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New directions in science and technology: two-dimensional crystals
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Rep. Prog. Phys. 74 (2011) 082501 (9pp) doi:10.1088/0034-4885/74/8/082501
New directions in science and technology:two-dimensional crystalsA H Castro Neto1,3 and K Novoselov2
1 Graphene Research Centre, National University of Singapore, 2 Science Drive 3, Singapore 117542,Singapore2 School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
E-mail: [email protected] and [email protected]
Received 21 February 2011, in final form 22 June 2011Published 25 July 2011Online at stacks.iop.org/RoPP/74/082501
AbstractGraphene is possibly one of the largest and fastest growing fields in condensed matterresearch. However, graphene is only one example in a large class of two-dimensional crystalswith unusual properties. In this paper we briefly review the properties of graphene and look atthe exciting possibilities that lie ahead.
(Some figures in this article are in colour only in the electronic version)
This article was invited by L H Greene.
Contents
1. Graphene is not the end of the road! 12. Graphene for dummies 23. Hype or hope? 34. Driving the ship to new lands 4
5. A lesson to take home 56. Looking into the future and conclusions 7Acknowledgments 7References 8
1. Graphene is not the end of the road!
The awarding of a Nobel Prize may indicate to some that a fieldhas reached its pinnacle, that it has been fully explored, and oneshould look for ‘scientific gold’ somewhere else. Appearancescan be deceiving. As it happens in any scientific endeavor,we can find ourselves, after a lot of struggle, in an unchartedterritory, in a deadly bottleneck or in front of a treasure. In fact,we should think of graphene as the beginning of an exploration,not the end of it, and that the real treasure remains to beexplored: the field of two-dimensional (2D) crystals.
Graphene research is a relatively young field, being‘founded’ in 2004–2005 by a series of papers that involvedseveral groups around the world including the Manchester[1–3] and Columbia groups [4]. Graphene was quicklyrecognized as an interesting material because there was anentire community of researchers working on related materials,namely graphite, fullerenes and carbon nanotubes. All these
3 On leave from Boston University, USA.
materials can be thought as directly related to graphene(graphite = stacked graphene, fullerenes = wrappedgraphene, nanotubes = rolled graphene—see figure 1). It wasrelatively simple for these researchers to move from an area thatwas scientifically saturated to a new one with minimal amountof investment in terms of resources and, especially, time.
Ludwig Wittgenstein once commented that ‘the aspectsof things that are most important to us are hidden because oftheir simplicity and familiarity’ [5]. In fact, graphene has beenhidden behind the pencil trace since it was invented in 1656in England [6]. One can say that this one-atom thick materialhas been produced by human beings since the 17th centurybut only recently, after more than 400 years, were we reallyable to study its properties closely. This material always hadan economic appeal; in the 17th century for the production ofpencils, and now in the 21st century as the next material ofchoice for high-end flexible electronics.
With the benefit of hindsight, it is not surprising thatthis one-atom thick material was extracted from graphitewith an adhesive tape. However, a large amount of work
0034-4885/11/082501+09$88.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA
Rep. Prog. Phys. 74 (2011) 082501 A H Castro Neto and K Novoselov
Figure 1. Graphene and its descendants: top right: graphene; topleft: graphite = stacked graphene; bottom right: nanotube = rolledgraphene; bottom left: fullerene = wrapped graphene (adaptedfrom [6]).
had to be done to bring graphene to the high standardsof modern nanotechnology. Without clean-room facilities,e-beam lithography or scanning electron microscopy, thediscoveries made in the last five years would not have beenpossible. The rapid evolution in nanotechnology in the lastdecade is what allowed for the experiments that opened thedoors for the understanding of the unusual properties of thismaterial (see figure 2).
