Plasmonic mass and Johnson–Nyquist noise

The fluctuation-dissipation theorem relates the thermal noise spectrum of a conductor to its linear response properties, with the ohmic resistance arising from the electron scattering being the most notable linear response property. But the linear response also includes the collective inertial acceleration of electrons, which should in principle influence the thermal noise spectrum as well. In practice, this effect would be largely masked by the Planck quantization for traditional conductors with short electron scattering times. But recent advances in nanotechnology have enabled the fabrication of conductors with greatly increased electron scattering times, with which the collective inertial effect can critically affect the thermal noise spectrum. In this paper we highlight this collective inertial effect-that is, the plasmonic effect-on the thermal noise spectrum under the framework of semiclassical electron dynamics, from both fundamental microscopic and practical modeling points of view. In graphene, where non-zero collective inertia arises from zero single-electron effective mass and where both electron and hole bands exist together, the thermal noise spectrum shows rich temperature and frequency dependencies, unseen in traditional conductors.