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Graphene plays billiards at the quantum scale
RESEARCH NEWS
Ripples in graphene: it’s all in the bonds CARBON
Graphene, the first and only two-dimensional crystal in nature, is attracting great attention as a new and unique electronic material. But graphene is not a perfectly flat sheet – recent experimental observations have found ripples in suspended sheets of the material [Meyer et al., Nature (2007) 446, 60]. Simulations of graphene carried out by researchers at Radboud University Nijmegen, The Netherlands, suggest that it is the bonding between carbon atoms in graphene that may be responsible for the ripples [Fasolino et al., Nat. Mater. (2007), doi: 10.1038/ nmat2011]. There is some debate surrounding the stability of two-dimensional layers and membranes. The long-range order of two-dimensional crystals is destroyed by long-wavelength fluctuations, according to the Mermin-Wagner theorem, and such two-dimensional crystals tend to ‘crumple’ in three-dimensional space. However, while soft condensed matter membranes are known to bend and form ripples, such behavior in solids like graphene is surprising. To better understand the unusual behavior of graphene, the researchers from Radboud University undertook atomistic Monte Carlo simulations at room (300 K) and high (1000 K, 2000 K, and 3500 K) temperatures. “[These] large-scale simulations, based on a very accurate description of the bonding in carbon,
Simulations may explain the origin of ripples in graphene sheets. (Courtesy of Annalisa Fasolino.)
show that graphene is intrinsically rippled as a consequence of thermal fluctuations,” says coauthor Annalisa Fasolino. Even at room temperature at equilibrium, graphene shows a broad distribution of height fluctuations. “However, the correlation function of the normals does not display the expected powerlaw behavior that would result if ripples of all sizes were present,” explains Fasolino. In fact, the ripples appear to have an average size of 80 Å. This finding is in good agreement with experimental observations of 50–100 Å ripples in graphene. The same results are found at high temperatures too. The researchers believe that the origin of the ripples is to be found in the carbon–carbon bonding in graphene. Even at room temperature, there is likely to be an uneven mixture of long/ short (single/double) bonds. This mixture of long and short bonds could give rise to the ripples in graphene sheets.
“The versatile nature of bonding in carbon and deviations from conjugated bonding characteristic of perfectly flat layers like graphene might explain this finding,” says Fasolino. Despite this intrinsic tendency to form ripples, the amplitude of the fluctuations is much smaller than the sample size. This means that the long-range order of graphene is preserved and it can still be considered ‘flat’ rather than crumpled. But understanding the reasons for graphene’s rippled structure is important. “This fact could be of consequence for the electronic properties of graphene and represents a major source of scattering,” notes Fasolino. However, she says, many questions remain open: what determines the typical ripple size, are ripples quenched when graphene is placed on a substrate, and what are the consequences for electronic transport? Cordelia Sealy
Graphene plays billiards at the quantum scale CARBON Many unique and novel phenomena are predicted or have been observed in graphene. Electron transport in graphene is of particular interest because of the material’s potential for a new generation of electronic devices. Many of the hopes for graphene rely on ballistic (i.e. scattering-free) transport, but this has not been clearly demonstrated until now. Using low-temperature transport spectroscopy, researchers at the University of California, Riverside believe that they have observed ballistic transport in single- and bilayer graphene [Miao et al., Science (2007) 317, 1530]. “We demonstrate, for the first time, that graphene can act as a quantum billiard table,” says Chun Ning (Jeanie) Lau. “[It is] a two-dimensional ballistic and phase-coherent electron system where scattering can only take place at boundaries and electrodes.” In such a system, electrons or holes play the role
of billiard balls on the graphene billiard table. The electrons or holes move across graphene without encountering any obstacles and are only reflected (or scattered) by the edge of the graphene sheet. “As the charge carriers interfere among multiply reflected paths, we realize a quantum wave resonator for electrons and holes with a phase-coherence length >5 µm,” adds Lau. The researchers also use low-temperature transport spectroscopy to address another of graphene’s mysteries – its conductivity at the Dirac point. Experimental results have seemed to indicate that conductivity in graphene is higher at the Dirac point than predicted by theory. Instead, the team demonstrates that this property of graphene is geometry-dependent. The conductivity of graphene only approaches the theoretical limit when the device has a small area (<0.2 µm2) and source– drain channel length (<500 nm).
Electrons are reflected at the edges of graphene sheets just like billiard balls bounce off the cushions of billard tables. (Courtesy of Jeanie Lau.) The results point to two transport regimes for graphene: ballistic transport in small and short graphene strips and diffusive transport in larger devices. These findings, together with those on ripples in graphene (above), have important implications for the realization of electronic devices using graphene.
