Transport in grapheneContact François Amet (amet@) for more informations.
Our group studies the electronic properties of graphene, a one atom thick carbon crystal with a honeycomb lattice. At low energy, the bandstructure of graphene has a linear dispersion relation [1], different from the usual quadratic dispersion of the valence and conduction bands in regular semiconductors. As a result, lowenergy quasiparticles are massless and described by the Dirac equation, which results in a wide variety of exotic electronic phenomena, such as an anomalous quantum Hall effect[2].
We use hexagonal boronnitride as a gate dielectric [3], an insulator whose crystal structure is very similar to that of graphite. Flakes of graphene and boronnitride are transferred on top of each other using a micro manipulator [Fig. 1]. The resulting heterostructures can have carrier mobilities of at least 400 000 cm^{2}/Vs at low temperature, which corresponds to mean free paths of several microns. This device quality allows us to study a variety of exotic electronic phenomena.
1. Integer and Fractional Quantum Hall effect In a large magnetic field B, the band structure of two dimensional electrons becomes a discrete set of highly degenerate Landau levels [Fig. 2]. With kinetic energy quenched, electron interactions determine the ground state of a partially filled Landau level. At high magnetic field, this yields a variety of new incompressible phases known as fractional quantum Hall (FQH) states. While such electronic phases have been thoroughly studied in GaAs twodimensional electron gas, their observation in graphene has been limited by disorder, potential fluctuations being larger than the FQH gaps in most devices. With improved fabrication methods, we observed a plethora of new FQH states in transport [Fig. 2(bc)], at particular fractional filling factors predicted by the composite fermion theory [4]. By controlling the in and outofplane magnetic fields as well as the carrier density, we study how these phases are affected by spin and valley symmetry breaking interactions. An alternative way to understand the quantum Hall effect is to study edge transport. Indeed, even when the bulk of the graphene sheet is in a gapped quantum Hall phase, charge carriers can still propagate in one dimensional channels along the edges of the sample. To understand the electronic properties of these edge states  and in particular how they scatter we measure the conductance of dualgated graphene devices [Fig. 3(a)] where the filling factors and therefore the number of edge states are different in adjoining regions [Inset Fig. 3(c)]. The observed plateaus of conductance depend on the mixing of edge states along the PN interface and the physical edges of the sample [Fig. 3(bc)]. When the SU(4) symmetry of the Landau level is lifted by interactions, edge states can be spin and/or valley polarized and we observe selection rules in their scattering properties. [5]
2. Substrate effects on graphene transport Graphene being gapless, its electronic properties around the charge neutrality point are highly affected by Fermi level fluctuations caused by disorder. Even the cleanest suspended graphene devices show a non zero minimum conductivity, which ultimately depends on the disorder density. In extremely clean graphene on boron nitride, we observed a strong insulating behavior [Fig. 4], attributed to the combined effect of the substrate induced sublattice symmetry breaking and screening from a proximal gate [6]. This phenomenon is now under intense scrutiny and paves the way towards exciting new device geometries.
3. Ballistic phenomena in graphene/boron nitride heterostructures The micronscale mean free path we observe in our graphene heterostructures allow us to study ballistic transport. For example, FabryPerot interferences [7] are observed in micronwide PNP cavities, due to electrons reflecting off the interfaces and selfinterfering [Fig. 5]. More broadly, we study the fascinating properties of Dirac fermions in graphene and its multilayers when they go through PN interfaces.
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