Field-induced Berry connection and planar Hall effect in tilted Weyl semimetals

We propose the linear and nonlinear planar Hall effect (PHE) in tilted Weyl semimetals in the presence of an in-plane magnetic and electric field, where the field-induced Berry connection (FBC) plays a key role. We show that the PHE is ascribed to the quantum metric, distinct from the well-known chiral anomaly-induced PHE arising from the Berry curvature. Using a tilting vector to describe the model, we demonstrate the constrains on the linear and nonlinear PHE by the tilting directions. The linear PHE is intrinsic that is determined by the topological properties of energy bands, whereas the nonlinear PHE is extrinsic. The predicted linear and nonlinear PHE are inherently different from others and may shed light on a deeper understanding on transport nature of the tilted Weyl semimetals.