Impact of Broken Inversion Symmetry on Molecular States in multi-Weyl fermions

We study inversion-symmetry (IS) breaking in impurity dimers coupled to topological multi-Weyl systems in the low-energy dispersion domain. In the IS-preserved multi-Weyl semimetal phase, Hubbard bands split into symmetric and antisymmetric molecular-like subbands. Breaking IS induces a transition to a multi-Weyl metal, lifting the degeneracy of the Weyl node and closing the pseudogap. This causes opposite energy shifts: valence-band symmetric (antisymmetric) subbands red- (blue-) shift, reversing in the conduction band until a degeneracy point. Beyond this threshold, symmetric bands flatten near band cutoffs, whereas antisymmetric bands form quasi-zero energy modes asymptotically approaching -- yet never crossing -- the Fermi level. Crucially, identical molecular symmetries maintain nondegeneracy even as energy separation vanishes with stronger IS breaking. Our results demonstrate symmetry-selective mechanisms for topological molecular states in multi-Weyl systems.