Scientists from Israel's Weizmann Institute of Science, in collaboration with teams at Manchester University and UC Irvine, have shown that an electronic fluid can flow through materials without any electrical resistance, thereby perfectly eliminating a fundamental source of resistance that forms the ultimate limit for ballistic electrons. This result could open the door to improved electronic devices that do not heat up as much as existing technologies.
When electrons flow in electrical wires, they lose part of their energy, which is wasted as heat. This heating is a major problem in everyday electronics. The heating occurs because electrical conductors are never perfect and have a resistance for the flow of electrical currents. Typically, this resistance originates from the scattering of the flowing electrons by imperfections in the host material. But it stands to reason that a perfect conductor, devoid of any imperfections, would have zero resistance. However, even if the conductor is perfectly clean and free from imperfections, the resistance does not vanish. Instead, a new source of resistance emerges, known as the Landauer-Sharvin resistance. In an electrical conductor, electrons flow in quantum channels, much like cars in highway lanes. Similar to highway lanes, each electronic channel has a finite capacity to conduct electrons, limited by the quantum of conductance. For a given conductor, the number of quantum channels is finite and determined by its physical width. Thus, even a perfect electronic device, devoid of any imperfections, will never have infinite conductance. It will always have resistance. In the absence of interactions between electrons, this Landauer-Sharvin resistance is unavoidable, putting a fundamental lower bound on the heating of computer chips, which becomes even more severe as transistors become smaller.
In recent years, researchers have realized that when the current flow involves frequent collisions between electrons, the flow changes its nature from that of a diffusive motion of gas molecules to that of a collective motion of a liquid. This new regime has been named “electron hydrodynamics”, and its various manifestations have been demonstrated in several theoretical and experimental works.
In particular, it was shown that when electrons are forced to flow through a constriction between two confining walls, they can conduct somewhat better than the Landauer-Sharvin limit. This was theoretically explained to result from the lubrication of these walls by the electronic fluid, naturally raising a fundamental question – how would hydrodynamic electrons behave when there are no walls at all?
A recent theory from Gregory Falkovich and collaborators suggested that this could be tested by flowing electrons in a DVD-like geometry termed a “Corbino disk”. In this geometry, electrons flow from an outer ring-shaped contact to an inner circular contact through a conducting disk, without ever encountering any physical wall.
One would imagine that there would be no electrical resistance when electrons flow through this disk ballistically, with no collisions along the way. Collisions, on the other hand, may be expected to generate resistance. It turns out that the opposite is true, as was revealed in the new experiment by the Weizmann-Manchester-Irvine team.
In this new experiment, the team (led by Shahal Ilani from the Weizmann Institute) imaged electronic flows in devices made of graphene encapsulated in hexagonal boron nitride (hBN) and patterned into the Corbino disk geometry. Special care was taken to fabricate extremely clean devices – such that electrons do not collide with any edges or lattice imperfections as they make their way through the disk.
The Corbino geometry does have a drawback, though: since there are no contacts in the bulk of the device, transport experiments can only measure the device’s total resistance and not how it is distributed in space.
To overcome this problem, Ilani and colleagues used a unique nanotube-based scanning single-electron transistor (SET) technique that can spatially map the potential drop associated with the flowing electrons with extreme sensitivity and without disturbing the flow. This technique allowed them to directly image the spatial distribution of the device’s resistance throughout the device.
The researchers first imaged the resistance distribution at liquid helium temperature (4.2 degrees Kelvin).
“At such a temperature, the scattering between electrons is negligible due to the Pauli exclusion principle that keeps electrons apart. Thus, the electrons behave effectively as independent ballistic particles,” says Chandan Kumar, a lead author on the research. “In the absence of impurities that can scatter the electrons, one would naively expect no resistance.”
The team discovered that there is significant resistance spread across the entire bulk of the disk, increasing as the current gets closer to the center of the disk. However, an even more fascinating phenomenon occurred when these devices were warmed up to temperatures above 100 degrees Kelvin.
“At these temperatures, electrons collide very frequently with other electrons", says John Birkbeck, another lead author of this study. “But instead of increasing the resistance, we saw that these collisions reduced it. In fact, we observed that in the bulk of the disk the resistance was perfectly eliminated – electrons were flowing with no resistance at all”
What makes freely-flowing electrons in a Corbino disk face resistance? And how can collisions remove this resistance? The team explained this in a complementary theory paper, showing that the answer lies in the “Landauer highway”: an electron starting at the outer perimeter of the disk has many quantum channels available for it to flow through. However, as it propagates toward the center of this disk, these channels get gradually blocked, forcing the electrons flowing in these channels to go back.
Although there is no physical barrier that scatters back the electrons, these electrons still experience a resistance that grows as they get closer to the center, matching nicely the experimental observations. This resistance is the fundamental Landauer-Sharvin resistance coming from the termination of conduction channels.
In contrast to conventional rectangularly-shaped devices, in which the number of quantum channels changes abruptly at the contacts, leading to the Landauer-Sharvin resistance appearing only at the contacts, in a Corbino disk the change in the number of channels is gradual, and therefore this resistance is now spread over the entire bulk of the disk.
While ballistic electrons cannot avoid this Landauer-Sharvin resistance, irrespective of the geometry of the device, the theory showed that the collisions between electrons can surprisingly help them completely evade this resistance. The key observation is that such collisions allow electrons to transfer from channels that are about to be blocked to propagating channels, rather than being scattered back.
Interestingly, the theory showed that when the blocking of channels happens over a large enough length scale, such that electrons scatter multiple times along this motion, this scattering can lead to perfect elimination of the Landauer-Sharvin resistance, as was observed in the experiments.
“This is a sort of ‘social mobility’ for these hydrodynamic electrons, allowing them to be scattered from a blocked lane to a privileged propagating lane” adds Ady Stern, who led the theoretical effort. “The result is lower resistance – and ultimately less heat being produced in the device.”
According to the researchers in this work, these findings could help researchers design and develop more efficient and improved electronics. “We showed that when electrons go into a fluid state, their dissipation drops dramatically. This suggests that if computers could be made of electronic devices that are based on hydrodynamic electron flow, they would have significantly reduced heating” says Ilani.