New type of quantum Hall effect in bilayer graphene

In the conventional integer quantum Hall effect occurring in two-dimensional electron systems the successive filling of Landau levels leads to an equidistant ladder of quantum Hall plateaus at integer filling N = 0, ±1, ±2, etc. with a quantized value s_xy = N e²/h.  Recently, a second type of quantum Hall effect was discovered in single-layer graphene where the relativistic dispersion of the electrons leads to quantum Hall plateaus at half-integer filling  ±1/2, ±3/2, etc [1].

Researchers from the Manchester Center of Mesoscience and Nanotechnology have now found a third type of quantum Hall effect in bilayer graphene. This work forms a collaboration with the Department of Physics at Lancaster University, the Institute for Microelectronics Technology in Chernogolovka and the Institute of Molecules and Materials of the Radboud University Nijmegen. Experiments in magnetic fields up to 33 T were performed at the High Field Magnet Laboratory in Nijmegen.

The figure summarizes the main experimental findings. In the left panel the Hall resistance r_xy and the resistivity r_xx of a graphene bilayer are plotted as a function of the magnetic field for a fixed electron concentration. The right panel shows the Hall conductivity as a function of the charge carrier concentration at fixed magnetic fields.  The bilayer is filled with electrons (positive n)or holes (negative n) using an external gate. From left to right hole-Landau levels are depopulated and electron-Landau levels are filled. Each Landau level is four-fold degenerate which leads to quantum Hall plateaus at hole-filling factors n = 4N =  -4, -8, etc. and electron filling factors n  = -4, -8, etc.

The novel type of quantum Hall effect shows up by a finite resistance and the absence of a N=0 quantum-Hall plateau at the transition from a hole system to an electron system. This implicates the existence of an eight-fold degenerate Landau level at zero energy containing both electrons and holes simultaneously.

This work was published in:

K.S. Novoselov, E. McCann, S.V. Morozov, V.I. Fal'ko, M.I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin and A.K. Geim,
Unconventional Quantum Hall Effect and Berry’s Phase of 2Pi in Bilayer Graphene,
Nature Physics 2, 177-180 (2006).

[1] K. Novosolov et al., Nature 438, 197 (2005).

Y. Zhang et al.,Nature 438, 201 (2005).