title: Measurement of collective dynamical mass of Dirac fermions in graphene.
abstract: Individual electrons in graphene behave as massless quasiparticles. Unexpectedly, it is inferred from plasmonic investigations 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 scattering. 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 layers, one-dimensional edge contacts and a proximate top gate configured as microwave ground 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.
authors: School of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge, Massachusetts 02138, USA.
authors: Hosang
authors: H
authors: Yoon
authors: Department of Physics, Columbia University, New York, New York 10027, USA.
authors: Carlos
authors: C
authors: Forsythe
authors: Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA.
authors: Lei
authors: L
authors: Wang
authors: Department of Physics, Columbia University, New York, New York 10027, USA.
authors: Nikolaos
authors: N
authors: Tombros
authors: National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan.
authors: Kenji
authors: K
authors: Watanabe
authors: National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan.
authors: Takashi
authors: T
authors: Taniguchi
authors: Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA.
authors: James
authors: J
authors: Hone
authors: Department of Physics, Columbia University, New York, New York 10027, USA.
authors: Philip
authors: P
authors: Kim
authors: School of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge, Massachusetts 02138, USA.
authors: Donhee
authors: D
authors: Ham