“Superballistic” electron flow verified, in graphene structures
“We know from school that additional disorder always creates extra electrical resistance. In our case, disorder induced by electron scattering actually reduces rather than increase resistance. This is unique and quite counter-intuitive: Electrons when [they] make up a liquid start propagating faster than if they were free, like in vacuum” – Professor Sir Andre Geim.
Behaving like particles in a viscous fluid can help ‘bunches’ of electrons ‘squeeze’ through a tight space, says the MIT report. (image above; MIT) The physical medium in which the effect was observed is graphene – a material in which the Manchester University team have been pioneers.
On the ‘everyday’ scale, multiple objects forced to pass through a constrained space experience a ‘bottleneck’ effect and slow down. The reverse is true for electrons, which can move through small openings more quickly when travelling in large groups than when ‘flying solo’.
The theory of so-called superballistic flow predicts that electrons can pass more easily through constrictions by interacting with one another, and thereby “cooperating,” than they can individually. The theory was proposed in a paper earlier in 2017 by a team led by MIT professor of physics Leonid Levitov. In this report, the team at the University of Manchester, working alongside Levitov and MIT undergraduate Haoyu Guo, have confirmed the theory in an experiment employing devices built from an atomically thin layer of graphene.
The idea behind superballistic flow is that interactions among electrons make them move in a highly coordinated manner, mimicking the behaviour of particles in highly viscous fluids. When electrons traveling individually pass through a constricted opening, they will bounce off the walls at either side, losing their momentum as well as some of their energy.
But when the electrons travel in dense groups, they are much more likely to bounce off each other than the walls. Such electron-electron collisions are known as “lossless,” since the total energy and the net momentum of the two particles are conserved. The momentum of individual electrons can change rapidly in the process, however the overall momentum conservation ensures that the losses are very low. As a result, together the electrons are able to travel more quickly, and pass through the constriction more easily, than they would alone.
“Viscous flows of electrons have been anticipated in theory but never observed, partly because the materials were not good enough at the time, and partly because there were no good proposals of what to look for,” Levitov says.
To make viscous flow easier to identify, Levitov’s theoretical paper suggested forcing electrons to travel through a constriction, generating an electric current. This is a similar idea to the way in which 19th century researchers studied viscosity by passing fluids through a narrow channel.
“If you run current through a constriction, and the conditions are right and the flow is viscous … the resistance of that flow will be anomalously low, namely lower than that expected for free particle flow,” Levitov says. This drop in resistance can be measured, revealing the presence of viscous flow.
next page; graphene structures…
Using the experimental set-up described theoretically in Levitov’s previous paper, the Manchester researchers, led by professor of physics and Nobel laureate Andre Geim, carefully etched a series of constrictions, or pinch points, within pieces of graphene encapsulated between boron-nitride crystals.
“The team etched the graphene sheets into a shape where they formed several constrictions, arranged in sequence, and they then applied a current such that it flowed through all of these constrictions one by one,” Levitov says.
The researchers then measured the drop in electric potential over each constriction independently, allowing them to detect the flow rate through each pinch point in the device. They found that the conductance of the electrons exceeded the maximum conductance possible for free electrons, known as Landauer’s ballistic limit. They also found that the conductance of the electrons increased with a rise in temperature.
In this way the researchers were able to verify Levitov and Guo’s original predictions within just a few days. Levitov says this is probably the fastest experimental confirmation of one of his predictions in his entire career, with the longest taking around 20 years to prove.
To confirm their findings, the researchers then repeated the experiment with a range of different graphene devices, and obtained the same results. The work points toward the possibility of using interactions among electrons to design low-power electronics, Levitov says. But more fundamentally, he says, it opens up new territory in our understanding of charge flow physics, in which electrons behave in a collective manner.
The research team at Manchester expands on the physical effects;
(image; University of Manchester)
Graphene is many times more conductive than copper thanks, in part, to its two-dimensional structure. In most metals, conductivity is limited by crystal imperfections which cause electrons to frequently scatter when they move through the material.
These observations in experiments at the National Graphene Institute have provided essential understanding as to the peculiar behaviour of electron flows in graphene, which need to be considered in the design of future nano-electronic circuits.
In some high-quality materials, like graphene, electrons can travel micron distances without scattering, improving conductivity by orders of magnitude. This so-called ballistic regime, imposes the maximum possible conductance for any normal metal, which is defined by the Landauer-Buttiker formalism.
The University of Manchester team, in collaboration with theoretical physicists led by Professor Marco Polini and Professor Leonid Levitov, show that Landauer’s fundamental limit can be breached in graphene. Even more fascinating is the mechanism responsible for this.
In 2016 a new field in solid-state physics termed ‘electron hydrodynamics’ generated huge scientific interest. Three different experiments, including one performed by The University of Manchester, demonstrated that at certain temperatures, electrons collide with each other so frequently they start to flow collectively like a viscous fluid.
The new research demonstrates that this viscous fluid is even more conductive than ballistic electrons. The result is rather counter-intuitive, since typically scattering events act to lower the conductivity of a material, because they inhibit movement within the crystal. However, when electrons collide with each other, they start working together and ease current flow.
This happens because some electrons remain near the crystal edges, where momentum dissipation is highest, and move rather slowly. At the same time, they protect neighbouring electrons from colliding with those regions. Consequently, some electrons become super-ballistic as they are guided through the channel by their ‘friends’.
Sir Andre Geim said: “We know from school that additional disorder always creates extra electrical resistance. In our case, disorder induced by electron scattering actually reduces rather than increase resistance. This is unique and quite counter-intuitive: Electrons when [they] make up a liquid start propagating faster than if they were free, like in vacuum”.
The researchers measured the resistance of graphene constrictions, and found it decreases upon increasing temperature, in contrast to the usual metallic behaviour expected for doped graphene.
By studying how the resistance across the constrictions changes with temperature, the scientists revealed a new physical quantity which they called the viscous conductance. The measurements allowed them to determine electron viscosity to such a high precision that the extracted values showed remarkable quantitative agreement with theory.
next page; nanoscale implications…
For an external perspective, the MIT report quotes Amir Yacoby, a professor of physics at Harvard University, who was not involved in the research; “Electron-electron interactions have been responsible for a huge variety of novel and exciting physics, but the effects of these interactions typically become stronger as the temperature is reduced…. The hydrodynamic electron flow regime is yet another incredibly rich manifestation of electron-electron interactions, and this time it grows with increasing temperature.”
This suggests that some of these effects might become more accessible to observation than ever before.
“The particular phenomena described in the theory and experiment are a beautiful example of a new regime of conductance that has not been explored before,” he says.
Levitov and his team are now investigating the implications of these findings. In particular they plan to study heat transport within the new fluid mechanics regime.
“It looks like heat transport in this new regime is also very surprising, and more interesting than we initially thought,” he says. “This fluid mechanics regime could possibly be used to control heat flow in electronic systems in new ways.”
University of Manchester; www.manchester.ac.uk
Report cited in; www.nature.com/nphys/