Connecting electron and phonon spectroscopy data to consistently determine quasiparticle-phonon coupling on the surface of topological insulators

Photoemission and phonon spectroscopies have yielded widely varying estimates of the electron-phonon coupling parameter $\lambda$ on the surfaces of topological insulators, even for a particular material and technique. We connect the results of these experiments by determining the Dirac fermion quasiparticle spectral function using information from measured spectra of a strongly interacting, low-lying optical surface phonon band. The manifest spectral features resulting from the coupling are found to vary on energy scales $<$1 meV and are distinct from those traditionally observed in the case of acoustic phonons in metals. We explore different means of determining $\lambda$ from the electron perspective and identify definitions that yield values consistent with phonon spectroscopy.

Figure 1

Imaginary and real parts of the DFQ self-energy for ${\text{Bi}}_2$${\text{Te}}_3$ at $T=0.01E_F$ (a, b) and $T=0.04E_F$ (c, d). The dashed red lines indicate a linear fit about $\omega =0$ meV, whose slope is used to determine $\lambda$ via Eq. (8).

Figure 2

Calculated spectral function and momentum distribution curve FWHM $\Delta k\left(\omega \right)$ for ${\text{Bi}}_2$${\text{Te}}_3$ at $T=0.01E_F$ (a, b) and $T=0.04E_F$ (c, d). The white space in panels (b, d) is used to indicate $\Delta k\left(\omega \right)$.

Figure 3

The temperature dependence of the electron-phonon parameter. After initially increasing in the region $0\le \frac{T}{E_F}\le 0.01$, the value of $\lambda$ begins to fall with temperature.

Figure 4

(a) The density of states per unit area $\mathcal{N}\left(\omega \right)$ obtained from the calculated spectral function at $T_1$. The dashed red line depicts the noninteracting density of states. (b) $\mathcal{N}\left(\omega \right)$ multiplied by the Fermi function for comparison with EDCs measured by ARPES. (c) $d\mathcal{N}/d\omega$ for comparison with $d^{2}I$/$d{V}^2$ STS spectra.