$$(2+1)$$ ( 2 + 1 ) -Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In $$(2+1)$$ -dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter $$k=1$$ and $$k\ne 1$$ ), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with $$k\ne 1$$ , we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.