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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 Bi$_2$Te$_3$ and Bi$_2$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 Bi$_2$Te$_3$ and Bi$_2$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.

We investigate coupled electron-lattice dynamics in the topological insulator Bi2Te3 with time-resolved photoemission and time-resolved x-ray diffraction. It is well established that coherent phonons can be launched by optical excitation, but selection rules generally restrict these modes to zone-center wavevectors and Raman-active branches. We find that the topological surface state couples to additional modes, including a continuum of surface-projected bulk modes from both Raman- and infrared-branches, with possible contributions from surface-localized modes when they exist. Our calculations show that this surface vibrational spectrum occurs naturally as a consequence of the translational and inversion symmetries broken at the surface, without requiring the splitting-off of surface-localized phonon modes. The generality of this result suggests that coherent phonon spectra are useful by providing unique fingerprints for identifying surface states in more controversial materials. These effects may also expand the phase space for tailoring surface state wavefunctions via ultrafast optical excitation.

Experimental investigations of the phase transition in GeTe provide contradictory conclusions regarding the nature of the phase transition. Considering growing interest in technological applications of GeTe, settling these disputes is of great importance. To that end, we present a molecular dynamics study of the structural phase transition in GeTe using a machine-learned interatomic potential with ab-initio accuracy. First, we calculate the asymmetric shape of the radial distribution function of the nearest-neighbor bonds above the critical temperature, in agreement with previous studies. However, we show that this effect is not necessarily linked with the order-disorder phase transition and can occur as a result of large anharmonicity. Next, we study in detail the static and dynamic properties of the order parameter in the vicinity of the phase transition and find fingerprints of both order-disorder and displacive phase transition.

Achieving high valley degeneracy (i.e. "band convergence") in a material usually results in considerably enhanced thermoelectric properties. However, it is still unclear why this strategy of designing efficient thermoelectric materials is so successful, since the benefit of increased density of states may be severely degraded by intervalley scattering. Using first-principles calculations, we investigate these effects in $p$-type PbTe, where temperature induces alignment of the $L$ and $\Sigma$ valleys at $\sim$~620~K. We explicitly show that the thermoelectric power factor and figure of merit peak near the band convergence temperature. The figure of merit maximum is larger than those of the individual $L$ and $\Sigma$ valleys. Surprisingly, intervalley scattering does not considerably affect the figure of merit near the band convergence temperature and optimal doping conditions, although it reduces the power factor by almost a factor of 2. Our results suggest that band convergence will significantly increase the figure of merit if intervalley scattering is roughly proportional to the density of states and the lattice thermal conductivity is considerably lower than the electronic thermal conductivity, even if intervalley scattering is strong., Comment: 15 pages, 6 figures, Journal publication

The passivation of thin Bi(1 1 1) films with hydrogen and oxide capping layers is investigated from first principles. Considering termination-related changes of the crystal structure, we show how the bands and density of states are affected. In the context of the much discussed semimetal-to-semiconductor transition and the band topology of the bulk material, we consider the effects of confinement in the whole Brillouin zone and go beyond standard density functional theory by including many-body interactions via the G$_0$W$_0$ approximation. The conductivity of unterminated films is calculated via the Boltzmann transport equation using the simple constant relaxation time approximation and compared to experimental observations that have suggested a two-channel model.

The electronic band structure of Bi is calculated using state of the art electronic structure methods, including density functional theory and G$_0$W$_0$ quasiparticle approximations. The delicate ordering of states at the L point of the Brillouin zone, which determines the topological character of the electronic bands, is investigated in detail. The effect on the bands of strain, changing the structural parameters of the rhombohedral crystal structure, is shown to be important in determining this ordering and the resulting topological character.

IV-VI materials are some of the most efficient bulk thermoelectric materials due to their proximity to soft-mode phase transitions, which leads to low lattice thermal conductivity. It has been shown that the lattice thermal conductivity of PbTe can be considerably reduced by bringing PbTe closer to the phase transition e.g. via lattice expansion. However, the effect of soft phonon modes on the electronic thermoelectric properties of such system remains unknown. Using first principles calculations, we show that the soft zone center transverse optical phonons do not deteriorate the electronic thermoelectric properties of PbTe driven closer to the phase transition via lattice expansion due to external stress, and thus enhance the thermoelectric figure of merit. We find that the optical deformation potentials change very weakly as the proximity to the phase transition increases, but the population and scattering phase space of soft phonon modes increase. Nevertheless, scattering between electronic states near the band edge and soft optical phonons remains relatively weak even very near the phase transition., Comment: 8 pages, 7 figures

The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity $\kappa$. However, the $\kappa$ of GeTe increases at the ferroelectric phase transition near $700$ K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in $\kappa$ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Negative thermal expansion increases phonon group velocities, which counteracts enhanced anharmonicity of phonon modes and boosts $\kappa$ close to the phase transition in the rhombohedral phase. A drastic decrease in the anharmonic force constants in the cubic phase increases the phonon lifetimes and $\kappa$. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a novel method of calculating $\kappa$ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates $\kappa$ near the phase transition. Our findings elucidate the influence of structural phase transitions on $\kappa$ and provide guidance for design of better thermoelectric materials.

