Fig. 2: Polaronic transport features at different temperatures.

a Comparison of the MSD based on polaron theory (magenta, open square) and formation of polaronic oscillations in the EQD–MSD (green, open circle). The dashed grey curve is the zero-EPC result (see main text). b MSD for a mode energy of 20 meV and g = 2.0 at two different temperatures. c Same as in b but with \(\hslash {\omega }_{{ph}}=10\,{{{{{\rm{meV}}}}}}\) and g = 2.83. d Extracted polaronic transfer integrals γ12 at 300 K as a function of the EPC coupling strength g2 (full circles) in comparison to analytical values of the renormalised, variational, and bare transfer integrals \({\widetilde{\varepsilon }}_{12}\) (green), \({\varepsilon }_{12}^{{{{{\mathrm{var}}}}}}\) (magenta, see Eq. (S46) in Supplementary Note 3), and ε12 (dashed grey line). The labels a–c inside the plot correspond to the values of γ12 extracted from the MSD shown in Fig. 2a–c. The inset in d zooms into the range of 0.6 ≤ g2 ≤ 4 for better comparison.