  We present the model of an ultrasensitive mid-infrared (mid-IR) photodetector
operating in the mid-wavelength infrared (MWIR) and long-wavelength infrared
(LWIR) domains consisting of a hybrid heterostructure made of nanopatterned
graphene (NPG) and vanadium dioxide (VO$_2$) which exhibits a large
responsivity of $R\sim 10^4$ V/W, a detectivity exceeding $D^*\sim 10^{10}$ J,
and a sensitivity in terms of noise-equivalent power $\mathrm{NEP}\sim 100$
fW/$\sqrt{\rm Hz}$ close to room temperature by taking advantage of the phase
change of a thin VO$_2$ film. Our proposed photodetector can reach an
absorption of nearly 100\% in monolayer graphene due to localized surface
plasmons (LSPs) around the patterned circular holes. The geometry of the
nanopattern and an electrostatic gate potential can be used to tune the
absorption peak in the mid-IR regime between 3 and 12 $\mu$m. After the photon
absorption by the NPG sheet and the resulting phase change of VO$_2$ from
insulating to metallic phase the applied bias voltage $V_b$ triggers a current
through the VO$_2$ sheet, which can be detected electronically in about 1 ms,
shorter than the detection times of current VO$_2$ bolometers. Our envisioned
mid-IR photodetector reaches detectivities of cryogenically cooled HgCdTe
photodetectors and sensitivities larger than VO$_2$ microbolometers while
operating close to room temperature.
