  Semiconductor transistors are essential elements of electronic circuits as
they enable, for example, the isolation or amplification of voltage signals.
While conventional transistors are point-type (lumped-element) devices, it may
be highly interesting to realize a distributed transistor-type optical response
in a bulk material. Here, we show that low-symmetry two-dimensional metallic
systems may be the ideal solution to implement such a distributed-transistor
response. To this end, using the semiclassical Boltzmann equation approach, we
characterize the optical conductivity of a two-dimensional material under a
static electric bias. It is found that similar to the nonlinear Hall effect,
the electron transport depends on the Berry curvature dipole. Our analysis
reveals that the electro-optic effect modifies the optical conductivity of the
material, breaking the electromagnetic reciprocity and yielding a dynamical
response that imitates that of a transistor but in a distributed volume.
Furthermore, the effective conductivity tensor can be non-Hermitian, opening
the possibility of optical gain. To maximize the non-Hermitian response, we
explore the specific case of strained twisted bilayer graphene. Our analysis
reveals that the optical gain for incident light transmitted through the biased
system depends on the light polarization, and can be quite large, especially
for multilayer configurations.
