Orbital enhanced intrinsic nonlinear planar Hall effect for probing topological phase transition in CuTlSe$_{2}$

The intrinsic nonlinear planar Hall effect proposed in recent studies offers a new way to probe intrinsic band geometric properties in a large class of materials. However, the search of material platforms with a large response remains a problem. Here, we suggest that topological Weyl semimetals can host enhanced intrinsic nonlinear planar Hall effect. From a model study, we show that the enhancement is mainly from the orbital contribution, and the response coefficient exhibits a characteristic resonance-like lineshape around the Weyl-point energy. Using first-principles calculations, we confirm these features for the concrete material CuTlSe$_{2}$. Previous studies have reported two different topological states of CuTlSe$_{2}$. We find this difference originates from two slightly different structures with different lattice parameters. We show that the nonlinear planar Hall response is much stronger in the Weyl semimetal state than in the topological insulator state, and the large response is indeed dominated by orbital contribution amplified by Weyl points. Our work reveals a close connection between nonlinear orbital responses and topological band features, and suggests CuTlSe$_{2}$ as a suitable platform for realizing enhanced nonlinear planar Hall effect.