Researchers at The University of Manchester have discovered unexpected phenomena in graphite thanks to their previous research on its two-dimensional (2D) relative—graphene.
The team led by Dr. Artem Mishchenko, Professor Volodya Fal’ko and Professor Sir Andre Geim, discovered the quantum Hall effect (QHE) in bulk graphite—a layered crystal consisting of stacked graphene layers. This is an unexpected result because the quantum Hall effect is possible only in two-dimensional materials where the movement of electrons’ motion is restricted.
They have also found that the material behaves differently depending on whether it contains odd or even number of graphene layers—even when the number of layers in the crystal exceeds hundreds. The work is an important step to the understanding of the fundamental properties of graphite, which have often been misunderstood.
“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.”
In the work, published in Nature Physics, Mishchenko and colleagues studied devices made from cleaved graphite crystals, which essentially contain no defects. The researchers preserved the high quality of the material by encapsulating it in another high-quality 2D layered material—hexagonal boron nitride. This allowed nearly perfect samples of thin graphite to measure electron transport in this material.
“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.
Fal’ko, who led the theory exploration, 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 comes from the fact that the applied magnetic field forces the electrons in graphite to move “in a reduced dimension,” with conductivity only allowed in one direction. Then, in thin enough samples, this one-dimensional motion can become quantized thanks to the formation of standing electron waves. The material goes from being a 3D electron system to a 0D one, with discrete energy levels in a magnetic field.
Another big surprise is that this QHE is very sensitive to even/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 formed from electrons of two different flavors sit on either even—or odd—numbered layers in graphite. In films with even number of layers, the number of even and odd layers is the same, so the energies of the standing waves of different flavors coincide.
The situation is different in films with odd numbers of layers, however, because the number of even and odd layers is different as there is always an extra odd layer. This results in the energy levels of the standing waves of different flavors shifting with respect to each other and means that these samples have reduced QHE energy gaps. The phenomenon even persists for graphite hundreds of layers thick.
The unexpected discoveries did not end there: the researchers also observed the fractional QHE in thin graphite at temperatures below 0.5 K. The fractional QHE is a result of strong interactions between electrons. These interactions, which can often lead to important collective phenomena such as superconductivity, magnetism and superfluidity, make the charge carriers behave as particles with a charge that is a 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.”
Graphene has been in the limelight these last 15 years, due to its many superlative properties, and graphite was pushed back a little by 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.
“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 plan to explore all those phenomena and theoretical predictions using the fact that their thin graphite samples are as perfect as materials can be.