  The electron gas hosted in a two-dimensional solid-state matrix, such as a
quantum well or a two-dimensional van der Waals heterostructure, supports the
propagation of plasma waves. Nonlinear interactions between plasma waves, due
to charge conservation and current convection, generate a constant density
gradient which can be detected as a dc potential signal at the boundaries of
the system. This phenomenon is at the heart of a plasma-wave photodetection
scheme which was first introduced by Dyakonov and Shur for electronic systems
with a parabolic dispersion and then extended to the massless Dirac fermions in
graphene. In this work, we develop the theory of plasma-wave photodetection in
bilayer graphene, which has the peculiarity that the dispersion relation
depends locally and dynamically on the intensity of the plasma wave. In our
analysis, we show how quantum capacitance effects, arising from the local
fluctuations of the electronic dispersion, modify the intensity of the
photodetection signal. An external electrical bias, e.g. induced by top and
bottom gates, can be used to control the strength of the quantum capacitance
corrections, and thus the photoresponse.
