The behaviour of electrons through graphene constrictions has been found to increase the material’s conductivity. Kathryn Allen reports.
Observations of the electron flow in graphene at the National Graphene Institute, University of Manchester, UK, have confirmed a theory proposed by MIT Professor Leonid Levitov’s team in March 2017 that electrons pass through constrictions more easily when they interact with each other.
The team, led by Professor of Physics Sir Andre Geim and made up of researchers from the University of Manchester, theoretical physicists led by Professor Marco Polini of the Institute of Technology, Italy, and Levitov, has also demonstrated that this viscous flow of electrons, which the team are calling superballistic, is more conductive than ballistic electrons. In a paper published in Nature Physics, the researchers demonstrate that this superballistic electron flow breaches the limit imposed by the Landauer-Buttiker formalism, which defines the maximum conductance for metals.
Geim’s team used devices made from atomically thin layers of graphene, which has a relatively high conductivity in comparison to metals such as copper. This is due to fewer imperfections in graphene, allowing electrons to move faster and scatter less.
Typically, scattering electrons reduce a metal’s conductivity by increasing resistance. However, this superballistic flow has been observed to reduce resistance, increasing conductivity. This is because some of the electrons stay near the crystal edges, moving relatively slowly, preventing other electrons from colliding with these areas. These other electrons move rapidly through the centre of the material, forming the superballistic flow.
Dr Roshan Krishna Kumar, post-doctoral researcher in the School of Physics and Astronomy at the University of Manchester, and co-author of the paper, told Materials World, ‘In typical metals and semi-conductors, electrons tend to collide with other bodies rather than themselves. Even in ultra-clean systems, where there are no impurities or defects in the crystal, at finite temperatures the lattice starts vibrating and electrons scatter more frequently with these vibrations than with each other. In graphene, however, the lattice vibrations are weak. This is the reason why graphene has such a large conductivity at room temperature. Consequently, electron–electron collisions become a dominant source of scattering in graphene, resulting in viscous flows.’ Electron–electron collisions do not result in a net loss of the electrons’ energy.
This viscous flow of electrons was recognised in 2016 by three separate experiments determining that at certain temperatures electron–electron collisions occur so frequently that they move as a viscous liquid. Kumar said, ‘Here in Manchester, we studied viscous electron whirlpools in graphene and were able measure the electron viscosity, which turned out to be 50 times greater than honey. In Harvard, USA, researchers observed a huge enhancement in the thermal conductivity of the electron-hole plasma in charge neutral graphene, caused by hydrodynamic transport of this so-called Dirac fluid. Finally, a third experiment demonstrated hydrodynamic electron flow in palladium cobalt nanowires.’
To examine this electron flow through graphene constrictions the team scratched markings onto pieces of graphene sandwiched between boron-nitride crystals and then applied a current to the material. The resistance across these markings, or constrictions, was measured and found to decrease as the temperature increased. The team refer to this relationship between resistance and temperature at the point of constriction as the viscous conductance.
An understanding of this behaviour could change the way future nano-electronic circuits and electronic devices are designed. Kumar said, ‘This research demonstrates the presence of viscous electron flows in a graphene channel, which seem to be present even at room temperature. With this respect, viscous flows might be considered in the design of graphene interconnects. As for more advanced device architectures, it is too early to say exactly where viscous conduction will be implemented. Although, considering its prominence in our transport experiments, it is likely to play a role in many functioning devices.’
Despite the attention this research has received, Kumar acknowledged that ‘the question remains as to what extent we can control this viscous behaviour in conducting materials’.
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