Anharmonic multiphonon origin of the valence plasmon in SrTi_1−xNb_xO₃

SrTiO₃ is a quantum paraelectric that, when doped with niobium or oxygen, exhibits superconductivity and a mid-IR optical response reminiscent of that in high temperature superconductors. One of the peculiar properties of doped SrTi_1-xNb_xO₃ is that its plasma frequency is highly temperature dependent, increasing by a factor of three when cooled from 300 K to 20 K. There is presently no understanding of what would lead to such a dramatic change. Here we present momentum-resolved electron energy loss spectroscopy (M-EELS) measurements of the IR response of SrTi_1-xNb_xO₃ (x=0, 0.002, 0.01, 0.014) at nonzero momentum, ranging from the Γ-point to the Brillouin zone boundary. We find that the IR feature previously identified as a plasmon is present in the insulator, SrTiO₃, and exhibits the same temperature dependence as in doped materials. We identify this feature as a multiphonon background arising from lattice anharmonicity. Nb doping increases the peak energy and total spectral weight in this background, and draws it to lower momentum where, at sufficient doping, it becomes visible in IR experiments. We conclude that the IR “plasmon” in doped SrTi_1-xNb_xO₃ is not a free-carrier mode, but a composite excitation with mixed electronic and multiphonon character that inherits its anomalous properties from the lattice anharmonicity of the insulator.