Imperfections, Disorder and Quantum Coherence

Steve Rolston [Image courtesy: University of Maryland, USA]

A new experiment conducted at the Joint Quantum Institute (JQI, operated jointly by the National Institute of Standards and Technology in Gaithersburg, MD and the University of Maryland in College Park, USA) examines the relationship between quantum coherence, an important aspect of certain materials kept at low temperature, and the imperfections in those materials. These findings should be useful in forging a better understanding of disorder, and in turn in developing better quantum-based devices, such as superconducting magnets. The new results are published in the New Journal of Physics [1].

Most things in nature are imperfect at some level. Fortunately, imperfections---a departure, say, from an orderly array of atoms in a crystalline solid---are often advantageous. For example, copper wire, which carries so much of the world’s electricity, conducts much better if at least some impurity atoms are present.

In other words, a pinch of disorder is good. But there can be too much of this good thing. The issue of disorder is so important in condensed matter physics, and so difficult to understand directly, that some scientists have been trying for some years to simulate with thin vapors of cold atoms the behavior of electrons flowing through solids trillions of times more dense. With their ability to control the local forces over these atoms, physicists hope to shed light on more complicated case of solids.

That’s where the JQI experiment comes in. Specifically, Steve Rolston and his colleagues have set up an optical lattice of rubidium atoms held at temperature close to absolute zero. In such a lattice atoms in space are held in orderly proximity not by natural inter-atomic forces but by the forces exerted by an array of laser beams. These atoms, moreover, constitute a Bose Einstein condensate (BEC), a special condition in which they all belong to a single quantum state.

This is appropriate since the atoms are meant to be a proxy for the electrons flowing through a solid superconductor. In some so called high temperature superconductors (HTSC), the electrons move in planes of copper and oxygen atoms. These HTSC materials work, however, only if a fillip of impurity atoms, such as barium or yttrium, is present. Theorists have not adequately explained why this bit of disorder in the underlying material should be necessary for attaining superconductivity.

The JQI experiment has tried to supply palpable data that can illuminate the issue of disorder. In solids, atoms are a fraction of a nanometer (billionth of a meter) apart. At JQI the atoms are about a micron (a millionth of a meter) apart. Actually, the JQI atom swarm consists of a 2-dimensional disk. “Disorder” in this disk consists not of impurity atoms but of “speckle.” When a laser beam strikes a rough surface, such as a cinderblock wall, it is scattered in a haphazard pattern. This visible speckle effect is what is used to slightly disorganize the otherwise perfect arrangement of Rb atoms in the JQI sample.

In superconductors, the slight disorder in the form of impurities ensures a very orderly “coherence” of the supercurrent. That is, the electrons moving through the solid flow as a single coordinated train of waves and retain their cohesiveness even in the midst of impurity atoms.

In the rubidium vapor, analogously, the slight disorder supplied by the speckle laser ensures that the Rb atoms retain their coordinated participation in the unified (BEC) quantum wave structure. But only up to a point. If too much disorder is added---if the speckle is too large---then the quantum coherence can go away. Probing this transition numerically was the object of the JQI experiment. The setup is illustrated in figure 1.

Figure 1: Two thin planes of cold atoms are held in an optical lattice by an array of laser beams. Still another laser beam, passed through a diffusing material, adds an element of disorder to the atoms in the form of a speckle pattern. [Image courtesy: Matthew Beeler]

And how do you know when you’ve gone too far with the disorder? How do you know that quantum coherence has been lost? By making coherence visible.

The JQI scientists cleverly pry their disk-shaped gas of atoms into two parallel sheets, looking like two thin crepes, one on top of each other. Thereafter, if all the laser beams are turned off, the two planes will collide like miniature galaxies. If the atoms were in a coherent condition, their collision will result in a crisp interference pattern showing up on a video screen as a series of high-contrast dark and light stripes.

