Orbital-dominated intrinsic nonlinear planar Hall response and its application in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>CuTlSe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

The intrinsic nonlinear planar Hall effect (NPHE) proposed in recent studies offers a new way to probe inherent band geometric properties in a large class of nonmagnetic materials. However, the search of material platforms with a large response remains a problem. Here, we show that the orbital contribution to NPHE, which was often neglected in previous studies, can be significantly amplified by topological band crossings and overwhelm the spin contribution. This suggests a general approach to achieve a large orbital-dominated NPHE response in topological metals. As an example, we show that the enhancement for a Weyl model, and find the orbital NPHE response coefficient exhibits a characteristic resonance-like lineshape around the Weyl-point energy. Using first-principles calculations, we confirm these features for a concrete material example ${\mathrm{CuTlSe}}_{2}$. Previous studies have reported two different topological states of ${\mathrm{CuTlSe}}_{2}$. We clarify this difference originates from two slightly different lattice structures. We show that the NPHE 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 the importance of orbital mechanism in NPHE, demonstrates a close connection between orbital NPHE and topological band features, and suggests ${\mathrm{CuTlSe}}_{2}$ as a suitable platform for realizing enhanced NPHE.