Recent advances in graphene and other 2D materials

ablo Ares , Kostya S. Novoselov

a Department of Physics & Astronomy and National Graphene Institute, University of Manchester, Manchester, M13 9PL, UK

b Centre for Advanced 2D Materials, National University of Singapore, 117546, Singapore

c Chongqing 2D Materials Institute Liangjiang New Area Chongqing, 400714, China

Keywords:2D materials Graphene Molybdenum disulphide Transition metal dichalcogenides Hexagonal boron nitride van der waals heterostructures Ultrathin nanomaterials

ABSTRACT The isolation of the first two-dimensional material, graphene – a monolayer of carbon atoms arranged in a hexagonal lattice - opened new exciting opportunities in the field of condensed matter physics and materials. Its isolation and subsequent studies demonstrated that it was possible to obtain sheets of atomically thin crystals and that these were stable, and they also began to show its outstanding properties, thus opening the door to a whole new family of materials, known as two-dimensional materials or 2D materials. The great interest in different 2D materials is motivated by the variety of properties they show, being candidates for numerous applications.Additionally, the combination of 2D crystals allows the assembly of composite, on-demand materials, known as van der Waals heterostructures,which take advantage of the properties of those materials to create functionalities that otherwise would not be accessible. For example, the combination of 2D materials, which can be done with high precision, is opening up opportunities for the study of new challenges in fundamental physics and novel applications.Here we review the latest fundamental discoveries in the area of 2D materials and offer a perspective on the future of the field.

Since the isolation of graphene in 2004 [1], the number of 2D materials discovered has been growing continuously, acquiring an astounding speed in the recent years [2–8], with the possibility to increase their number even further,as indicated by recent predictions that estimate about 5600 layered compounds, of which more than 1800 would be either easily or potentially exfoliable [9]. The large family of two-dimensional materials thus covers an extremely wide range of properties, which can be additionally combined stacking different 2D crystals together in the so-called van der Waals (vdW)heterostructures,or the same crystals with different orientations,allowing the exploration of new physical effects [5,10–12], as well as the fabrication of new devices with novel capabilities [2,5,13].

Despite the fact that graphene and related 2D materials have been extensively investigated,recent studies revealing new phenomena do not cease to enlarge the already broad number of exiting effects found in these materials.The use of hexagonal boron nitride(hBN)as a substrate for graphene and other 2D materials significantly improved the quality of substrate-supported graphene devices and opened many new opportunities[14,15],allowing the possibility of stacking atomically-thin layers of different crystals to create new heterostructured materials [5,13,16,17]. It has been recently demonstrated experimentally in graphene samples encapsulated in hexagonal boron nitride that electrons can behave like highly viscous fluids and exhibit a hydrodynamic behaviour similar to that of classical liquids [18,19]. Graphene electron-electron collisions are frequent enough to provide local equilibrium above the liquid nitrogen temperature and electron-phonon scattering is very weak.Studying electron transport through graphene constrictions [20], it has been observed that below 150 K the resistance decreases as temperature increases,a dependence typical for insulators,in contrast with a metallic behaviour expected for doped graphene[21].The measured conductance presented a value higher than the maximum conductance expected for free electrons,in a‘superballistic’fashion,and is attributed to a collective electron viscous flow, where the electrons move similarly to a liquid stream with different velocities, slowing down near the edges of the constriction. This behaviour can potentially help the fabrication of improved graphene-based devices [20]. It has been even possible to visualize the evolution of the electronic fluid flow, from ballistic to the Poiseuille flow[22].

The close values of lattice constants of graphite and hBN (there is a lattice mismatch of only～1.8%)also allows an extra degree of freedom when fabricating vdW heterostructures: the angle between the crystallographic axes of the two crystals (or ‘twist’ angle). Aligning crystallographic orientations between hBN and graphene allows formation of superlattices that produce a periodic moir′e potential greatly influencing the electronic spectrum of graphene [23–28]. When graphene is aligned with the underlying hBN substrate (the angle between crystallographic axes is～0°),a moir′e pattern with a～14 nm periodicity appears[29].As the alignment angle increases,a moir′e pattern will still be present, but its period decreases. Additionally, in some cases the interlayer interaction between layers of 2D materials stacked in vdW heterostructures can lead to a lattice distortion that can create a moir′e different from the purely geometric one[30–33].High quality devices of graphene encapsulated between two hBN crystals with precisely controlled alignment angles [16,34] have recently led to exciting new scientific discoveries. For example, it has allowed the observation of quantum magneto-oscillations in its transport characteristics well above room temperature - the Brown-Zak oscillations [35]. The presence of superlattices introduces repetitive changes in the electronic structure such that at simple fractions of the flux quantum, the charge carriers effectively experience zero magnetic field.Very recently,following up on these observations, a new family of quasiparticles named Brown-Zak fermions has been proposed in graphene-based superlattices under high magnetic fields [36]. Whereas usual electrons in graphene, which behave as Dirac fermions, feel the presence of a magnetic field,Brown-Zak fermions set at specific magnetic field values move ballistically in straight-line trajectories with high mobilities as if the magnetic field is zero.

