  Field-effect phototransistors were fabricated based on individual carbon
nanotubes (CNTs) sensitized by CH$_3$NH$_3$PbI$_3$ nanowires (MAPbI$_3$NW).
These devices represent light responsivities of R=7.7x10$^5$ A/W at
low-lighting conditions in the nWmm$^{-2}$ range, unprecedented among CNT-based
photo detectors. At high incident power (~1 mWmm$^{-2}$), light soaking results
in a negative photocurrent, the device turns insulating. We interpret the
phenomenon as a result of efficient electron-hole separation and charge
transfer of holes from the perovskite to the carbon nanotube, which improves
conductance by increasing the number of carriers, but leaves electrons behind.
At high illumination intensity the random electrostatic potential of these
quench the mobility in the nanotube. The single CNT device geometry allows the
local study of the MAPbI$_3$NW/CNT interface for metallic and semiconducting
CNTs separately. Infrared and Raman spectroscopy studies of
CNT-CH$_3$NH$_3$PbI$_3$ composites revealed that photo-doping takes place at
the interface.
