High-resolution tunnelling spectroscopy of a graphene quartet

Abstract

Electrons in a single sheet of graphene behave quite differently from those in traditional two-dimensional electron systems. Like massless relativistic particles, they have linear dispersion and chiral eigenstates. Furthermore, two sets of electrons centred at different points in reciprocal space (‘valleys’) have this dispersion, giving rise to valley degeneracy. The symmetry between valleys, together with spin symmetry, leads to a fourfold quartet degeneracy of the Landau levels, observed as peaks in the density of states produced by an applied magnetic field. Recent electron transport measurements have observed the lifting of the fourfold degeneracy in very large applied magnetic fields, separating the quartet into integer1,2,3,4 and, more recently, fractional5,6 levels. The exact nature of the broken-symmetry states that form within the Landau levels and lift these degeneracies is unclear at present and is a topic of intense theoretical debate7,8,9,10,11. Here we study the detailed features of the four quantum states that make up a degenerate graphene Landau level. We use high-resolution scanning tunnelling spectroscopy at temperatures as low as 10 mK in an applied magnetic field to study the top layer of multilayer epitaxial graphene. When the Fermi level lies inside the fourfold Landau manifold, significant electron correlation effects result in an enhanced valley splitting for even filling factors, and an enhanced electron spin splitting for odd filling factors. Most unexpectedly, we observe states with Landau level filling factors of 7/2, 9/2 and 11/2, suggestive of new many-body states in graphene.

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Figure 1: Landau level spectroscopy of epitaxial graphene on SiC.
Figure 2: Landau levels of epitaxial graphene on SiC as a function of magnetic field.
Figure 3: Electron density and filling-factor variation as a function of magnetic field in epitaxial graphene.
Figure 4: High-resolution Landau level spectroscopy of the fourfold states that make up the N = 1 Landau level.
Figure 5: Energies in the epitaxial graphene N = 1 Landau level.

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Acknowledgements

We thank N. Zhitenev for discussions, S. Blankenship, A. Band and F. Hess for their technical contributions to the construction of the millikelvin scanning probe microscopy system, V. Shvarts for his advice on cryogenics and U. D. Ham for instructions on making silver probe tips. This work was supported in part by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF- 2006-214-C00022), the NSF (DMR-0820382 [MRSEC], DMR-0804908, DMR-0606489), the Welch Foundation and the Semiconductor Research Corporation (NRI-INDEX programme).

Author information

Y.J.S, A.F.O, Y.K. and J.A.S designed and constructed the millikelvin scanning probe microscopy system. The graphene scanning tunnelling microscopy/scanning tunnelling spectroscopy measurements were performed by Y.J.S, A.F.O and J.A.S. The graphene sample was grown by Y.H and W.A.d.H., and the surface was prepared and characterized by D.B.T and P.N.F. A theoretical analysis of the epitaxial graphene multilayer system was performed by H.M., S.A., M.D.S and A.H.M.

Correspondence to Joseph A. Stroscio.

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Song, Y., Otte, A., Kuk, Y. et al. High-resolution tunnelling spectroscopy of a graphene quartet. Nature 467, 185–189 (2010). https://doi.org/10.1038/nature09330

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