The team of B. Hackens in the NAPS/IMCN laboratory at UCLouvain, in collaboration with the group of C. Stampfer in RWTH Aachen, revealed a new detailed microscopic picture of the “quantum Hall effect” in graphene. This breakthrough was made possible thanks to experimental data obtained by Nicolas Moreau (PhD student, funded by a FRIA fellowship), with a home-made “scanning gate microscope” capable of imaging charge carriers’ behavior at the nanometer scale inside graphene devices.
Classically, when a magnetic field is applied perpendicular to a current-carrying conductor, electrical charges are deflected towards the edges of the conductor, which then causes the emergence of a transverse electric voltage: the Hall voltage. When charges are confined in a very thin layer of conducting material (ultimately, a one-atom-thick conductor like graphene), and the Hall voltage is measured at low temperature and high magnetic field, one can reach the quantum version of the Hall effect. In this case, the channels where charges are travelling at the edges of the material are perfect one-dimensional “edge states” where charge backscattering is prohibited due to the presence of the insulating region inside the sample (the edge states are said to be “topologically protected”), and the Hall voltage becomes quantized. Measurements indeed show that dividing the current by the Hall voltage yields integer multiples of the universal constant e2/h, where e is the electron charge and h the Planck constant. For this reason, the quantum Hall effect became a central tool in metrology, both to measure the fundamental constants and to devise extremely precise electrical resistance standards in all metrology institutes.
The quantum Hall effect is in principle intrinsically more robust in graphene than in other two-dimensional systems: it has even been observed up to room temperature in this material. However, recent observations show that the conventional picture of the quantum Hall effect in graphene can not explain all observations. For example, quantum Hall signatures have been measured even when the sample interior is not insulating. The images obtained by Nicolas Moreau reveal that the “hotspots” where charges are backscattered in this regime can be found all along the edges of graphene devices. This experimental observation can be explained in the framework of a new microscopic picture of the quantum Hall effect where, instead of being located at opposite edges of the sample, quantum Hall channels are propagating in opposite directions along the same sample edge. The observed hotspots correspond to the position of defects with discrete set of energy levels. At the position of these defects, charges can tunnel between the counter-propagating edge states through the available empty energy levels.
This new mechanism is the “Achilles’ tendon” of graphene quantum Hall effect. Fortunately, it could be avoided: the presence of counterpropagating edge states is related to electrostatics, and device design can be adapted to overcome the problem. Beside providing a new understanding of this fundamental quantum effect, this work therefore constitutes an important step towards robust design of quantum Hall standards in graphene.
a Schematic of the studied sample. The graphene is protected by two layers of insulating hexagonal boron nitride (in blue) and a constriction shape has been defined. Four metalic contacts (in gold) are used to measure the device's resistance Rxx. A back gate allows to tune the graphene charge carriers density. Finally, a sharp metalic tip is biased by a voltage Vtip and is used to spot where the backscattering of charge carriers occurs in the quantum Hall regime.
b Schematic of the energy landscape at the sample edge (in the orange region in a, with border in red). At high magnetic field, the energy is quantized (blue layers that follow the potential landscape) and 1D edge channels appear where these levels cross the Fermi energy EF (electrochemical potenital). Here, counter-propagating edge channels flow along the same edge (blue and red) and an antidot (the loop) can appear between them, triggering charge carriers backscattering.
Online : https://www.nature.com/articles/s41467-021-24481-2#Abs1