Transport in graphene

Contact 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 band-structure 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, low-energy 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 boron-nitride as a gate dielectric [3], an insulator whose crystal structure is very similar to that of graphite. Flakes of graphene and boron-nitride 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 cm2/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.


Fig. 1: Schematic of a graphene on boron nitride device with a graphite back-gate.
The whole structure rests on an oxidized silicon wafer.

 

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 two-dimensional 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(b-c)], at particular fractional filling factors predicted by the composite fermion theory [4]. By controlling the in- and out-of-plane magnetic fields as well as the carrier density, we study how these phases are affected by spin and valley symmetry breaking interactions.


Fig. 2: (a) Landau Fan diagram of the longitudinal resistance ρxx(B,n) as a function of the magnetic field B and the density n, measured at 20mK. Dark blue regions of vanishing ρxx indicate quantum Hall phases at integer filling factor ν = nh/eB. (b) As T is lowered, fractional quantum Hall phases are visible at ν = 7/3, 12/5, 17/7, 18/7, 13/5, 8/3... (measured at B=14T). (c) Similar FQH states are observed in the zeroth LL, here between ν=0 and 1. The position of the FQH states in density scales with B.

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 dual-gated 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(b-c)]. 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]



Fig. 3: (a) Scanning electron micrograph of a dual-gated graphene device, the top-gate (red) being suspended 70nm above substrate (blue). Scale bar=1μm. (b) Two terminal conductance as a function of both gate voltages at B=14T. When the spin and valley symmetry of the LL is broken, filling factors under and outside the top-gate (νT and νB) are controlled independently and span every integer value from 0 to 6. (c) When νT < νB, νT edge states are fully transmitted through the interface while the others are fully reflected (Top right inset). When νT > νB, new plateaus of conductance are visible due to the selective equilibration of edge states.

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.


Fig. 4: (a) Extremely clean graphene devices on boron nitride can turn insulating at low temperature when the sublattice symmetry is broken by the substrate. (T=2K) Inset: This insulating behavior persists in a magnetic field and directly transitions to the ν=0 quantum Hall phase.

 

3. Ballistic phenomena in graphene/boron nitride heterostructures

The micron-scale mean free path we observe in our graphene heterostructures allow us to study ballistic transport. For example, Fabry-Perot interferences [7] are observed in micron-wide PNP cavities, due to electrons reflecting off the interfaces and self-interfering [Fig. 5]. More broadly, we study the fascinating properties of Dirac fermions in graphene and its multilayers when they go through PN interfaces.


Fig. 5: Fabry-Perot interference in a graphene bipolar junction, measured at T=2K. The distance between both PN interfaces is 1.2 μm, indicating that the mean free path is well over 1μm at these temperatures.

 

References

  1. A. H. Castro-Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov & A. K. Geim. "The Electronic Properties of Graphene," Review of Modern Physics 81, 109-162 (2009). .
  2. Y. Zhang, Y. W. Tan, H. L. Stormer & P. Kim. "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005). .
  3. C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard & J. Hone. "Boron nitride substrates for high-quality graphene electronics," Nature Nanotechnology 5, 722–726 (2010). .
  4. F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi & D. Goldhaber-Gordon. "Composite Fermions and Broken Symmetries in Graphene," Under review.
  5. F. Amet, J. R. Williams, K. Watanabe, T. Taniguchi & D. Goldhaber-Gordon. "Selective Equilibration of Spin and Valley Polarized Quantum Hall Edge States," arXiv:1307.4408 (2013). .
  6. F. Amet, J. R. Williams, K. Watanabe, T. Taniguchi & D. Goldhaber-Gordon. "Insulating Behavior at the Neutrality Point in Dual-Gated Monolayer Graphene," Physical Review Letters 110, 216601 (2013)
  7. A. F. Young & P. Kim, "Quantum Interference and Klein Tunnelling in Graphene Heterojunctions," Nature Physics 5, 222-226(2009).