Electron-phonon coupling in copper intercalated Bi${}_2$Se${}_3$

We report charge and heat transport studies in copper-intercalated topological insulator Bi${}_2$Se${}_3$ hybrid devices. Measured conductivity shows impact of quantum corrections, electron-electron and electron-phonon interactions. Our shot noise measurements reveal that heat flux displays a crossover between $T^2$ and $T^4$ with the increase of temperature. The results can be explained by a model of inelastic electron scattering on disorder, increasing the role of transverse acoustic phonons in the electron-phonon coupling process.