Cordelia Sealy
NOVEMBER 2007 | VOLUME 10 | NUMBER 11
9
Ripples in graphene: it’s all in the bonds CARBON
Graphene, the first and only two-dimensional crystal in nature, is attracting great attention as a new and unique electronic material. But graphene is not a perfectly flat sheet – recent experimental observations have found ripples in suspended sheets of the material [Meyer et al., Nature (2007) 446, 60]. Simulations of graphene carried out by researchers at Radboud University Nijmegen, The Netherlands, suggest that it is the bonding between carbon atoms in graphene that may be responsible for the ripples [Fasolino et al., Nat. Mater. (2007), doi: 10.1038/ nmat2011]. There is some debate surrounding the stability of two-dimensional layers and membranes. The long-range order of two-dimensional crystals is destroyed by long-wavelength fluctuations, according to the Mermin-Wagner theorem, and such two-dimensional crystals tend to ‘crumple’ in three-dimensional space. However, while soft condensed matter membranes are known to bend and form ripples, such behavior in solids like graphene is surprising. To better understand the unusual behavior of graphene, the researchers from Radboud University undertook atomistic Monte Carlo simulations at room (300 K) and high (1000 K, 2000 K, and 3500 K) temperatures. “[These] large-scale simulations, based on a very accurate description of the bonding in carbon,
Simulations may explain the origin of ripples in graphene sheets. (Courtesy of Annalisa Fasolino.)
show that graphene is intrinsically rippled as a consequence of thermal fluctuations,” says coauthor Annalisa Fasolino. Even at room temperature at equilibrium, graphene shows a broad distribution of height fluctuations. “However, the correlation function of the normals does not display the expected powerlaw behavior that would result if ripples of all sizes were present,” explains Fasolino. In fact, the ripples appear to have an average size of 80 Å. This finding is in good agreement with experimental observations of 50–100 Å ripples in graphene. The same results are found at high temperatures too. The researchers believe that the origin of the ripples is to be found in the carbon–carbon bonding in graphene. Even at room temperature, there is likely to be an uneven mixture of long/ short (single/double) bonds. This mixture of long and short bonds could give rise to the ripples in graphene sheets.
“The versatile nature of bonding in carbon and deviations from conjugated bonding characteristic of perfectly flat layers like graphene might explain this finding,” says Fasolino. Despite this intrinsic tendency to form ripples, the amplitude of the fluctuations is much smaller than the sample size. This means that the long-range order of graphene is preserved and it can still be considered ‘flat’ rather than crumpled. But understanding the reasons for graphene’s rippled structure is important. “This fact could be of consequence for the electronic properties of graphene and represents a major source of scattering,” notes Fasolino. However, she says, many questions remain open: what determines the typical ripple size, are ripples quenched when graphene is placed on a substrate, and what are the consequences for electronic transport? Cordelia Sealy
Graphene plays billiards at the quantum scale CARBON Many unique and novel phenomena are predicted or have been observed in graphene. Electron transport in graphene is of particular interest because of the material’s potential for a new generation of electronic devices. Many of the hopes for graphene rely on ballistic (i.e. scattering-free) transport, but this has not been clearly demonstrated until now. Using low-temperature transport spectroscopy, researchers at the University of California, Riverside believe that they have observed ballistic transport in single- and bilayer graphene [Miao et al., Science (2007) 317, 1530]. “We demonstrate, for the first time, that graphene can act as a quantum billiard table,” says Chun Ning (Jeanie) Lau. “[It is] a two-dimensional ballistic and phase-coherent electron system where scattering can only take place at boundaries and electrodes.” In such a system, electrons or holes play the role
of billiard balls on the graphene billiard table. The electrons or holes move across graphene without encountering any obstacles and are only reflected (or scattered) by the edge of the graphene sheet. “As the charge carriers interfere among multiply reflected paths, we realize a quantum wave resonator for electrons and holes with a phase-coherence length >5 µm,” adds Lau. The researchers also use low-temperature transport spectroscopy to address another of graphene’s mysteries – its conductivity at the Dirac point. Experimental results have seemed to indicate that conductivity in graphene is higher at the Dirac point than predicted by theory. Instead, the team demonstrates that this property of graphene is geometry-dependent. The conductivity of graphene only approaches the theoretical limit when the device has a small area (<0.2 µm2) and source– drain channel length (<500 nm).
Electrons are reflected at the edges of graphene sheets just like billiard balls bounce off the cushions of billard tables. (Courtesy of Jeanie Lau.) The results point to two transport regimes for graphene: ballistic transport in small and short graphene strips and diffusive transport in larger devices. These findings, together with those on ripples in graphene (above), have important implications for the realization of electronic devices using graphene.
Cordelia Sealy
NOVEMBER 2007 | VOLUME 10 | NUMBER 11
9