Topological States and Adiabatic Pumping in Quasicrystals

Left to right: Kobi E. Kraus, Oded Zilberberg, Yoav Lahini, Zohar Ringel and Mor Verbin

Authors: 
Yaacov E. Kraus¹, Yoav Lahini^2,3, Zohar Ringel¹, Mor Verbin², Oded Zilberberg¹

Affiliation:
¹Dept. of Condensed Matter Physics, Weizmann Institute of Science, Israel
²Dept. of Physics of Complex Systems, Weizmann Institute of Science, Israel
³Department of Physics, Massachusetts Institute of Technology, USA

The materials that make up our world have a variety of electrical properties. Some materials, such as metals, conduct electricity extremely well, while others are insulators, and are very efficient as shields from electric currents.

Recently, a new discovery revolutionized the prevailing paradigm of electrical properties of materials, when a new type of material was discovered [1, 2]. These materials are termed “topological insulators”, and have very unique electrical properties. For example, electricity would flow smoothly on the surface of a topological insulator, while the interior will be completely insulating. Interestingly, if one would cut this material in half, the new surface that is created, which was previously buried within the insulating interior, will suddenly become conducting. If the material is cut repeatedly, the same will happen each time.

Past 2Physics article by Yoav Lahini:
November 07, 2010: "Hanbury Brown and Twiss Interferometry with Interacting Photons"
by Yoav Lahini, Yaron Bromberg, Eran Small and Yaron Silberberg

In addition to this peculiar property, the electrical behavior on the surface itself reveals unique phenomena that are even expected to simulate bizarre new particle excitations [3]. As a result, these fascinating materials generated much activity in the condensed matter physics community, in an attempt to find new topological materials and to study their intriguing properties.

In a recent paper [4], we found that other unconventional materials, known as quasicrystals, are in fact also members of the topological materials family. Moreover, the topological behavior that they exhibit is similar to that of usual topological materials in some aspects, but differs from them in others.

Quasicrystals are materials in which the atoms are arranged in a distinct way. In most solid materials, the atoms are arranged in space either periodically or in a completely random fashion. Quasicrystals are an intermediate type of solid - they are neither periodic nor random. Rather, there is some non-repeating (i.e. non periodic) but well defined rule to the arrangement of their atoms [5, 6]. Despite the fact that quasicrystals have been experimentally observed already in 1982 [5], for a long time there was a debate between crystallographers whether they exist at all, as it was assumed that all crystalline materials are necessarily periodic. The conclusion that quasicrystals are a new type of solid revolutionized material science, updated the physical definition of what is a crystal, and culminated in the awarding of the Nobel Prize in Chemistry to its discoverer, Dan Shechtman from the Technion - Israel Institute of Technology [7].

Yet, many of the physical properties of quasicrystals, such as their electrical conductance, are not fully understood. The work recently published by our group in Physical Review Letters [4], discusses the electrical properties of surfaces of quasicrystals, and finds a new and surprising connection between quasicrystals and topological states of matter. Specifically, we show that a one-dimensional quasicrystal behaves, to some extent, like two-dimensional topological matter known as quantum Hall systems. We prove this claim theoretically and measure it experimentally.

The experiments were done on a novel type of quasicrystals, known as photonic quasicrystals [8, 9]. These systems are made of quasi-periodic arrangements of transparent materials, rather than atoms. In these systems, one studies the optical properties, rather than the electrical, but the underlying physics is very much the same. A major advantage of using photonic quasicrystals is the ability to fabricate one-dimensional materials, and to directly image the propagation of light within them.

In our experiments, we have realized a one-dimensional photonic quasicrystal, and measured the boundary (the surface of a one-dimensional system) properties of these quasicrystals. We found that the photonic states that reside at the boundary are localized -- meaning that light that is injected to that boundary will stay there. This is analogous to the electric currents on the surface of topological matter, which do not penetrate the interior of the material, but remain confined to the surface. This finding was surprising, as common wisdom was that -- generally, such a behavior is not supposed to occur in one-dimensional systems.

Our theory explains how that becomes possible in quasicrystals. In brief, the arrangement of atoms in a quasicrystal can be mathematically described as some type of projection of a periodic system on a system of lower dimension – for example, projection of a two-dimensional square lattice onto a one-dimensional line [10]. Note that this description defines the position of the atoms of the quasicrystal, but do not imply the properties of any electrons (or photons) moving through it. In our case, the one-dimensional quasicrystalline models we worked with can be described as another type of one-dimensional projection of a quantum Hall system, known as “dimensional reduction” [3]. Most importantly, the novel projection used to define our one-dimensional quasicrystals preserves the topological properties! Thus, we find that beyond their mere structure, quasicrystals can, in some sense, also “inherit” nontrivial topological properties from their higher-dimensional periodic “ancestors”.

