated unit.

"If our hypothesis proves to be correct, it could point the way to the creation of smaller, very-low-heat producing, highly energy efficient electronic devices based upon graphene," said Shaffique Adam, a postdoctoral researcher who assisted with theoretical analysis of the measurements.

The group's work was also recently featured in another paper in Nature Physics [3], in which they describe how the energy levels of graphene's electrons vary with position as they move along the material's crystal structure. The way in which the energy varies suggests that interactions between electrons in neighboring layers may play a role.

References
[1] Y.J. Song, A.F. Otte, Y. Kuk, Y.Hu, D.B. Torrance, P.N. First, W.A. de Heer, H. Min, S. Adam, M.D. Stiles, A.H. MacDonald and J.A. Stroscio, "High Resolution Tunnelling Spectroscopy of a Graphene Quartet", Nature, 467, 185–189 (09 September, 2010). Abstract.
[2] D.L. Miller, K.D. Kubista, G.M. Rutter, M. Ruan, W.A. de Heer, P.N. First and J.A. Stroscio. "Observing the quantization of zero mass carriers in graphene". Science, 324, 924 - 927 (May 15, 2009). Abstract.
[3] D.L. Miller, K.D. Kubista, G.M. Rutter, Ming Ruan, W.A. de Heer, M. Kindermann, P.N. First and J.A. Stroscio, "Real-space mapping of magnetically quantized graphene states", Nature Physics. Published online Aug. 8, 2010. doi:10.1038/nphys1736. Abstract.

Topological Insulators : A New State of Quantum Matter

M. Zahid Hasan

[This is an invited article based on a series of recent works by the author and his collaborators -- 2Physics.com]

Author: M. Zahid Hasan

Affiliation: Joseph Henry Laboratories of Physics, Department of Physics,
Princeton University, USA

Most quantum states of condensed-matter systems or the fundamental forces are categorized by spontaneously broken symmetries. The remarkable discovery of quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based not on the broken symmetry but only on the topological distinctions in the presence of time-reversal symmetry breaking [1,2]. In the past few years, theoretical developments suggest that new classes of topological states of quantum matter might exist in nature [3,4,5]. Such states are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field : "Quantum Hall-like effects without magnetic field".

Research Team at Princeton University: [L to R] David Hsieh, Dong Qian, L. Andrew Wray, YuQi Xia

This exotic phase of matter is a subject of intense research because it is predicted to give rise to dissipationless (energy saving) spin currents, quantum entanglements and novel macroscopic behavior that obeys axionic electrodynamics rather than Maxwell's equations [6]. Unlike ordinary quantum phases of matter such as superconductors, magnets or superfluids, topological insulators are not described by a local order parameter associated with a spontaneously broken symmetry but rather by a quantum entanglement of its wave function, dubbed topological order. In a topological insulator this quantum entanglement survives over the macroscopic dimensions of the crystal and leads to surface states that have unusual spin textures.

Topologically ordered phases of matter are extremely rare and are experimentally challenging to identify. The only known example was the quantum Hall effect discovered in the 1980s by von Klitzing (Nobel Prize 1985). It was identified by measuring a quantized magneto-transport in a two-dimensional electron system under a large external magnetic field at very low temperatures, which is characterized by robust conducting states localized along the one-dimensional edges of the sample. Two-dimensional topological insulators, on the other hand, are predicted to exhibit similar edge states even in the absence of a magnetic field because spin-orbit coupling can simulate its effect (Fig.1A) due to the relativistic terms added in a band insulator's Hamiltonian.

Remarkably, three-dimensional topological insulators, an entirely new state of matter with no charge quantum Hall analogue, are also postulated to exist. And its topological order or exotic quantum entanglement is predicted to give rise to unusual conducting two-dimensional surface states (Fig.1B) that have novel spin-selective energy-momentum dispersion relations. Utilizing state-of-the-art angle-resolved photoemission spectroscopy, an international collaboration led by scientists from Princeton University have studied the electronic structure of several bismuth based spin-orbit materials [7,8,9]. By systematic tuning of the incident photon energy, it was possible to isolate surface quantum states from the bulk states, which confirmed that these materials realized a three-dimensional topological insulator phase.