We note that it was quite obvious from the verybeginning that mechanical exfoliation (the so-called ‘scotchtape’ method) [1] is a big limitation for the use of thismaterial in applications, that is, one would have to developa mass production method. In fact, even before 2004, manyresearchers worked on the growth of graphene by artificialmeans. The growth out of SiC, for instance, is considered oneof the most promising ways to produce large-area graphenefor electronic applications [7]. More recently, chemical vapordeposition (CVD) [8] has become extremely popular becauseof its simplicity and low cost (and possibly its interestingenvironmental impact: CO2 capture for graphene production).Each method has its pros and cons: strong interaction withthe substrate can lead to large charge transfer and difficultiesin transferring the material to an appropriate (say, flexible)substrate; mechanical stability during the transfer process toplastic (for flexible electronics) can lead to structural failure;formation of extended defects due to heterogeneous growthcan reduce the electronic mobility. Only time and investmentcan tell which of these methods will be the dominant onein the industrial use of graphene. The fact of the matteris that today it is possible to produce large-area graphene(even square meters) using CVD with reasonable electronicmobilities (>5000 cm2 V−1 s−1) [9]. Hence, it is clear thatthe barrier for large-area production has been broken. This isnot to say that much development is still needed to make thematerial of the highest quality (single crystal) given that theCVD growth is heterogeneous and produces polycrystallinesamples [10].
2. Graphene for dummies
One of the most important properties of graphene comes fromits unusual electronic excitations that can be described in termsof massless two-dimensional Dirac particles [11] (see figure 3).The interference between electronic waves, as they propagatethrough the graphene crystal, allows for this unusual electronicbehavior. Hence, the ‘diracness’ of the electrons in grapheneis ‘protected’ by crystal symmetry. At low energies and longwavelengths, the electrons in graphene are not characterizedby their mass but by their speed of propagation, the so-calledFermi–Dirac velocity, which is of the order of 106 m s−1 (thatis, approximately 300 times smaller than the speed of light).At low energies, the electrons in graphene obey a relativisticwave equation in two dimensions. This property created aheated interest in the theoretical community. From the pointof view of solid-state physics, however, graphene is alsointeresting because its electronic density of states vanisheslinearly with energy at the Dirac point. Thus, neutral grapheneis a strange material, a mix between a metal and an insulator.Graphene is not a metal because it has a vanishing density ofstates. Graphene is also not a semiconductor (or insulator)because it does not have a gap in the spectrum. Thus, unlikea semiconductor, it does not have a threshold for electronicexcitations.
Also, from the structural point of view, graphene is notan ordinary material. The interaction between carbon atomsis made through strong sigma bonds (similar to the ones indiamond) through the overlap of the in-plane sp2 orbitals.Because of that, graphene has a very high spring constant [12],K (∼50 eV Å−2), and its Young’s modulus, Y (∼1 TPa), is oneof the largest in nature [13]. As a result, its optical phononfrequencies, ω0 (∼0.2 eV–1600 cm−1), are one of the highestamong all materials.
Another fascinating property of graphene is related toits softness. Because the material is only one-atom thick,it can be easily deformed in the direction normal to itssurface. In the absence of any external constraints (such assubstrates, scaffolds and impurities), graphene can sustain‘flexural phonon’ modes whose frequency, ωF, is a quadraticfunction of the wavevector [14], q (ωF (q) = (κ/σ )1/2q2,where κ ∼ 1 eV is the so-called bending rigidity and σ is thesurface mass density of graphene). Note that unlike acousticalphonon modes (that is, sound waves), these modes do notpropagate since they have a vanishing group velocity at longwavelengths [12]. These modes represent the displacementof the center of mass of the whole graphene sheet in thedirection normal to its surface. The presence of flexural modesis guaranteed by symmetry in all 2D crystals. Hence, 2Dcrystals are all membranes (albeit with different stiffnesses)(see figure 4).
In the absence of external effects that break thetranslational symmetry in the perpendicular direction, it costszero energy to translate the whole graphene crystal. However,in the presence of factors that break this symmetry, thefrequency of the flexural modes is affected. An applied tension,which breaks rotational symmetry, changes the dispersion fromparabolic to linear (that is, sound waves appear), and the
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Figure 2. Graphene device: optical picture of a graphene device made out of a lithographically cut graphene sheet on top of SiO2, with goldelectrodes and a doped Si back gate.
Figure 3. Right: lattice structure of graphene with sublattices A and B; middle: graphene’s Brillouin zone. Left: band structure of graphenewith the Dirac cones located at the K and K’ points in the Brillouin zone (adapted from [12]).
presence of a scaffold or substrate, which explicitly breaktranslational symmetry, makes these modes dispersionless,that is, it requires energy to move graphene out of its flatconfiguration.