A discovery that has recently revolutionized not only the field of 2D materials but the entire community of condensed matter is the realization of intrinsic unconventional superconductivity in graphene superlattices[10]. When two layers of graphene are stacked together with a small twist angle close to the a‘magic’angle value predicted theoretically to be～1.05°[37], the two layers become more strongly coupled and the electronic band structure flattens near certain filling factors(i.e.for given numbers of charge carriers).These flat bands lead to correlated insulating states [38,39] that can be easily tuned just by varying the electrostatic doping of the twisted bilayer graphene (TBG) by small changes of the gate voltage.By doing so,the charge carrier density was easily changed in situ away from the correlated insulating states,and led to the observation of zero-resistance states with critical temperatures up to 1.7 K [10],replicated in several works [40–43]. The phase diagram of this unconventional superconductivity shows superconducting domes near the half-filling(±2 electrons per moir′e unit cell)of the flat band,resembling the superconducting phase diagram of high-transition-temperature superconductors based in cuprate compounds. Since superconductivity in magic-angle TBG can be easily precisely tuned and is a relative simple system(just two layers of carefully arranged carbon atoms),this system has become an ideal platform to study strongly correlated phenomena,which could lead for instance to a better understanding of the physics of high-temperature superconductivity [44]. Although finding the magic-angle where the bands are flattened in TBG requires exquisite adjustment and therefore presents a challenge to fabrication, its possibilities are attracting a lot of interest for the study of correlated states in other 2D crystal systems [45–51], and has also led to the recent fabrication of Josephson junctions and tunnelling transistors in a single material defined just by electrostatic gates [52] and the realization of unconventional switchable ferroelectricity in Bernal-stacked bilayer graphene aligned with the top and/or bottom encapsulating hBN crystals,observed through hysteresis in the resistance of the graphene bilayer[53].

Control of the structure of graphene at the atomic level has been demonstrated recently to allow tuning its properties.For instance,using a scanning tunnelling microscope tip, it is possible to position hydrogen atoms absorbed on graphene with atomic precision, inducing and tailoring magnetism in selected graphene regions [54]. Or by manipulating a large number of H atoms,individual nanostructures can be built,confining in this way graphene Dirac quasiparticles very efficiently[55].Using a bottom-up approach it has been shown that the synthesis of graphene can be controlled with atomic precision by the design of the molecular precursors. In this way, nanoporous graphene comprising an ordered array of pores separated by ribbons was fabricated,presenting a highly anisotropic electronic structure making it an ideal candidate for combined semiconducting and sieving functionalities[56].

Graphene is considered to be impermeable to all gases and liquids except hydrogen, which has been observed to be able to permeate through graphene membranes. The mechanism is attributed to the dissociation of molecular hydrogen in catalytic zones as wrinkles, followed by the adsorbed atoms flipping to the other side of the graphene sheet[57].Due to its impermeability,graphene has also been explored as a membrane for molecular sieving by creating subnanometer pores[58–61]. However, since it is difficult to achieve the density and pore uniformity required for industrial applications, an alternative that has recently proven more feasible is the use of graphene oxide (GO) membranes [62–68]. These are formed by a collection of micron-sized GO crystallites forming interlocked, laminated layered structures [69,70],that have been shown to present very remarkable properties. Such membranes are impermeable to organic solvents[67],allow electrically controllable permeation of water thanks to the formation of conductive filaments in the GO membranes via controllable electrical breakdown[68], or allow tuning the diffusion of ions by controlling the interlayer spacing in the GO membranes[62]or internal osmotic pressure[71],to name a few.

Graphene and other single-layer 2D materials such as hBN and mica have also revealed as excellent proton conductors [72–74], where protons can pierce their electron clouds in a thermally activated process.The excellent proton conductivity and selectivity of these 2D materials make them very attractive for various separation technologies [75], as for sieving hydrogen isotopes[76,77],or enhancing the performance of fuel cells[78].