Taking things a step forward, we have shown that the boundary states observed in the experiments indeed possess nontrivial topological properties, by demonstrating a topological “pumping” of light from one side of the quasicrystal to the other [4].

Figure 1: Experimental observation of adiabatic pumping via topologically protected boundary states in a photonic quasicrystal. (a) An illustration of the adiabatically modulated photonic quasicrystal, constructed by slowly varying the spacing between the waveguides along the propagation axis z. Consequently, the injected light is pumped across the sample. (b) Experimental results: Light was injected into the rightmost waveguide. The measured intensity distributions as a function of the position are presented at different stages of the adiabatic evolution, i.e., different propagation distances. It is evident that along the adiabatic evolution the light crossed the lattice from right to left.

This fascinating discovery appears to be just the beginning. Our results suggest that additional quasicrystals should exhibit topological states [11, 12], and that these states will always be linked to systems of a higher dimension. This approach might mean that three-dimensional quasicrystalline materials -- either photonic or electronic -- would exhibit strange surface properties, which can be explained as originating from a six-dimensional topological system. These subjects are currently under active investigation.

References:
[1] “Colloquium: Topological Insulators”, M.Z. Hasan and C.L. Kane, Reviews of Modern Physics, 82, 3045 (2010). Abstract.
[2] “Topological insulators and superconductors”, Xiao-Liang Qi and Shou-Cheng Zhang , Reviews of Modern Physics, 83, 1057 (2011). Abstract.
[3] “Topological field theory of time-reversal invariant insulators”, Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang, Physical Review B 78, 195424 (2008). Abstract.
[4] "Topological States and Adiabatic Pumping in Quasicrystals”, Yaacov E. Kraus, Yoav Lahini, Zohar Ringel, Mor Verbin, and Oded Zilberberg, Physical Review Letters, 109, 106402 (2012). Abstract.
[5] “Metallic Phase with Long-Range Orientational Order and No Translations Symmetry”, D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Physical Review Letters, 53, 1951 (1984). Abstract.
[6] "Quasicrystals: A New Class of Ordered Structures", Dov Levine and Paul Joseph Steinhardt, Physical Review Letters, 53, 2477 (1984). Abstract.
[7] See http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html .
[8] “Wave and defect dynamics in nonlinear photonic quasicrystals”, Barak Freedman, Guy Bartal, Mordechai Segev, Ron Lifshitz, Demetrios N. Christodoulides and Jason W. Fleischer, Nature, 440, 1166 (2006). Abstract.
[9] “Observation of a Localization Transition in Quasiperiodic Photonic Lattices”, Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson and Y. Silberberg, Physical Review Letters, 103, 013901 (2009). Abstract.
[10] “Algebraic theory of Penrose's non-periodic tilings of the plane”, N.G. de Bruijn, Kon. Nederl. Akad. Wetensch. Proc. Ser. A (1981).
[11] “Topological Equivalence Between The Fibonacci Quasicrystal and The Harper Model”, Yaacov E. Kraus and Oded Zilberberg, Physical Review Letters, 109, 116404 (2012). Abstract.
[12] “Observation of Topological Phase Transitions in One-Dimensional Photonic Quasicrystals”, M. Verbin, Y. E. Kraus, O. Zilberberg, Y. Lahini and Y. Silberberg, in preparation. 

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.

Avian Compass Reloaded

Dagomir Kaszlikowski

Author: Dagomir Kaszlikowski

Affiliation: Centre for Quantum Technologies, Department of Physics, National University of Singapore, Singapore

Recently there has been a fundamental change in our understanding of how biological systems operate; new research revealed that quantum phenomena could play an essential part in biological processes. Understanding the fundamental mechanisms contributing to biological processes is an essential step in developing our understanding of life, its origins and evolution. However, one has to be cautious how to approach this problem to avoid triviality.

Molecules are purely quantum mechanical objects which must behave according to quantum mechanical laws. Therefore life is governed by the laws of quantum mechanics; it is the result of a series of chemical reactions between molecules happening inside of any living organism. There is nothing insightful in this observation. However, if one could demonstrate that biological systems utilize certain peculiar aspects of quantum mechanics such as coherence, entanglement or tunneling to their advantage, it would be a highly non-trivial statement.

Scientists have recently discovered strong evidence for complex quantum mechanical mechanisms in two interesting biological processes: photosynthesis [1] and the avian compass [2,3]. In this article I would like to focus on the latter.

It has been observed that some species of migratory birds can sense the direction of the Earth’s magnetic field. They use this sensitivity to the geomagnetic field to navigate during seasonal migration. This is extremely surprising because the magnetic field of our planet is very weak and it is difficult to imagine how it can affect a bird’s nervous system or trigger a behavioral response. In 2008 scientists realized that birds may directly observe the magnetic field by utilizing a magnetically sensitive photochemical reaction called the radical pair mechanism.