The extreme membrane-like nature of graphene, togetherwith the tough in-plane sigma bonds, leads to graphene’snegative thermal expansion coefficient (that is, grapheneshrinks when it is warmed and it expands when it is cooled).This happens because most of the horizontal displacement ofthe graphene sheet comes from the flexural modes, with verylittle contribution from the in-plane phonons. When grapheneis cooled, the number of flexural modes is substantially reducedand the horizontal length of the graphene sheet is increased.When graphene is in contact with materials with a positivethermal expansion coefficient (which is the case for most 3Dsolids) many interesting structural effects happen when thetemperature is varied [15]. In fact, we can say that graphene isthe only example of an electrically conductive membrane and,thus, it unifies topics in hard and soft condensed matter [16].From this perspective, graphene adds a new chapter in thesolid-state textbooks.
These amusing properties have a huge impact on theexperimental properties of graphene. The sigma bondsare extremely exclusive and directional and hence do noteasily accept foreign atoms. Hence, natural graphene(that is, graphene in the form of graphite) is a very
pure material with no extrinsic disorder. Most of thedisorder found in graphene samples obtained by mechanicalexfoliation comes from either molecules or atoms adsorbedin its two surfaces, or by structural deformations (wrinkles,ripples, folds, blisters, etc). Thus, natural graphene hasthe highest electronic mobility of all electronic materials(>100 000 cm2 V−1 s−1 at 300 K) [17, 18], much larger thanSi (∼1500 cm2 V−1 s−1) or ‘cleaner’ semiconductors such asAlGaAs/InGaAs (∼8500 cm2 V−1 s−1).
Furthermore, because the optical phonon frequenciesare so high, the thermal conductivity of graphene [19]is comparable to that of diamond (∼50 W cm−1 K−1), andone order of magnitude larger than ordinary semiconductors(in Si, for instance, the thermal conductivity is of order1 cm2 V−1 s−1). These unprecedented properties makegraphene a unique material with characteristics that can leadto an enormous number of applications in a large number ofdifferent areas, from high-end electronics and biosensors tometallic paints and surface impermeabilization.
3. Hype or hope?
The graphene field has grown tremendously fast in the lastsix years. While in the early days graphene conferences wouldattract only a handful of researchers, nowadays they attracthundreds, even thousands, of scientists. Nevertheless, so far,
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Rep. Prog. Phys. 74 (2011) 082501 A H Castro Neto and K Novoselov
Figure 4. Phonon spectrum of graphene along the Brillouin zone.ZA and ZO are acoustical and optical flexural modes (adaptedfrom [15]).
graphene has not been used in any devices that you can find inthe market. So, is graphene all hype and no substance?
At least at the laboratory level, graphene has been shownto have huge potential. Graphene’s sensitivity to electrostaticcharges allows for detection of single molecules [20] and DNAsequencing [21, 22]. The optical response of neutral graphene(that is, when it is not biased by external electric fields) isindependent of material properties in a wide frequency range[23] allowing for the use of graphene for optical standards andin lasers applications [24, 25]. Since the electronic mobility ofgraphene is so high, and its spectral range is so large, graphenecan be used in ultrafast photodetectors [26]. Because of itsflexibility, strength, high conductivity, transparency and lowcost, it has been proposed that graphene can replace indiumtin oxide (ITO) in solar cells [27] and organic light-emittingdiodes (OLEDs), touch screens and lighting applications [28].Because of its enormous surface-to-volume ratio, graphenecan also be used in ultracapacitor applications [29]. Inbiological applications graphene can be used as a scaffold fortransmission electron microscopy (TEM) [30] for the study ofliving microorganisms [31], and also as a biodevice to either‘asphyxiate’ bacteria [32] or, in the inverse mode, for drugdelivery to specific places in the body.
One of the great barriers for the use of graphene inhigh-end electronics is the lack of a spectral gap. Althoughgraphene is a semimetal, not a semiconductor, it is possible,in principle, to ‘carve’ graphene sheets into quantum dots andnanowires to create, via quantum confinement, gaps in thespectrum [33]. The creation of gaps in graphene would havea huge impact in the electronic industry for its direct use indigital applications. Moreover, because the sigma bonds ingraphene are as strong as in diamond, it is possible to carvegraphene down to a few benzene rings without losing structuralstability. Unfortunately, graphene is very sensitive to edgedisorder (this has to do with the slow decay of the electronicwavefunctions away from the edge [12]) and the gaps that arecurrently observed in experiments [34, 35] are not spectral gaps(they are not gaps between valence and conduction bands),but transport gaps due to strong Anderson localization andCoulomb blockade effects [36, 37].