The second most widely studied 2D material is probably molybdenum disulphide (MoS2), representing the family of the transition metal dichalcogenides(TMDs)compounds of the type MX2,with M a transition metal atom(Mo,W,etc.)and X a chalcogen atom(S,Se,or Te).TMDs in general, and MoS2in particular, exhibit versatile chemistry and have tunable electronic properties from metallic to insulating depending on their composition,crystal symmetry and the number of layers[5].Thus,they have been subjected to many studies for the fundamental exploration of novel physical phenomena and for their potential applications in a variety of fields including optoelectronics, nanophotonics, catalysis, energy storage or sensors and actuators in the nanoscale [3,79]. Many layered TMDs are semiconductors under ambient conditions. MoS2presents an indirect gap of～1.2 eV in bulk.With decreasing thickness,there is a progressive shift in the indirect gap to～1.8 eV,exhibiting a crossover from an indirect-to a direct-gap in the monolayer due to quantum confinement [80,81]. Single-layer MoS2transistors fabricated using different approaches showed high mobilities and high on/off ratios at room temperatures [82,83]. Additionally, since the fabrication of ultranarrow channels in silicon-based devices becomes problematic as short-channel effects arise,2D semiconductor materials have been shown to overcome this issue:as they are naturally ultrathin,atomically flat and free of surface dangling bonds, all the electrons are confined in atomically thin channels and hence leakage current is almost eliminated.Sub-10 nm channel length MoS2transistors have been realized, using partially metallized MoS2as channels [84] or graphene electrodes with grain boundary etched channels [85]. The use of large-area MoS2as an active channel material for logic-in-memory devices has been reported[86], using MoS2floating-gate field-effect transistors (FGFETs) as the building blocks for making reprogrammable low-power logic devices.

In the monolayer limit, MoS2and some other TMDs possess direct bandgaps,turning them into promising materials for optoelectronics and nanophotonics. For instance, ultrasensitive photodetectors based on monolayer MoS2have been recently demonstrated [87]. Among their intriguing optical properties,excitons(bound states of an electron and a hole)in these materials have very strong binding energies,making them ideal to study excitonic physics[88].Furthermore,it has been observed that tunable single-photon emitters can be formed in such materials, as for example in WSe2[89–93],and it has been recently demonstrated the possibility of selectively generating single-photon emitters in monolayer MoS2by deterministically creating defects through ion bombardment[94]. In addition,the existence of other excitonic quasiparticles such as trions[95,96](bound states of two electrons and a hole,or two holes and an electron) and bi-excitons[97,98] have been observed in TMDs.

TMDs, and in particular MoS2, also present remarkable mechanical properties,allowing strains as high as 11%[99],making it a very suitable material for flexible devices and strain engineered applications, as its bandgap has been shown to be strain tunable [100–103], which is already starting to be used to fabricate optoelectronic devices such as broadband flexible photodetectors [104] or optical modulators [105,106],to name a few.An important property that has also been observed in MoS2is piezoelectricity. For an odd number of layers, MoS2presents broken inversion symmetry, its structure becomes non-centrosymmetric and therefore piezoelectricity, the conversion of mechanical strain into electric charges, arises [107,108], opening up the possibility of MoS2self-powered devices based on its piezoelectric properties.In relation to power generation, it has been demonstrated that single-layer MoS2nanopores can function as osmotic power generators,inducing a current when there is a salt gradient that has been shown to be sufficient to self-power a single-layer MoS2transistor[109].

After graphene and MoS2, hexagonal boron nitride (hBN) is among the most popular 2D materials.hBN is a wide bandgap(～6 eV) layered material with a lattice constant similar to that of graphite and an atomically flat surface free of dangling bonds. Thanks to these properties,since 2010 it has been used as the substrate of choice for graphene devices[14],and its presence is now almost ubiquitous in any high quality 2D material device. In addition, it has been reported the fabrication of 3-nm-thick mechanically and electrically robust amorphous boron nitride films with ultralow dielectric constant (<2, near that of the air,equal to 1) [110], with a great potential as an interconnect isolation material for high-performance electronics. However, in the last years interest in hBN has grown far beyond its mere use as a substrate for other 2D materials. Recent research has revealed that hBN possess a unique combination of properties that make it a promising candidate for multiple applications.It has been shown that it can withstand temperatures up to 700°C before oxidation in air [111] and that it is one of the strongest electrically insulating materials, with a Young's modulus comparable to that of graphene and presenting also a high breaking strength [112]. These properties make hBN very suitable for reinforcement and high temperature applications.

