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Unidirectional valley-contrasting photo-current in strained transition metal dichalcogenide monolayers

We examine the full static non-linear optical response of uniaxially strained transition metal dichalcogenide monolayers doped with a finite carrier density in the conduction band, in the presence of disorder. We find that the customary shift current is suppressed, yet we identify a strong, valley-dependent non-reciprocal response, which we term a \textit{unidirectional valley-contrasting photo-current} (UVCP). This DC current originates from the combined effect of strain and Kramers symmetry breaking by trigonal warping, while the contributions due to individual valleys can be separated by introducing an energy offset between them by means of a magnetization. This latter fact enables one to monitor inter-valley transitions. The UVCP is proportional to the mobility and is enhanced by the excitonic Coulomb interaction and inter-valley scattering, as well as by a top gate bias. We discuss detection strategies in state-of-the-art experiments.