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Dimensional reduction, quantum Hall effect and layer parity in graphite films


The quantum Hall effect (QHE) originates from discrete Landau levels forming in a two-dimensional electron system in a magnetic field1. In three dimensions, the QHE is forbidden because the third dimension spreads Landau levels into overlapping bands, destroying the quantization. Here we report the QHE in graphite crystals that are up to hundreds of atomic layers thick, a thickness at which graphite was believed to behave as a normal, bulk semimetal2. We attribute this observation to a dimensional reduction of electron dynamics in high magnetic fields, such that the electron spectrum remains continuous only in the field direction, and only the last two quasi-one-dimensional Landau bands cross the Fermi level3,4. Under these conditions, the formation of standing waves in sufficiently thin graphite films leads to a discrete spectrum allowing the QHE. Despite the large thickness, we observe differences between crystals with even and odd numbers of graphene layers. Films with odd layer numbers show reduced QHE gaps, as compared to films of similar thicknesses but with even numbers because the latter retain the inversion symmetry characteristic of bilayer graphene5,6. We also observe clear signatures of electron–electron interactions including the fractional QHE below 0.5 K.

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Fig. 1: QHE in 3D graphite.
Fig. 2: Landau levels in thin graphite films.
Fig. 3: Thickness and layer-parity dependence of the 2.5D QHE.
Fig. 4: Hierarchy of QHE gaps and level crossings in the UQR.

Data availability

All relevant data are available from the corresponding authors on reasonable request.


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This work was supported by the EU Graphene Flagship Program, the European Research Council, the Royal Society and the Engineering and Physical Sciences Research Council. J.Y. and A.M. acknowledges the support of EPSRC Early Career Fellowship EP/N007131/1.

Author information




A.M., A.K.G. and J.Y. conceived the experiments. J.Y., I.L., S.O. and B.P. conducted the transport measurements. J.Y., Y.C., S.H., Y.Y. and S.-K.S. prepared the samples. A.M. and J.Y. performed data analysis. S.S. and V.F. developed theory and S.S., V.F. and F.G. interpreted the data and performed the tight-binding simulations. T.T. and K.W. provided hBN crystals. A.M. wrote the manuscript with input from V.F., A.K.G., J.Y., S.S., K.S.N and F.G.

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Correspondence to A. K. Geim or Vladimir Fal’ko or Artem Mishchenko.

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Yin, J., Slizovskiy, S., Cao, Y. et al. Dimensional reduction, quantum Hall effect and layer parity in graphite films. Nat. Phys. 15, 437–442 (2019).

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