Paper detail

Revisiting longitudinal optical modes in materials with plasmon and plasmon-like absorptions -- SrTiO$_3$ and $β$-Ga$_2$O$_3$

We investigate exemplary the longitudinal optical (LO) mode order in compounds with a plasmon or plasmon-like phonon mode and additional phonon modes. When the oscillator strength of the plasmon or plasmon-like mode is gradually increased, a reordering of the modes takes place. Since it is not possible in crystals with orthorhombic or higher symmetry that a LO mode crosses a transverse optical (TO) mode's position, this reordering takes place via mode hybridization. During this mode hybridization, the plasmon or plasmon-like LO mode gradually becomes the originally higher situated LO mode while the latter morphs into the former. As a consequence, an inner (LO-TO) and an outer (TO-LO) mode pair is formed. This process continues until the LO oscillator strength is so high that all other phonons are inverted and form LO-TO pairs within the outer TO-LO mode pair of the plasmon or plasmon-like mode. These insights can be readily transferred to other semiconductors or many mode materials with reststrahlen bands and allow simple mode assignments. These mode assignments will help to understand the nature of surface modes of structured layers of these materials for application of surface plasmon polariton and surface phonon polaritons based metamaterials.