If, however, the imposed disorder had been too high, resulting in a loss of coherence among the atoms, then the interference pattern will be washed out. Figure 2 shows this effect at work. Frames b and c respectively show what happens when the degree of disorder is just right and when it is too much.

Figure 2: Interference patterns resulting when the two planes of atoms are allowed to collide. In (b) the amount of disorder is just right and the pattern is crisp. In (c) too much disorder has begun to wash out the pattern. In (a) the pattern is complicated by the presence of vortices in the among the atoms, vortices which are hard to see in this image taken from the side. [Image courtesy: Matthew Beeler]

“Disorder figures in about half of all condensed matter physics,” says Steve Rolston. “What we’re doing is mimicking the movement of electrons in 3-dimensional solids using cold atoms in a 2-dimensional gas. Since there don’t seem to be any theoretical predictions to help us understand what we’re seeing we’ve moved into new experimental territory.”

Where does the JQI work go next? Well, in figure 2a you can see that the interference pattern is still visible but somewhat garbled. That arises from the fact that for this amount of disorder several vortices---miniature whirlpools of atoms---have sprouted within the gas. Exactly such vortices among electrons emerge in superconductivity, limiting their ability to maintain a coherent state.

Another of the JQI scientists, Matthew Beeler, underscores the importance of understanding the transition from the coherent state to incoherent state owing to the fluctuations introduced by disorder: “This paper is the first direct observation of disorder causing these phase fluctuations. To the extent that our system of cold atoms is like a HTSC superconductor, this is a direct connection between disorder and a mechanism which drives the system from superconductor to insulator.”

Reference:
[1] M C Beeler, M E W Reed, T Hong, and S L Rolston, "Disorder-driven loss of phase coherence in a quasi-2D cold atom system", New Journal of Physics, 14, 073024 doi:10.1088/1367-2630/14/7/073024 (2012). Abstract. Full Article.

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.

Quantum Gravity: Can It Be Empirically Tested?

Claus Kiefer (left) and Manuel Krämer (right) 

[Every year (since 1949) the Gravity Research Foundation honors best submitted essays in the field of Gravity. This year's prize goes to Claus Kiefer and Manuel Krämer for their essay "Can Effects of Quantum Gravity Be Observed in the Cosmic Microwave Background?". The five award-winning essays will be published in a special issue of the International Journal of Modern Physics D (IJMPD). Today we present here an article by Claus Kiefer and Manuel Krämer on their current work. -- 2Physics.com ]

Authors: Claus Kiefer and Manuel Krämer

Affiliation: University of Cologne, Germany 

Quantum theory seems to be a universal framework for physical interactions. The Standard Model of particle physics, for example, is described by a quantum field theory of the strong and electroweak interactions. The only exception so far is gravity, which is successfully described by a classical theory: Einstein's theory of general relativity. The general expectation, however, is that general relativity is incomplete and must merge with quantum theory to a fundamental theory of quantum gravity [1,2]. One reason is the singularity theorems in Einstein's theory, the other is the universal coupling of gravity to all forms of energy and thus to the energy of all quantum fields.

2Physics articles by past winners of the Gravity Research Foundation award:
Mark Van Raamsdonk (2010): "Quantum Gravity and Entanglement"
Alexander Burinskii (2009): "Beam Pulses Perforate Black Hole Horizon"
T. Padmanabhan (2008): "Gravity : An Emergent Perspective"
Steve Carlip (2007): "Symmetries, Horizons, and Black Hole Entropy"

Despite many attempts in the last 80 years, a final quantum theory of gravity is elusive. There are various approaches, which all have their merits and shortcomings [1,2]. A major problem in the search for a final theory is the lack of empirical tests so far. This problem is usually attributed to the fact that the Planck scale, on which quantum gravity effects are supposed to become strong, is far remote from any other relevant scale. Expressed in energy units, the Planck scale is 15 orders of magnitude higher than even the energy reachable at the Large Hadron Collider (LHC) in Geneva. It is thus hopeless to probe the Planck scale directly by scattering experiments.

