We present an ab initio study that identifies the main electron-phonon scattering channels in $n$-type PbTe. We develop an electronic transport model based on the Boltzmann transport equation within the transport relaxation time approximation, fully parametrized from first-principles calculations that accurately describe the dispersion of the electronic bands near the band gap. Our computed electronic mobility as a function of temperature and carrier concentration is in good agreement with experiments. We show that longitudinal optical phonon scattering dominates electronic transport in $n$-type PbTe, while acoustic phonon scattering is relatively weak. We find that scattering due to soft transverse optical phonons is by far the weakest scattering mechanism, due to the symmetry-forbidden scattering between the conduction band minima and the zone center soft modes. Soft phonons thus play the key role in the high thermoelectric figure of merit of $n$-type PbTe: they do not degrade its electronic transport properties although they strongly suppress the lattice thermal conductivity. Our results suggest that materials like PbTe with soft modes that are weakly coupled with the electronic states relevant for transport may be promising candidates for efficient thermoelectric materials.

We present a first-principles-based model of electron-phonon scattering mechanisms and thermoelectric transport at the $L$ and $\mathrm{\Sigma }$ valleys in $p$-type PbTe, accounting for their thermally induced shifts. Our calculated values of all thermoelectric transport parameters at room temperature are in very good agreement with experiments for a wide range of doping concentrations. Scattering due to longitudinal optical phonons is the main scattering mechanism in $p$-type PbTe, while scattering due to transverse optical modes is the weakest. The $L$ valleys contribute most to thermoelectric transport at 300 K due to the sizable energy difference between the $L$ and $\mathrm{\Sigma }$ valleys. We show that both scattering between the $L$ and $\mathrm{\Sigma }$ valleys and additional transport channels of the $\mathrm{\Sigma }$ valleys are beneficial for the overall thermoelectric performance of $p$-type PbTe at 300 K. Our findings thus support the idea that materials with high valley degeneracy may be good thermoelectrics.

We report a fully ab initio calculation of the temperature dependence of the electronic band structure of PbTe. We address two main features relevant for the thermoelectric figure of merit: the temperature variations of the direct gap and the difference in energies of the two topmost valence band maxima located at L and $\mathrm{\Sigma }$. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the nonadiabatic Allen-Heine-Cardona formalism within density functional perturbation theory and the local density approximation. We capture the increase of the direct gap with temperature in very good agreement with experiment. We also predict that the valence band maxima at L and $\mathrm{\Sigma }$ become aligned at $\sim 600–700\mathrm{K}$. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. The Fan-Migdal and Debye-Waller terms are of almost equal magnitude but have an opposite sign, and the delicate balance of these terms gives the correct band shifts. The electron-phonon induced renormalization of the direct gap is produced mostly by high-frequency optical phonons, while acoustic phonons are also responsible for the alignment of the valence band maxima at L and $\mathrm{\Sigma }$.

We present a first-principles method for the calculation of the temperature-dependent relaxation of symmetry-breaking atomic driving forces in photoexcited systems. We calculate the phonon-assisted decay of the photoexcited force on the low-symmetry $E_g$ mode following absorption of an ultrafast pulse in Bi, Sb, and As. The force decay lifetimes for Bi and Sb are of the order of 10 fs and in agreement with recent experiments, demonstrating that electron-phonon scattering is the primary mechanism relaxing the symmetry-breaking forces. Calculations for a range of absorbed photon energies suggest that larger amplitude, symmetry-breaking atomic motion may be induced by choosing a pump photon energy which maximizes the product of the initial $E_g$ force and its lifetime. The high-symmetry $A_{1g}$ force undergoes a partial decay to a nonzero constant on similar timescales, which has not yet been measured in experiments. The average imaginary part of the electron self-energy over the photoexcited carrier distribution provides a crude indication of the decay rate of symmetry-breaking forces.

Quantifying electron-phonon interactions for the surface states of topological materials can provide key insights into surface-state transport, topological superconductivity, and potentially how to manipulate the surface state using a structural degree of freedom. We perform time-resolved x-ray diffraction (XRD) and angle-resolved photoemission (ARPES) measurements on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, following the excitation of coherent $A_{1g}$ optical phonons. We extract and compare the deformation potentials coupling the surface electronic states to local $A_{1g}$-like displacements in these two materials using the experimentally determined atomic displacements from XRD and electron band shifts from ARPES. We find the coupling in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to be similar and in general in agreement with expectations from density functional theory. We establish a methodology that quantifies the mode-specific electron-phonon coupling experimentally, allowing detailed comparison to theory. Our results shed light on fundamental processes in topological insulators involving electron-phonon coupling.

The temperature renormalization of the bulk band structure of a topological crystalline insulator, SnTe, is calculated using first-principles methods. We explicitly include the effect of thermal-expansion-induced modification of electronic states and their band inversion on electron-phonon interaction. We show that the direct gap decreases with temperature, as both thermal expansion and electron-phonon interaction drive SnTe towards the phase transition to a topologically trivial phase as temperature increases. The band gap renormalization due to electron-phonon interaction exhibits a nonlinear dependence on temperature as the material approaches the phase transition, while the lifetimes of the conduction band states near the band edge show a nonmonotonic behavior with temperature. These effects should have important implications on bulk electronic and thermoelectric transport in SnTe and other topological insulators.