Figure 5. Temperature versus frequency of operation of variousquantum detectors.
However, the absence of a spectral gap does not limitthe use of graphene in high-frequency transistors [38]. Thehigh electronic mobility of graphene due to the specificity ofthe sigma bonds plays a fundamental role. Because graphenehas two surfaces and no bulk, it can be chemically modifiedto create new materials with tailored properties. Currentexamples are hydrogenated and fluorinated graphene [39, 40].
It is clear that graphene has huge potential for applicationsand the experiments discussed above are essentially ‘proof-of-concept’. The industry does not respond as fast as scientiststo new developments. It has to take into account the financialissues. Hence, it may take some time before we see the firstgraphene applications on the market but it seems certain thatit will happen in the next few years.
4. Driving the ship to new lands
There are certain fields where graphene can have a huge impactbut where the exploration has not even started yet. Oneexample is the field of quantum detectors, that is, materialsthat detect quanta of electromagnetic radiation and convertthem into a proportionate electrical signal. These devices donot operate under the rules of classical electromagnetism butexplicitly use the quantum nature of light. They can be usedfor a plethora of applications including communications andquantum information. For instance, ordinary antennas operateon the concept of resonance, that is, the size of the antenna isdirectly related to the wavelength of the electromagnetic waveit detects. The resonance condition substantially limits thefrequency range an antenna can detect. In quantum detectorsone would be able to directly deal with the amplitude of theelectric and magnetic fields allowing for the construction ofantennas with broadband and no size limitations [41].
The current technology uses semiconductors andsuperconductors as quantum detectors. The nature of thesematerials limits the frequency (from 1012 to 1015 Hz) andtemperature (in the case of superconductors, it requires verylow temperatures for operation—see figure 5) at which thedevices operate. The frequency range is limited by thespectral gap and the temperature range by the electronicstability. There is a huge demand for quantum detectorsthat operate at low frequencies (here the absence of a gap in
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Figure 6. By placing graphene between different substrates or by patterning a given substrate, it is possible to create an interface whichcontrols the flux of current from one side to the other side of the graphene sheet.
graphene is a clear advantage) and high temperatures. Low-frequency operation requires very large electronic mean freepaths and high electronic mobilities, two characteristics ofgraphene. Nevertheless, we are unaware of any graphenequantum detectors so far.
Strain engineering [42], that is the use of strain tomodify the electronic, optical [43] and structural propertiesof graphene, is an emerging field. Uniaxial strain can generatespectral gaps in the π -bands of graphene but it requires uniaxialstrain in an excess of 20% [44], which is close (or above) tothe limit where graphene breaks (in fact, graphene is a verybrittle material, namely it responds elastically up to the pointthat it ruptures). Moreover, these high strains also modify thesigma bands [45]. However, it is possible to create transportgaps in graphene at much smaller values of strain by usinguniaxial strain to create interfaces within a graphene sheet [42].Imagine that we apply uniaxial strain on graphene locally, ina way to separate graphene into two regions, say, strained andunstrained (see figure 6). At a finite chemical potential, theFermi surfaces of these two regions will be shifted relative toeach other and any current that flows from one side to anotherwill be sensitive to this shift. By doing it appropriately itis possible to get the total reflection of the current from oneside to another. In this way one can create a device thatresponds as a transistor without having a gap in the spectrum.However, spectral gaps can be created by producing specialstrain patterns [46]. This type of mechanism has recently beenobserved in graphene nanobubbles grown on Pt [47].
As mentioned previously, carbon produces a largenumber of different structures but very little has been donein hybrid structures that involve graphene, fullerenes andnanotubes. Carbon nanotubes, for instance, can be growneither perpendicular [48] or parallel to the graphene sheets inorder to create 3D structures, and fullerenes can be introducedbetween graphene sheets [49] to create new intercalatedstructures of pure carbon.