In our prize-winning essay [3], we have addressed the question whether effects of quantum gravity can be observed in a cosmological context. More precisely, we have investigated the presence of possible effects in the anisotropy spectrum of the cosmic microwave background (CMB) radiation.

But given the presence of many approaches, which framework should one use for the calculations? We have decided to be as conservative as possible and to base our investigation on quantum geometrodynamics, the direct quantization of Einstein's theory. The central equation in this approach is the Wheeler-DeWitt equation, named after the pioneering work of Bryce DeWitt and John Wheeler [4]. It is a conservative approach because the Wheeler-DeWitt equation is the quantum equation that directly leads to general relativity in the semiclassical limit. It possesses for gravity the same value that the Schrödinger equation has for mechanics.

While the Wheeler-DeWitt equation is difficult to solve in full generality, it can be treated in an approximation scheme that is similar to a scheme known from molecular physics - the Born-Oppenheimer approximation. It basically consists of an expansion with respect to the Planck energy. It is thus assumed that the relevant expansion parameter is (the square of) the relevant energy scale over the Planck energy. A Born-Oppenheimer scheme of this type has been applied to gravity in [5]. In this way, one first arrives at the limit of quantum field theory on a fixed background. The next order then gives quantum-gravitational corrections that are inversely proportional to the Planck mass squared. It is these correction terms that we have evaluated for the CMB. The quantitative discussion, on which our essay is based, is presented in [6]. We assume that the Universe underwent a period of inflationary expansion at an early stage and that it was this inflation that produced the CMB anisotropies out of which all structure in the Universe evolved.

What are the results? The calculations show that the quantum-gravitational correction terms lead to a modification of the anisotropy power spectrum that is most pronounced for large scales, that is, large angular separations at the sky. More precisely, one finds a suppression of power at large scales. Such a suppression can, in principle, be observed. Since up to now no such signal has been identified, not even in the measurements of the WMAP satellite, we can find from our investigation only an upper limit on the expansion rate of the inflationary Universe. The effect is therefore too small to be seen, it seems, although it is expected to be considerably larger than quantum-gravitational effects in the laboratory.

A similar investigation was done for loop quantum cosmology [7]. It was found there that quantum gravitational effects lead to an enhancement of the power at large scales, instead of a suppression. These considerations may thus be able to discriminate between different approaches to quantum gravity.

What are the implications for future research? It remains to be seen whether the size of quantum-gravitational corrections terms can become large enough to be observable in other circumstances. One may think of the polarization of the CMB anisotropies or at the correlations functions of galaxies. Such investigations are important because there will be no fundamental progress in quantum gravity research without observational guidance. We hope that our essay will stimulate research in this direction.

References
[1] C. Kiefer, "Quantum Gravity" (Oxford University Press, Oxford, 3rd edition, 2012).
[2] S. Carlip, "Quantum gravity: a progress report", Reports on Progress in Physics, 64, 885-942 (2001).Abstract.
[3] C. Kiefer and M. Krämer, "Can effects of quantum gravity be observed in the cosmic microwave background?",  To appear in Int. J. Mod. Phys. D. Available at: arXiv:1205.5161 [gr-qc],
[4] B. S. DeWitt, "Quantum theory of gravity. I. The canonical theory", Phys. Rev., 160, 1113-1148 (1967). Abstract; J. A. Wheeler, "Superspace and the nature of quantum geometrodynamics", in: "Battelle rencontres", ed. by C. M. DeWitt and J. A. Wheeler (Benjamin, New York, 1968), pp. 242-307.
[5] C. Kiefer and T. P. Singh, "Quantum gravitational correction terms to the functional Schrödinger equation", Phys. Rev. D, 44, 1067-1076 (1991).Abstract.
[6] C. Kiefer and M. Krämer, "Quantum Gravitational Contributions to the CMB Anisotropy Spectrum", Phys. Rev. Lett., 108, 021301 (2012).Abstract.
[7] M. Bojowald, G. Calcagni, and S. Tsujikawa, "Observational Constraints on Loop Quantum Cosmology", Phys. Rev. Lett., 107, 211302 (2012). Abstract.

