Anomalous Acoustic Plasmons in Two-Dimensional Over-Tilted Dirac Bands

The over-tilting of Dirac cones has led to various fascinating quantum phenomena. In this study, we demonstrate that the distinct geometry of two-dimensional type-II Dirac cones dictates the emergence of anomalous acoustic plasmons (AAPs) that deviate from that of the conventional \sqrtq plasmon. The first AAP originates from the strong hybridization of two pockets with large velocity anisotropy at one Dirac point. The second AAP is attributed to the significant enhancement in band correlation around the open Fermi surface. These plasmons exhibit valley-dependent chirality along the tilting direction caused by chiral electron dispersion. Meanwhile, we discuss the tunability of plasmon dispersion and lifetime by tuning the gap and dielectric substrate. Our work provides a promising framework to generate novel plasmons in Dirac materials.