We present flexible photodetectors (PDs) for visible wavelengths fabricated by stacking centimetre-scale chemical vapour deposited (CVD) single layer graphene (SLG) and single layer CVD MoS2, both wet transferred onto a flexible polyethylene terephthalate substrate. The operation mechanism relies on injection of photoexcited electrons from MoS2 to the SLG channel. The external responsivity is 45.5A/W and the internal 570A/W at 642nm. This is at least two orders of magnitude higher than bulk-semiconductor flexible membranes and other flexible PDs based on graphene and layered materials. The photoconductive gain is up to 4x10^5. The photocurrent is in the 0.1-100 uA range. The devices are semi-transparent, with just 8% absorption at 642nm and work stably upon bending to a curvature of 6cm. These capabilities and the low voltage operation (<1V) make them attractive for wearable applications.
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