We present a first principles based model of electron-phonon scattering mechanisms and thermoelectric transport at the L and $\Sigma$ valleys in <200b>$p$-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 sizeable energy difference between the L and $\Sigma$ valleys. We show that both scattering between the L and $\Sigma$ valleys and additional transport channels of the $\Sigma$ 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., Comment: 16 pages, 6 figures

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 non-linear dependence on temperature as the material approaches the phase transition, while the lifetimes of the conduction band states near the band edge show a non-monotonic behavior with temperature. These effects should have important implications on bulk electronic and thermoelectric transport in SnTe and other topological insulators., Comment: 10 pages, 8 figures. Accepted for publication in Phys. Rev. B on June 8, 2020

Ferroelectric domain walls are boundaries between regions with different polarization orientations in a ferroelectric material. Using first principles calculations, we characterize all different types of domain walls forming on ($11\bar{1}$), ($111$) and ($1\bar{1}0$) crystallographic planes in thermoelectric GeTe. We find large structural distortions in the vicinity of most of these domain walls, which are driven by polarization variations. We show that such strong strain-order parameter coupling will considerably reduce the lattice thermal conductivity of GeTe samples containing domain walls with respect to single crystal. Our results thus suggest that domain engineering is a promising path for enhancing the thermoelectric figure of merit of GeTe.

We calculate the electronic structure of the narrow gap semiconductors PbTe, SnTe and GeTe in the cubic phase using density functional theory (DFT) and the $G_0W_0$ method. Within DFT, we show that the band ordering obtained with a conventional semilocal exchange-correlation approximation is correct for SnTe and GeTe but wrong for PbTe. The correct band ordering at the high-symmetry point L is recovered adding $G_0W_0$ quasiparticle corrections. However, one-shot $G_0W_0$ produces artifacts in the band structure due to the wrong orbital character of the DFT single-particle states at the band edges close to L. We show that in order to correct these artifacts it is enough to consider the off-diagonal elements of the $G_0W_0$ self-energy corresponding to these states. We also investigate the pressure dependence of the band gap for these materials and the possibility of a transition from a trivial to a non-trivial topology of the band structure. For PbTe, we predict the band crossover and topological transition to occur at around 4.8 GPa. For GeTe, we estimate the topological transition to occur at 1.9 GPa in the constrained cubic phase, a pressure lower than the one of the structural phase transition from rombohedral to cubic. SnTe is a crystalline topological insulator at ambient pressure, and the transition into a trivial topology would take place under a volume expansion of approximately $10\%$., Comment: 8 pages, 4 figures

We determine experimentally the excited-state interatomic forces in photoexcited bismuth. The forces are obtained by a constrained least-squares fit of the excited-state dispersion obtained by femtosecond time-resolved x-ray diffuse scattering to a fifteen-nearest neighbor Born-von Karman model. We find that the observed softening of the zone-center $A_{1g}$ optical mode and transverse acoustic modes with photoexcitation are primarily due to a weakening of three nearest neighbor forces along the bonding direction. This provides a more complete picture of what drives the partial reversal of the Peierls distortion previously observed in photoexcited bismuth., Comment: 6 pages, 3 figures, plus 3 pages, 3 figures of supplemental information

Unlike in many other semiconductors, the band gap of PbTe increases considerably with temperature. We compute the thermoelectric transport properties of n-type PbTe from first principles including the temperature variation of the electronic band structure. The calculated temperature dependence of the thermoelectric quantities of PbTe is in good agreement with previous experiments when the temperature changes of the band structure are accounted for. We also calculate the optimum band gap values which would maximize the thermoelectric figure of merit of n-type PbTe at various temperatures. We show that the actual gap values in PbTe closely follow the optimum ones between 300 K and 900 K, resulting in the high figure of merit. Our results indicate that an appreciable increase of the band gap with temperature in direct narrow-gap semiconductors is very beneficial for achieving high thermoelectric performance., Comment: 10 pages, 9 figures

The structure of thin terminated Bi(1 1 1) films of approximately 1 nm thickness is investigated from first principles. Our density functional theory calculations show that covalent bonds to the surface can change the orientation of the films completely. For thicker films, the effect is limited to the surface only. Based on these observations, we further present a simple model structure for the native oxide and chemically similar oxides, which form a protective capping layer, leaving the orientation of the films unchanged. The advantages of this energetically favorable layered termination are discussed in the context of the films' technological exploitation in nanoelectronic devices., Comment: final version

