Hyperbolic response and low-frequency ultra-flat plasmons in inhomogeneous charge-distributed transition-metal monohalides.

Plasmon, the collective oscillations of free electron gas in materials, determines the long-wavelength excitation spectrum and optical response, are pivotal in the realm of nanophotonics and optoelectronics. In this study, using the first-principles calculations, we systematically investigated the dielectric response and plasmon properties of bulk transition-metal monohalides MXs (M = Zr, Mo; X = Cl, F). Due to the strong electronic anisotropy, MXs exhibit a broadband type-II hyperbolic response and direction-dependent plasmon modes. Particularly, local field effect (LFE) driven by the charge distribution inhomogeneity, significantly modifies the optical response and excitation spectra in MX along the out-of-plane direction. Taking into account LFE, the energy dissipation along the out-of-plane direction is almost completely suppressed, and an ultra-flat and long-lived plasmon mode with a slow group velocity is introduced. This finding reveals the role of charge density in modifying the optical response and excitation behavior, shedding light on potential applications in plasmonics.