Figure 1. (A) Schematic of the 1D edge states in a 2D topological insulator. The red and blue curves represent the edge current with opposite spin character. (B) Schematic of the 2D surface states in a 3D topological insulator. (C) Most elemental topological Insulators exhibit odd number of Dirac cones on their surface unlike the even numbers observed in graphene. Topological insulator Dirac cones are spin polarized where as Dirac cones in graphene are not.

The remarkable property of the surface states of a 3D topological insulator is that its Fermi surface supports a geometrical quantum entanglement phase, which occurs when the spin-polarized Fermi surface encloses the Kramers' points and on the surface Brillouin zone an odd number of times in total (Fig.2B). ARPES intensity map of the (111) surface states of bulk insulating Bi1-xSbx (Fig.2A) shows that a single Fermi surface encloses . However, determination of the degeneracy of the additional Fermi surface around requires a detailed study of its energy-momentum dispersion. ARPES spectra along the - direction (Fig.2C) reveal that the Fermi surface enclosing is actually composed of two bands, therefore two Fermi surfaces enclose , leading to a total of seven and Fermi surface enclosures.

Figure 2. (A) ARPES surface state (SS) Fermi surface of insulating Bi1-xSbx showing spin polarization directions as indicated by red and blue arrows. (B) Schematic of the SS Fermi surface of a 3D topological insulator. (C) ARPES energy-momentum dispersion of the surface states. The shaded areas denote the bulk bands while the dashed white lines are guides to the eye for surface state dispersions. (D) A single Dirac cone is observed in Bi2Te3.

These results constitute the first direct experimental evidence of a topological insulator in nature which is fully quantum entangled. The observed spin-texture in BiSb is consistent with a magnetic monopole image field beneath the surface. It shows that spin-orbit materials are a new family in which exotic topological order quantum phenomena, such as dissipationless spin currents and axion-like electrodynamics, may be found without the need for an external magnetic field. The results presented in this study also demonstrate a general measurement algorithm of identifying and characterizing topological insulator materials for future research which can be utilized to discover, observe and study other forms of topological order and quantum entanglements in nature. A detailed study of topological order and quantum entanglement can potentially pave the way for fault-tolerant (topological) quantum computing [10].

Figure 3: A new type of quantum matter called a topological insulator contains only half an electron pair (represented by just one Dirac cone in schematic crystal structure at top left), which is observed in the form of a single ring (red) in the center of the electron-map (top right) with electron spin in only one direction. This highly unusual observation shows that if an electron is tagged "red" and then undergoes a full 360-degree revolution about the ring, it does not recover its initial face as an ordinary everyday object would, but instead acquires a different color "blue" (represented by the changing color of the arrows around the ring). This new quantum effect can be the basis for the realization of a rare quantum phase that had been a long-sought key ingredient for developing quantum computers that can be highly fault-tolerant.

References:
[1] K. von Klitzing, G. Dorda, M. Pepper, "New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance", Phys. Rev. Lett. 45, 494-497 (1980). Abstract.
[2] D.C. Tsui, H. Stormer, A.C. Gossard, "Two-dimensional magnetotransport in the extreme quantum limit", Phys. Rev. Lett. 48, 1559-1562 (1982). Abstract.
[3] L. Fu, C. L. Kane and E. J. Mele, "Topological insulators in three dimensions", Physical Review Letters 98, 106803 (2007). Abstract.
[4] J. E. Moore and L. Balents, "Topological invariants of time-reversal-invariant band structures", Physical Review B 75, 121306(R) (2007). Abstract.
[5] S.-C. Zhang, "Topological states of quantum matter", Physics 1, 6 (2008). Abstract.
[6] M. Franz, "High energy physics in a new guise", Physics 1, 36 (2008). Abstract.
[7] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan, "A topological Dirac insulator in a quantum spin Hall phase", Nature 452, 970 (2008). Abstract.
[8] Y. Xia, D. Qian, L. Wray, D. Hsieh, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of a large-gap topological insulator class with single surface Dirac cone”, Nature Physics 5, 398 (2009). Abstract.
[9] D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of Unconventional Quantum Spin Textures in Topological Insulators", Science 323, 919 (2009). Abstract.
[10] A. Akhmerov, J. Nilsson, C. Beenakker, “Electrically detected interferometry of Majorana fermions in a topological insulator”, Phys. Rev. Lett. 102, 216404 (2009). Abstract.