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Long carrier lifetimes and diffusion lengths form the basis for thesuccessful application of the organic-inorganic perovskite(CH$_3$NH$_3$)PbI$_3$ in solar cells and lasers. The mechanism behind the longcarrier lifetimes is still not completely understood. Spin-split bands and aresulting indirect band gap have been proposed by theory. Using near band-gapleft-handed and right-handed circularly polarized light we induce photocurrentsof opposite directions in a single-crystal (CH$_3$NH$_3$)PbI$_3$ device at lowtemperature ($4~\mathrm{K}$). The phenomenom is known as the circularphotogalvanic effect and gives direct evidence for phototransport in spin-splitbands. Simultaneous photoluminecence measurements show that the onset of thephotocurrent is below the optical band gap. The results prove that an indirectband gap exists in (CH$_3$NH$_3$)PbI$_3$ with broken inversion symmetry as aresult of spin-splittings in the band structure. This information is essentialfor understanding the photophysical properties of organic-inorganic perovskitesand finding lead-free alternatives. Furthermore, the optically driven spincurrents in (CH$_3$NH$_3$)PbI$_3$ make it a candidate material for spintronicsapplications.

Spin-split bands cause the indirect band gap of (CH$_3$NH$_3$)PbI$_3$: Experimental evidence from circular photogalvanic effect