hBN is also extensively studied because of its remarkable optical properties [113]. It is a natural hyperbolic material (its permittivity is different along orthogonal axes and opposite in sign)in the mid-infrared range [114,115], where there are almost no alternatives for photonic materials. Thanks to its direct bandgap in the ultraviolet region, it is a promising material for ultraviolet emission[116].Two-dimensional hBN has also been shown to host bright, polarized and stable single-photon emission at room temperature [117,118], holding great promise for quantum information processing, nanophotonics and optoelectronics.Single-photon emission is originated by optically active atomic-scale defects with ground and excited states within the gap of hBN, but despite many efforts the exact nature of the defects causing the observed light emission is not completely clear[119–121].

Interest in hBN for its electronic properties is currently on the rise.As in the case of MoS2and other TMDs,with odd numbers of hBN layers its inversion symmetry is broken, and therefore piezoelectricity was expected[122,123].The observation of piezoelectricity in monolayer hBN has recently been reported using electrostatic force microscopy techniques, directly visualizing the strained-induced electric field around naturally occurring bubbles and creases in hBN single layers deposited on other 2D materials [124]. Another property that has been recently observed in hBN is ferroelectricity. In commonly used hBN, boron and nitrogen atoms are aligned in the out-of-plane direction of neighbouring layers,known as AA’stacking.By stacking two crystals of hBN at a small twist angle,the atoms at the interface of the crystals can be aligned with the AB(Bernal)stacking,giving rise to robust ferroelectric-like domains arranged in triangular superlattices with a large surface potential at room temperature [125–127]. The formation of these extremely sharp lateral potential steps opens many possibilities, such as the creation of a modulation potential template to modify the properties of adjacent 2D materials or for ferroelectric memories.

In the last few years,a large number of 2D materials has been isolated and started to be studied,greatly expanding possible novel phenomena to be explored and options for choosing the most suitable material for a given application. Here we can first mention other monoelemental 2D materials, obtained by at least one of the conventional methods (mechanical exfoliation, chemical vapour deposition or molecular beam epitaxy), such as borophene [128], silicene [129], germanene [130],stanene [131], plumbene [132], and group-VA semiconductors [8],where we can highlight phosphorene [133], antimonene [134] and bismuthene [135] due to their intriguing structures and fascinating electronic properties. In particular phosphorene, a monolayer of black phosphorus[136–138],has been recently the subject of many studies due to its direct bandgap,high carrier mobility and optoelectronic properties,among others.

Another branch of 2D materials recently discovered are the MXenes,which are those with the general formula Mn+1XnTx,where M is an early transition metal,such as Ti,Mo,Nb,V,Cr,Zr,Ta,etc.,X is carbon and/or nitrogen,n=1–4,and Txrepresents surface terminations[6].Thanks to their structure, in which transition metal atoms are arranged in layers with carbon or nitrogen atoms, the MXenes show a lot of possible compositions and tunable properties,making them excellent candidates for a variety of applications, including energy storage, optoelectronics or catalysis,to name a few.

Some 2D materials have risen a lot of interest in the last years due to their optoelectronic and photonic properties. Together with the TMDs and hBN already discussed,we can highlight here indium selenide,InSe,showing high carrier mobilities, thickness dependent bandgap and an anomalous optical response [139–141], or molybdenum trioxide,α-MoO3, a naturally biaxial hyperbolic crystal, which has been recently the subject of intensive research due to the presence of confined anisotropic and ultra-low-loss polaritons (quasiparticles resulting from the mixing of a photon with a polar excitation in a material)[142–144].2D layered hybrid lead halide perovskite semiconductors are another type of bidimensional materials that in the last years have attracted a lot of attention thanks to their high photovoltaic and light-emitting efficiencies[145–147].

2D materials cover a wide range of attributes,but it has not been until recently that atomic crystals exhibiting intrinsically important properties such as magnetism [11,148,149] or superconductivity [150,151] have been isolated and studied.In the last years,initial reports giving indirect evidence of the magnetic order in single-layer 2D materials such as NiPS3[152], FePS3[153–155], and CrSiTe3[156], gave way to the clear experimental observation of magnetism in atomically thin compounds such as Cr2Ge2Te6[157], CrI3[158] and CrBr3[159] at low temperatures,and in VSe2[160],MnSe2[161]and Fe3GeTe2[162]at even room temperature. Intrinsic superconducting 2D materials such as Bi2Sr2CaCu2O8+x(Bi2212) [163] and the widely studied NbSe2[164–166], have lately attracted research interest due to their possibilities for the exploration of new quantum physics and high-temperature superconductivity.

