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We consider the current induced in a quantum wire by external electromagnetic radiation. The photocurrent is caused by the interplay of spin-orbit interaction (Rashba and Dresselhaus terms) and an external in-plane magnetic field. We calculate this current using a Wigner functions approach, taking into account radiation-induced transitions between transverse subbands. The magnitude and the direction of the current depends on the Dresselhaus and Rashba constants, strength of magnetic field, radiation frequency, and intensity. The current can be controlled by changing some of these parameters.

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