Charge Carrier Interaction with a Purely Electronic Collective Mode: Plasmarons and the Infrared Response of Elemental Bismuth

We present a detailed optical study of single-crystal bismuth using infrared reflectivity and ellipsometry. Large changes in the plasmon frequency are observed as a function of temperature due to charge transfer between hole and electron Fermi pockets. In the optical conductivity, an anomalous temperature dependent midinfrared absorption feature is observed. An extended Drude model analysis reveals that it can be connected to a sharp upturn in the scattering rate, the frequency of which exactly tracks the temperature dependent plasmon frequency. We interpret this absorption and increased scattering as direct optical evidence for a charge carrier interaction with a collective mode of purely electronic origin, here electron-plasmon scattering. The observation of a plasmaron as such is made possible only by the unique coincidence of various energy scales and exceptional properties of semimetal bismuth.

Figure 1

Single-crystal bismuth reflectivity vs wave number ($\omega /2\pi c$) for temperatures from 290 to 20 K. The pronounced shifting of the minimum in the range $180–350{\mathrm{cm}}^{-1}$ represents the position of the screened plasma frequency ${\omega }_p^{*}$.

Figure 2

(a) Optical conductivity derived from Kramer-Kronig analysis for selected temperatures. (b) The imaginary dielectric constant ${ϵ}_2$ over a much smaller energy range that emphasizes the remarkable prepeak structure. (c) Log-Log scale plot of ${\sigma }_1(\omega )$ for $T=290\mathrm{K}$, units are meV.

Figure 3

Frequency dependent scattering rate (a) and effective mass (b) normalized to their dc values, calculated from the optical data with Eq. (1) using ${\epsilon }_{\infty }$ smoothly varying between 134 (20 K) to 108 (290 K). An approximately frequency independent region is interrupted by a sharp onset in scattering and peak in the mass ratio.

Figure 4

(a) A parametric plot ${\omega }_{\tau }$ vs ${\omega }_p^{*}$ shows a slope of 1 supporting the hypothesis of an electron-plasmon interaction. (b) The 20 K loss function presents the main plasmon peak and a plasmaron peak appearing as a shoulder of the main one.