Fig. 3: Inversion symmetry breaking in MAPbBr₃ evidenced by the two-photon bulk photovoltaic effect.

a Schematic of the strain gradient confined to the domain wall and the resulting gradients of polarization \({{{\bf{P}}}}\) and potential \(\phi\) induced by the flexoelectric effect. b Schematic of the photocurrent measurement setup. The sample can be moved relative to the beam to measure the current flowing in vertical or horizontal directions for each position of the excitation spot. c Schematic of the photoexcited carrier separation caused by internal electric fields. The dashed white line marks the part of the sample where the current measurements were performed. d Energy diagram of the two-photon absorption process. e Spatial distribution of the photocurrent measured in the vertical and horizontal directions. Each point represents the current measured when the sample is excited at the corresponding location. The scale bars are 500 µm. f Schematic of electrostatic potential distribution \(\phi (x)\) in a sample with domain-wall flexoelectricity. The dashed lines represent domain walls. g Typical time-resolved photocurrent transient acquired in a horizontal direction. The top inset illustrates the temporal evolution of polarization \({{{\bf{P}}}}\) and current \(I\) following optical excitation. The bottom inset shows schematic microscopic pictures of the charge separation and recombination phases of the photocurrent generation.