  Photodetector based on two-dimensional (2D) materials is an ongoing quest in
optoelectronics. These 2D photodetectors are generally efficient at low
illuminating power but suffer severe recombination processes at high power,
which results in the sublinear power dependence of photoresponse and lower
optoelectronic efficiency. The desirable superlinear photocurrent is mostly
achieved by sophisticated 2D heterostructures or device arrays, while 2D
materials rarely show intrinsic superlinear photoresponse. Here, we report the
giant superlinear power dependence of photocurrent based on multi-layer
Ta$_2$NiS$_5$. While the fabricated photodetector exhibits good sensitivity
($3.1 mS/W$ per square) and fast photoresponse ($31 \mu$$s$), the bias-,
polarization-, and spatial-resolved measurements point to an intrinsic
photoconductive mechanism. By increasing the incident power density from $1.5
\mu$W/$\mu$$m^{2}$ to $200 \mu$W/$\mu$$m^{2}$, the photocurrent power
dependence varies from sublinear to superlinear. At higher illuminating
conditions, a prominent superlinearity is observed with a giant power exponent
of $\gamma=1.5$. The unusual photoresponse can be explained by a
two-recombination-center model where the distinct density of states of the
recombination centers effectively closes all recombination channels. The
fabricated photodetector is integrated into camera for taking photos with
enhanced contrast due to the superlinearity. Our work provides an effective
route to enable higher optoelectronic efficiency at extreme conditions.
