Quantum Hall Effect Observed in Bulk Graphite with Graphene Layers
Researchers at the University of Manchester have identified surprising phenomena in graphite thanks to the team's previous research on its two-dimensional relative, graphene. The team led by Dr Artem Mishchenko, Professor Volodya Fal'ko, and Professor Sir Andre Geim, found the quantum Hall effect (QHE) in bulk graphite, a layered crystal consisting of stacked graphene layers. (See image above).
This discovery is a surprising result because the quantum Hall effect was thought to be possible only in two-dimensional materials in which the movement of electrons' motion is limited. They also found that the material behaves differently depending on whether or not it contains an odd or even number of graphene layers. This effect of odd or even numbers of layers extends to when the number of layers exceeds hundreds.
While graphene has been in the spotlight these last 15 years, due to its many excellent properties, graphite was seen as less interesting than its one-layer-thick offspring. Mishchenko adds, "We have now come back to this old material. Knowledge gained from graphene research improved experimental techniques (such as van der Waals assembly technology) and a better theoretical understanding (again from graphene physics), has already allowed us to discover this novel type of the QHE in graphite devices we made."
"For decades graphite was used by researchers as a kind of 'philosopher's stone' that can deliver all probable and improbable phenomena including room-temperature superconductivity," Geim commented. "Our work shows what is, in principle, possible in this material, at least when it is in its purest form."
For the work, detailed in Nature Physics, Mishchenko and colleagues examined devices made from cleaved graphite crystals, which basically contain no defects. The researchers protected the high quality of the material by encapsulating it in another high-quality 2D layered material, hexagonal boron nitride. This encapsulation allowed the researchers to measure electron transport in nearly perfect samples of thin graphite.
"The measurements were quite simple," explains Dr Jun Yin, the first author of the paper. "We passed a small current along the device, applied strong magnetic field and then measured voltages generated along and across the device to extract longitudinal resistivity and Hall resistance.
Prof Fal'ko who led the study of the theory said, "We were quite surprised when we saw the quantum Hall effect accompanied by zero longitudinal resistivity in our samples. These are thick enough to behave just as a normal bulk semimetal in which QHE should be strictly forbidden."
The researchers say that the QHE results from the applied magnetic field that forces the electrons in graphite to move ‘in a reduced dimension,' with conductivity only allowed in one direction. Then, in samples that are thin enough, this one-dimensional motion can become quantized thanks to the formation of standing electron waves. With discrete energy levels exposed to a magnetic field, the material goes from being a 3D electron system to a 0D one.
Another unexpected finding is that this QHE is very sensitive to an even or odd number of graphene layers. The electrons in graphite are similar to those in graphene and come in two "flavors" (called valleys). The standing waves created from electrons of two different flavors sit on either even- or odd-numbered layers in graphite.
In films with an even number of layers, the numbers of even and odd layers are the same. So, the energies of the standing waves of different flavors match.
However, the situation is different in films with odd numbers of layers because the number of even and odd layers is different due to the always extra odd layer. This odd number of layers results in the energy levels of the standing waves of different flavors shifting with respect to each other. These shifting of energy levels means that these samples have reduced QHE energy gaps. The odd/even phenomenon was shown to even persist for graphite hundreds of layers thick.
The researchers also saw the fractional QHE in thin graphite at temperatures below 0.5 K. The fractional QHE results from strong interactions between electrons. These interactions, which can often lead to critical collective phenomena such as superconductivity, magnetism, and superfluidity, make the charge carriers act as particles with a charge that is a mere fraction of that of an electron.
"Most of the results we have observed can be explained using a simple single-electron model but seeing the fractional QHE tells us that the picture is not so simple," says Mishchenko. "There are plenty of electron-electron interactions in our graphite samples at high magnetic fields and low temperatures, which shows that many-body physics is important in this material."
"Our work is a new stepping stone to further studies on this material, including many-body physics, like density waves, excitonic condensation or Wigner crystallization."
The Manchester researchers say they now intend to study all those phenomena and theoretical predictions resulting from the nearly perfect graphite samples.
