We demonstrate that the injection of the ballistic electrons into the two-dimensional electron plasma in lateral n+-i-n-n+ graphene field-effect transistors (GFETs) might lead to a substantial Coulomb drag of the quasiequilibrium electrons due the violation of the Galilean and Lorentz invariance in the systems with a linear electron dispersion. This effect can result in S-shaped current-voltage (I-V) characteristics. The resulting negative differential conductivity enables the hysteresis effects and current filamentation that can be used for the implementation of voltage-switching devices. Due to a strong nonlinearity of the I-V characteristics, the GFETs can be used for an effective frequency multiplication and detection of terahertz radiation.
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