Measurement of collective dynamical mass of Dirac fermions in graphene

Abstract

Individual electrons in graphene behave as massless quasiparticles1,2,3,4,5,6,7,8. Unexpectedly, it is inferred from plasmonic investigations9,10,11,12 that electrons in graphene must exhibit a non-zero mass when collectively excited. The inertial acceleration of the electron collective mass is essential to explain the behaviour of plasmons in this material, and may be directly measured by accelerating it with a time-varying voltage and quantifying the phase delay of the resulting current. This voltage–current phase relation would manifest as a kinetic inductance, representing the reluctance of the collective mass to accelerate. However, at optical (infrared) frequencies, phase measurements of current are generally difficult, and, at microwave frequencies, the inertial phase delay has been buried under electron scattering13,14,15. Therefore, to date, the collective mass in graphene has defied unequivocal measurement. Here, we directly and precisely measure the kinetic inductance, and therefore the collective mass, by combining device engineering that reduces electron scattering and sensitive microwave phase measurements. Specifically, the encapsulation of graphene between hexagonal boron nitride layers16, one-dimensional edge contacts17 and a proximate top gate configured as microwave ground18,19 together enable the inertial phase delay to be resolved from the electron scattering. Beside its fundamental importance, the kinetic inductance is found to be orders of magnitude larger than the magnetic inductance, which may be utilized to miniaturize radiofrequency integrated circuits. Moreover, its bias dependency heralds a solid-state voltage-controlled inductor to complement the prevalent voltage-controlled capacitor.

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Figure 1: Collective electrodynamics of graphene electrons.
Figure 2: Device description and d.c. measurements.
Figure 3: Microwave s-parameter measurements.
Figure 4: Extracted graphene kinetic inductance and collective electron mass.

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Acknowledgements

D.H. and H.Y. acknowledge support from the Air Force Office of Scientific Research (contract no. FA9550-13-1-0211), from the Office of Naval Research (contract no. N00014-13-1-0806), from the National Science Foundation (NSF; contract no. DMR-1231319), from the Samsung Advanced Institute of Technology and its Global Research Opportunity programme (contract no. A18960). P.K. acknowledges support from the Nano Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2012M3A7B4049966). J.H. and L.W. acknowledge support from the NSF (contract no. DMR-1124894) and the Office of Naval Research (award no. N000141310662). C.F. acknowledges support of the Columbia Optics and Quantum Electronics IGERT under NSF grant DGE-1069420. N.T. acknowledges support from the Netherlands Organisation for Scientific Research Device fabrication was performed in part at the Center for Nanoscale Systems at Harvard University.

Author information

H.Y., P.K. and D.H. conceived the project. K.W. and T.T. fabricated the h-BN. H.Y., C.F., L.W., N.T. and J.H. fabricated the stacked layers of h-BN, graphene and h-BN. H.Y. designed the device. H.Y. and C.F. fabricated the device. H.Y. performed the experiments. H.Y., P.K. and D.H. analysed the data. H.Y., P.K. and D.H. wrote the paper. All authors discussed the results and reviewed the manuscript.

Correspondence to Philip Kim or Donhee Ham.

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Yoon, H., Forsythe, C., Wang, L. et al. Measurement of collective dynamical mass of Dirac fermions in graphene. Nature Nanotech 9, 594–599 (2014). https://doi.org/10.1038/nnano.2014.112

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