One can also use the fact that graphene is a verysoft material and can be folded, wrinkled, rippled, etc, to
create new geometries [50]. For instance, graphene scrollshave electro-mechanical properties that can be used for aseries of different devices and new applications such asnew metamaterials with tunable properties [51]. This newfield of ‘origami engineering’ is very promising and remainsessentially unexplored.
5. A lesson to take home
Graphene is a material which, due to its pure carbon structure,has properties that make it very special. What made thegraphene literature explode was its ‘extraction’ from 3Dgraphite. However, graphite is not the only material that islayered and has striking properties. There is an enormousnumber of other materials, not based on carbon, that are equallyinteresting from the basic science and applications point ofview.
High-temperature superconductors (HTC), for instance,are made out of weakly coupled CuO2 planes and have exoticelectronic properties that are still the object of controversy,almost two decades after their discovery. The strongCoulomb interactions in the Cu d-bands lead to Mott insulatingphases and, upon doping, to high superconducting transitiontemperatures [52]. One of the few points of agreement amongresearchers is the fact that the essential features of thesematerials are described by the 2D CuO2 planes. The 3Dcoupling only serves to stabilize long-range magnetic andsuperconducting order that is observed in them. As in the caseof graphene, this material can be exfoliated into isolated planeson top of SiO2 substrates (see figure 7) [3]. However, no signsof superconductivity (or even superconducting fluctuations, ala Kosterlitz–Thouless [53]) have been observed. One cannotavoid wondering about the reason for this unexpected result.Could it be that exfoliation is too abrasive and introducesdisorder in the system killing the many-body effects? Doesthe substrate affect the superconducting fluctuations and, ifso, can we use other substrates, like BN, which are much lessinvasive [54], to recover superconductivity? After all, is the
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Figure 7. Crystal structure of different layered 3D materials and their 2D descendants obtained by exfoliation (adapted from [3]).
3D nature of the material fundamental for superconductivity?These interesting questions can be answered. Who will?
Charge density wave (CDW) systems have been a subjectof research in the condensed matter community for a longtime [55]. In these materials, electron–electron and electron–phonon interactions lead to a new type of electronic orderwith the modulation of the electronic density, that is, an‘electronic crystal’ (another example is the so-called Wignercrystal that occurs at extremely low electronic densities [56]).Perhaps, the most famous examples of those systems are theso-called transition metal dichalcogenides (TMD), such asNbSe2, TaSe2, NbS2 or TaS2, which present CDW transition athigh temperatures which is accompanied by a superconductingone at lower temperatures [57]. CDW systems tend to beinsulating with a gap at the Fermi surface but these materialsare better metals in the CDW phase and the superconductingstate emerges out of a strange metal, creating an interestingquestion on the nature of the competition between CDW andsuperconductivity [58]. These materials are also layered andsingle layers have been extracted (see figure 7) [3] but nosigns of superconductivity or CDW have been observed intransport experiments. Once again, the reason for that remainsa mystery.
MoS2 is another dichalcogenide which has layeredstructure but, unlike NbS2, is an insulator with a gap of orderof 2 eV and hence not chemically reactive [59]. This materialcan also be exfoliated (see figure 7) and is commonly used asa lubricant (in an analogous way to graphite). Because of itssemiconducting properties, MoS2 can in principle be used fordc transistors [60]. However, so far, its electronic mobilities aremuch lower than graphene and its gap is too large for practical
device applications. The electronic properties of this materialmay be tailored by reduction of the gap and/or increase in themobility with the use of Li. Li can be intercalated in the 3Dmaterial [61] and it might be possible to do so in its 2D version,although we are not aware of any attempts at this point of time.
The common theme among these systems is that theyare layered and, in principle, can be exfoliated to their2D form for studies. Obviously these are only a fewexamples but there are numerous others: layered manganites[62], such as La1−xSr1+xMn(2)O4(7), which are magneticand present colossal magneto-resistance (CMR) and metal–insulator transition (MIT); layered titanates [63], such asNa2Ti3O7 or H2Ti3O7, which present strong photoelectriceffects and can be used as ion exchangers, adsorbents, photo-catalysts and catalyst supports; and layered cobaltates [64],such as NaCoO2 which present a fascinating number of many-body phenomena such as magnetism, and charge ordering, andLiCoO2, which are usually used in high-performance lithium-ion batteries. All these materials are interesting on their ownright, namely they present correlated electronic states wherecharge, spin, orbital, valley, lattice degrees of freedom playan important role. These electronic states are stabilized bythe weak interaction between layers but it is not known howthese states will behave when the layers are actually decoupled.Thermal and quantum fluctuations are much stronger in 2Dthan in 3D and electronic states are very sensitive to those. Thepossibility of creating pure 2D strongly correlated electronicstates is a dream of condensed matter researchers.