In a nutshell: it is assumed that the bird’s retina contains a photoreceptor pigment with molecular axis direction dependent on its position in the retina. Absorption of incident light by a part of the pigment results in electron transfer to a suitable nearby part and in this way a radical pair is formed, i.e. a pair of charged molecules each having an electron with unpaired spin. In the external magnetic field the state of the electron spins undergoes singlet-triplet transitions and at random times the radical pairs recombine forming singlet (triplet) chemical reaction products. In a bird’s brain, the amount of these chemical products varies along the retina as the direction of molecular axis changes, and the shape of this profile is believed to be correlated with the orientation of the geomagnetic field. I would like to mention at this point that singlet and triplet states of two electrons, which are examples of entangled states, are purely quantum mechanical phenomena that cannot be modeled using classical physics.

We need to put this hypothesis in the context of behavioral experiments carried on European Robins. During these experiments researchers determined that (i) the avian compass is only sensitive to inclination of the magnetic field, not its polarity; (ii) investigated birds were disoriented after being subjected to a weak radio frequency magnetic field whose frequency is adjusted to the characteristic frequency of the radical pair mechanism; (iii) the compass stopped working if the local geomagnetic field was weakened or strengthened by around 30%.

There are two essential physical parameters, in the radical pair mechanism model, which determine a bird’s ability to navigate: the average lifetime of the radical pair and its robustness to disturbances from the environment. The lifetime of the radical pair must be long enough to produce the chemical product profile necessary to stimulate the bird’s nervous system. Disturbances from the environment is called decoherence in quantum theory. Decoherence directly effects electronic singlet and triplet states making them lose their entanglement. This results in the bird’s compass being insensitive to the inclination of the magnetic field. The coherence time of the radical pair must be sufficient to prevent this from happening.

My colleagues from the National University of Singapore and Oxford University (UK) showed, in their recent paper [2], that both the average lifetime and the coherence time of the radical pair in the European Robin’s eye can be of the order of 100 microseconds. This is a surprising result, given that the longest coherence times of molecular electron spin states achieved in the laboratory (where the influence of the environment is minimized as much as possible) are 80 microseconds! It would imply that evolution created protection for fragile quantum processes beyond what humans can engineer.

In my recent paper [3] -- together with my collaborators Tomek Paterek and Jayendra Bandyopadhyay -- we arrived at different lifetime and coherence time estimations based on the same radical pair mechanism model. We estimated that lifetime and coherence of radical pair in the European Robin’s eye is of the order of 10 microseconds. The difference between our results and those in [2] stems from the fact that we considered all the results (i) to (iii) of the behavioral experiments whereas the result (iii) was not accounted for in the paper by my colleagues. Let me explain this.

The graphs above represent the angular dependence of the yield of radical pair chemicals produced in the theoretical model of the avian compass. The black curve corresponds to the local geomagnetic field near Frankfurt, Germany, where the behavioral experiments were carried out. The blue curve represents a static magnetic field that is 30% weaker than the one in Frankfurt. The green curve is the yield in the presence of a weak radio frequency oscillating magnetic field. The inverse of the parameter k is the lifetime of radical pair and a parameter in the theoretical model that must be adjusted in order to reproduce the experimental data.

According to behavioral experiments (ii) and (iii) a European Robin becomes disoriented if either it is subjected to a weak radio frequency magnetic field oscillating at a specific frequency or if the magnitude of the local geomagnetic field is changed by 30%. Therefore, for those values of the parameter k for which the green curve enters the region (called the “functional window” of the compass) one gets contradiction with the experiment because birds were disoriented in the presence of the RF magnetic field. As you can see from the right-most graphs this happens for radical pair lifetimes of the order of 10 microseconds. This is our estimation of the average lifetime of the radical pair in the European Robin’s retina. It also agrees with in vitro experiments on cryptochrome molecules [4]. These molecules are believed to constitute the photo-receptor pigment responsible for the radical pair based avian compass of European Robins.

Based on this value of the parameter k we were able to investigate the sensitivity of the avian compass as a function of the environmental noise as shown in graphs below:

The upper graph corresponds to the situation where the coupling strength of one of the electrons from the radical pair is slightly stronger than the strength of the geomagnetic field in Frankfurt (Larmor precession period of 0.78 microseconds). The lower graph corresponds to where the coupling is slightly weaker. I would like to mention that the compass only works for a small range of the coupling strength centered on 0.78 microseconds.