In light of the new developments that have been carried out in recent years on 2D materials,we envision significant advances in fundamental knowledge thanks to them in the near future.In addition to the multiple 2D materials isolated in the last years,many new systems with intriguing properties that have been predicted using computational methods and are awaiting to be realized [9,167,168], will enlarge the already rich family of 2D materials and promise many more exciting discoveries.But not only each of the materials in their own,their combination in van der Waals heterostructures will greatly expand their possibilities. For example, it has been demonstrated that the combination of the 2D ferromagnet CrBr3on a NbSe2superconducting substrate leads to 2D topological superconductivity in the system [169]. Moreover, the combined application of other approaches with such heterostructures will for sure pave the way for the discovery of new fundamental phenomena in the near future.

The application of twistronics and moir′e materials will allow tunable electrical and optical properties and a very convenient platform for the study of topological and strongly correlated phenomena [170,171]. For instance, it will have a significant impact on nanophotonics, as demonstrated by the effect of moir′e potentials on light emission and absorption in heterobilayers of different TMDs, such as combinations of MoS2/-MoSe2[172], MoSe2/WSe2[173,174], WSe2/WS2[175–177] or MoSe2/WS2[178]. Or the achievement of precise control of the propagation of light in twisted layers of α-MoO3(in particular,phonon polaritons, which result from coupling an infrared photon with an optical phonon)[179–181]. We will also see significant advances in the understanding of superconductivity and strongly correlated phenomena thanks to the development of tunable moir′e superconductors, as is the case of the recent new generation of superconductivity in magic-angle trilayer graphene [182,183], and the recent development of a general and scalable synthesis of large-sized highly crystalline 2D superconducting monolayers in solution phase,demonstrated with NbSe2[184],that can be integrated in inks for the fabrication of wafer-scale superconducting devices.

The use of strain engineering methods in 2D systems, the so-called“straintronics” [185], will also allow introducing technological innovations,such as novel strain tunable single-layer MoS2 photodetectors[186],opening the possibility of developing adaptable artificial photonic elements, or inducing novel physical effects, as for example the conversion of excitons to trions in WS2at room temperature up to 100% efficiency under non-uniform strain without electrical gating [187], giving evidence of negligible funnelling (the transport of excitons) at room temperature in two-dimensional semiconductors.Engineering symmetry breaking in 2D layered materials is another fascinating approach to tune their physical properties and introduce completely new physics and technological innovations[188].

In addition to the opportunities of these heterostructures in their own,they house multiple possibilities for assembling devices to study other phenomena. For instance,van der Waals assemblies have facilitated the fabrication of atomically thin nanochannels[189],allowing the study of molecular transport under extreme confinement [190–193] and even solving long-standing fundamental questions,as the value of the dielectric constant of interfacial water,finding an anomalously low value of ≈2 for the out-of-plane component[194],or the validity of the macroscopic Kelvin equation to describe the condensation transition in atomically thin capillaries[195].

Despite the extensive research into 2D systems over the last 15 years,it may only be the tip of the iceberg of novel phenomena in the field of 2D materials.In the coming years,the use of available and undiscovered 2D materials will be combined with the application of multiple techniques simultaneously to manipulate and tune their properties. These include stacking at precise and controlled angles, strain engineering, defect engineering, functionalization, chemical doping or symmetry breaking,among others.While some of these techniques are well developed,there is room for improvement to precisely control the fabrication of devices from 2D materials. For example, to facilitate the development of twistronics, improved tools will have to be developed to ease the precise alignment of layers or to obtain exquisitely clean and homogeneous interfaces in heterostructures. This will allow further progress in fundamental studies of these systems,leading to a wealth of new and exciting knowledge.

Declaration of competing interest

The authors declare no competing financial interest.

Acknowledgements

We thank NRF (Singapore) for financial support through the project Medium-Sized Centre programme R-723-000-001-281. K.S.N. acknowledges support from EU Flagship Programs(Graphene CNECTICT-604391 and 2D-SIPC Quantum Technology),European Research Council Synergy Grant Hetero2D, the Royal Society, EPSRC grants EP/N010345/1, EP/P026850/1,EP/S030719/1.