As mentioned previously, it is very hard to exchange theC atoms in graphene by any other types of atoms but there areother 2D systems where this may be possible. Consider, for
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Figure 8. Interpolating between a BN semiconductor and a graphene semimetal by incorporating C in the BN lattice.
instance, the case of BN. BN has the same lattice structure asgraphene where the B and N atoms occupy the two differentsublattices (see figure 8) [65]. In this case the sublatticesymmetry is explicitly broken leading to a gap in the spectrumwith the valence band being 5 eV away from the conductionband. This large gap makes BN a very inert system anda great scaffold for other 2D materials, including graphene.However, the bonding between B and N is not as strongas in graphene and it is theoretically possible to replacethese atoms by others, including C. Hence, we can imaginean entire family of stoichiometric compounds with chemicalformula B1−xCx+yN1−y and with the structure of graphene thatinterpolate between a wide gap semiconductor (x = y = 0)and a semimetal (x = y = 1) [66]. Obviously this would openthe doors for band gap engineering.
Finally it should be stressed that, as in the case of graphene,these materials can also be grown artificially on different sub-strates by different methods such as molecular beam epitaxy(MBE) and/or CVD. Two-dimensional crystal growth is verydifferent from its 3D counterpart because thermal fluctuationsplay a very important role and its kinetics is special, given thatthe atoms cannot use the third dimension for diffusion [67].Very little is known, experimentally or theoretically, about thekinetics of these processes and this is an open field.
The most important lesson from the graphene story isprobably this one: there is a universe of 2D crystals out therejust waiting to be studied. Each one of them has its own beautyand purpose. Paraphrasing Isaac Newton we can say that weare still in the infancy of a broad field and diverting ourselveswith graphene, a material that looks more interesting thanordinary, whilst a great field of 2D crystals lay all undiscoveredbefore us.
6. Looking into the future and conclusions
We have learned that 2D crystals can be obtained by severalmethods such as exfoliation, MBE and CVD. We alsoknow that the physical and chemical properties of these
2D crystals can be modified by chemical or molecular doping,by application of strain, shear or pressure, and by intercalationwith different types of atoms and molecules. We can createin this way a new class of 2D artificial materials that donot exist in nature and whose properties we can control foran enormous number of applications: flexible electronics,electronic circuits, electro-actuators, chemical and biosensors,supercapacitors, OLEDs, solar cells, photosensors, infraredfilters, fuel cells, just to mention a few.
It is not hard to imagine that we can take all these 2Dcrystals and pile them into 3D structures. This can be donethrough what we would call combinatorial multi-stacking (inanalogy with combinatorial chemistry). Given that each oneof these 2D crystals has a different functionality we can createmulti-functional materials with an enormous economy in termsof energy and volume. Imagine, for instance, combining threetypes of 2D crystals into a single 3D structure: one that canconvert light into electrical current, one that is conductiveand transparent, and finally another one that can store theelectricity efficiently. By putting together efficient conversion,transportation and storage of energy, one is capable of creatinga device that works as an artificial ‘green plant’, with anextreme economy in operational volume and energy.
We can imagine creating a library of 2D crystals and usingadvanced robotics to make new 3D structures efficiently at lowcost and high speed. The outcome of such a scheme wouldbe a large portfolio of new materials with different degrees ofcommercialization. In this way, we could develop a ‘materials-on-demand’ strategy for novel complex architectures andstructures with precisely tailored properties for emergingtechnological applications.
Acknowledgments
The authors would like to thank Andre Geim and theircolleagues at NUS, especially Yuan Ping Feng, Kian Ping Loh,Barbaros Ozyilmaz, Vitor Pereira and Andrew Wee, for manyenlightening discussions.
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