First Material with Longitudinal Negative Compressibility

Adilson E. Motter (Left) and Zachary G. Nicolaou (Right)
















Authors: Zachary G. Nicolaou^1,2 and Adilson E. Motter¹
Affiliation:
¹Department of Physics and Astronomy, Northwestern University, USA
²Department of Physics, California Institute of Technology, USA

Conventional materials deform along the direction of the applied force in such a way that they expand when the force is tensional and contract when it is compressive. But our new paper [1] published this month in Nature Materials demonstrates that not all materials have to be that way. We explored network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). This effect is achieved through destabilizations of metastable equilibria of the constituents of the material. These destabilizations give rise to a stress-induced phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The proposed materials are the first to exhibit longitudinal negative compressibility at zero frequency.

Negative compressibility surface. When pressured, the surface expands instead of contracting [Image copyright: Adilson E Motter]

.
The motivation for this work comes from our previous research on networks. It has been known that some networks respond in a surprising way to various types of perturbations. For example, in previous research our group has shown that the removal of a gene from the metabolic network of a living cell can often be compensated by the removal (not addition) of other genes [2]. Our hypothesis was that, with the right design, similarly counter-intuitive responses could occur in materials as well, which are essentially networks of interacting particles. The idea of using network concepts to design a material that could contract longitudinally when tensioned was particularly attractive because no existing material (natural or engineered) had been found to exhibit that property.

Negative compressibility cube. When tensioned, the cube contracts instead of expanding [Image copyright: Adilson E Motter]. 

.
There are numerous potential applications for materials with negative compressibility transitions. They include the development of new actuators, microelectromechanical systems, and protective devices---from ordinary ones, such as seat belts, to devices that reduce the consequences of equipment failure. These materials may also lead to force amplification devices, which could be used to sense minute forces and transform them into large ones. Indeed, the strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. Other potential applications would be to improve the durability of existing materials, such as in crack closure of fractured materials. In fact, we expect other researchers to come up with yet different applications that we have not even thought about.

Negative compressibility material. The material at the center of the image expands vertically as it is squeezed [Image copyright: Adilson E Motter].

.
The most surprising aspect of this research is the very finding that you can create a material that contracts when it would be expected to expand and expands when it would be expected to contract. Think of a piece of rod that you tension by pulling its ends with your fingers. It would normally get longer, but for these materials it can get shorter. This has been generally assumed not to be possible for the excellent reason that no known material behaves that way. Moreover, it is easy to show that this is indeed impossible if we assume that the material will respond continuously to the applied force. Our work shows, however, that this unfamiliar form of compressibility can occur by means of an abrupt change---a phase transition. A posteriori, perhaps another surprising aspect of our research was the simplicity of the system once we understood how it works, and this can have practical implications for the fabrication of the material.

This work illustrates rather dramatically how deceiving it is to assume that a material’s property will be limited by those of existing ones, the reason being that existing materials explore only a tiny fraction of the space of all possibilities. Previous research has pushed the boundaries of electromagnetic properties and led, for example, to materials with negative refractive index [3]. Our research shows that even mechanical properties that have no immediate analogs in electromagnetic metamaterials can be tailored and even inverted. At the end, the material’s properties are only limited by how different interacting parts can be assembled together. For a related discussion in the context of networks, see Ref. [4].

References:
[1] Z. G. Nicolaou and A. E. Motter, Mechanical metamaterials with negative compressibility transitions, Nature Materials 11, 608-613 (2012). Abstract.
[2] A. E. Motter, "Improved network performance via antagonism: From synthetic rescues to multi-drug combinations", BioEssays 32, 236-245 (2010). Full Article.
[3] R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction", Science 292(5514), 77-79 (2001). Abstract.
[4] A. E. Motter and R. Albert, "Networks in motion", Physics Today 65(4), 43-48 (2012). Abstract.