If the coupling strength is larger than the strength of the geomagnetic field then the sensitivity of the compass in the presence of the environmental noise (corresponding to coherence time of the order of one microsecond) is better than if there is no noise! This is not the case if the coupling strength is weaker but we still observe a local increase in the sensitivity for a coherence time of around one microsecond. A similar phenomenon is also found in studies of energy transfer during photosynthesis [5].

A plausible conclusion one can draw from these results is that nature may be optimizing performance of some biological processes by utilizing inevitable noise present in the environment, which is definitely a non-trivial statement about the role quantum mechanics can play in biology. More insight into this conjecture can be obtained from further studies of the resonance that magnetic sensitivity displays as a function of environmental noise -- as identified in this work.

References:
[1] Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomá Manal, Yuan-Chung Cheng, Robert E. Blankenship, Graham R. Fleming, "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems", Nature 446, 782 (2007). Abstract.
[2] Erik M. Gauger, Elisabeth Rieper, John J. L. Morton, Simon C. Benjamin, and Vlatko Vedral, "Sustained Quantum Coherence and Entanglement in the Avian Compass", Physical Review Letters, 106, 040503 (2011). Abstract.
[3] Jayendra N. Bandyopadhyay, Tomasz Paterek, and Dagomir Kaszlikowski, "Quantum Coherence and Sensitivity of Avian Magnetoreception", Physical Review Letters, 109, 110502 (2012). Abstract.
[4] Till Biskup, Erik Schleicher, Asako Okafuji, Gerhard Link, Kenichi Hitomi, Elizabeth D. Getzoff, Stefan Weber, "Direct Observation of a Photoinduced Radical Pair in a Cryptochrome Blue-Light Photoreceptor", Angewandte Chemie International Edition, 48, 404 (2009). Abstract.
[5] Masoud Mohseni, Patrick Rebentrost, Seth Lloyd, and Alán Aspuru-Guzik, "Environment-assisted quantum walks in photosynthetic energy transfer", Journal of Chemical Physics, 129, 174106 (2008). Abstract.

Physics Nobel Prize 2012: Quantum Measurement

Serge Haroche (left) and David J. Wineland (right)










The 2012 Nobel Prize in Physics has been awarded to Serge Haroche (Collège de France and Ecole Normale Supérieure, Paris, France) and David J. Wineland (National Institute of Standards and Technology (NIST) and University of Colorado Boulder, CO, USA) "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems".

Serge Haroche and David J. Wineland have independently invented and developed methods for measuring and manipulating individual particles while preserving their quantum-mechanical nature, in ways that were previously thought unattainable.

The Nobel Laureates have opened the door to a new era of experimentation with quantum physics by demonstrating the direct observation of individual quantum particles without destroying them. For single particles of light or matter the laws of classical physics cease to apply and quantum physics takes over. But single particles are not easily isolated from their surrounding environment and they lose their mysterious quantum properties as soon as they interact with the outside world. Thus many seemingly bizarre phenomena predicted by quantum physics could not be directly observed, and researchers could only carry out thought experiments that might in principle manifest these bizarre phenomena.

Past 2Physics articles on works of Serge Haroche and David J. Wineland:

Jul 10, 2011: "Chilling of Micromechanical Motion to the Quantum Ground State"
Sep 26, 2010: "Aluminum Atomic Clocks Reveal Einstein's Relativity at a Personal Scale"
Feb 21, 2010: "World’s Most Precise Clock : NIST Developed Second ‘Quantum Logic Clock’ Based on Aluminum Ion"
Aug 15, 2009: "NIST Physicists Demonstrate Sustained Quantum Processing in Step Toward Building Quantum Computers "
Mar 28, 2008: "‘Quantum Logic Clock’ Rivals Mercury Ion as World’s Most Accurate Clock : A new limit on change in fine-structure constant"
Mar 15, 2007: "Life & Death of a Single Photon Observed"

Through their ingenious laboratory methods Haroche and Wineland together with their research groups have managed to measure and control very fragile quantum states, which were previously thought inaccessible for direct observation. The new methods allow them to examine, control and count the particles.

Their methods have many things in common. David Wineland traps electrically charged atoms, or ions, controlling and measuring them with light, or photons.

Serge Haroche takes the opposite approach: he controls and measures trapped photons, or particles of light, by sending atoms through a trap.

Homepage of Serge Haroche at Collège de France, Paris >>

Both Laureates work in the field of quantum optics studying the fundamental interaction between light and matter, a field which has seen considerable progress since the mid-1980s. Their ground-breaking methods have enabled this field of research to take the very first steps towards building a new type of super fast computer based on quantum physics. Perhaps the quantum computer will change our everyday lives in this century in the same radical way as the classical computer did in the last century. The research has also led to the construction of extremely precise clocks that could become the future basis for a new standard of time, with more than hundred-fold greater precision than present-day caesium clocks.

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.