The major obstacle in the design of materials with low lattice thermal conductivity is the difficulty in efficiently scattering phonons across the entire frequency spectrum. Using first principles calculations, we show that driving PbTe materials to the brink of the ferroelectric phase transition could be a powerful strategy to solve this problem. We illustrate this concept by applying tensile [001] strain to PbTe and its alloys with another rock-salt IV-VI material, PbSe; and by alloying PbTe with a rhombohedral IV-VI material, GeTe. This induces extremely soft optical modes at the zone center, which increase anharmonic acoustic-optical coupling and decrease phonon lifetimes at all frequencies. We predict that PbTe, Pb(Se,Te) and (Pb,Ge)Te alloys driven close to the phase transition in the described manner will have considerably lower lattice thermal conductivity than that of PbTe (by a factor of 2-3). The proposed concept may open new opportunities for the development of more efficient thermoelectric materials., Comment: 9 pages, 3 figures

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 the prototypical group-V semimetals, Bi, Sb and As. The force decay lifetimes for Bi and Sb are of the order of $10$ fs and in good agreement with recent experiments, demonstrating that electron-phonon scattering is the dominant 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 maximises the product of the initial $E_g$ force and its lifetime. We also find that the high-symmetry $A_{1g}$ force undergoes a partial decay to a non-zero constant on similar timescales, which has not yet been measured in experiments. We observe that the imaginary part of the electron self-energy, averaged over the photoexcited carrier distribution, provides a reasonable estimate for the decay rate of symmetry-breaking forces., Comment: 7 pages, 9 figures

We present an \emph{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 report a fully {\it 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 $\Sigma$. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the non-adiabatic 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 $\Sigma$ become aligned at $\sim 600-700$ 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 $\Sigma$., Comment: 12 pages, 12 figures

We calculate the uniaxial and dilatation acoustic deformation potentials, $\Xi^{\text{L}}_{u}$ and $\Xi^{\text{L}}_{d}$, of the conduction band L valleys of PbTe from first principles, using the local density approximation (LDA) and hybrid functional (HSE03) exchange-correlation functionals. We find that the choice of a functional does not substantially affect the effective band masses and deformation potentials as long as a physically correct representation of the conduction band states near the band gap has been obtained. Fitting of the electron-phonon matrix elements obtained in density functional perturbation theory (DFPT) with the LDA excluding spin orbit interaction (SOI) gives $\Xi^{\text{L}}_u = 7.0$~eV and $\Xi^{\text{L}}_d = 0.4$~eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives $\Xi^{\text{L}}_u = 5.5$~eV and $\Xi^{\text{L}}_d = 0.8$~eV, in good agreement with the DFPT values. Our calculated values of $\Xi^{\text{L}}_u$ agree fairly well with experiment ($\sim 3-4.5$~eV). The computed values of $\Xi^{\text{L}}_d$ are substantially smaller than those obtained by fitting electronic transport measurements ($\sim 17-22$~eV), indicating that intravalley acoustic phonon scattering in PbTe is much weaker than previously thought., Comment: 13 pages, 4 figures

GeTe is a well-known ferroelectric and thermoelectric material that undergoes a structural phase transition from a rhombohedral to the rocksalt structure at $\sim 600-700$ K. We present a first principles approach to calculate the thermal expansion of GeTe in the rhombohedral phase up to the Curie temperature. We find the minimum of the Helmholtz free energy with respect to each structural parameter in a manner similar to the traditional Gr{\"u}neisen theory, and account for the temperature dependence of elastic constants. We obtain the temperature variation of the structural parameters of rhombohedral GeTe in very good agreement with experiments. In particular, we correctly reproduce a negative volumetric thermal expansion of GeTe near the phase transition. We show that the negative thermal expansion is induced by the coupling between acoustic and soft transverse optical phonons, which is also responsible for the low lattice thermal conductivity of GeTe.

We observe anharmonic decay of the photoexcited coherent A1g phonon in bismuth to points in the Brillouin zone where conservation of momentum and energy are satisfied for three-phonon scattering. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This results in energy transfer through resonant squeezing of the target modes. Using ultrafast diffuse x-ray scattering, we observe build up of coherent oscillations in the target modes driven by this parametric resonance over a wide range of the Brillouin zone. We compare the extracted anharmonic coupling constant to first principles calculations for a representative decay channel., Comment: 5 pages, 6 figures

A method is presented for the optimization of one-body and inhomogeneous two-body terms in correlated electronic wave functions of Jastrow-Slater type. The most general form of inhomogeneous correlation term which is compatible with crystal symmetry is used and the energy is minimized with respect to all parameters using a rapidly convergent iterative approach, based on Monte Carlo sampling of the energy and fitting energy fluctuations. The energy minimization is performed exactly within statistical sampling error for the energy derivatives and the resulting one- and two-body terms of the wave function are found to be well-determined. The largest calculations performed require the optimization of over 3000 parameters. The inhomogeneous two-electron correlation terms are calculated for diamond and rhombohedral graphite. The optimal terms in diamond are found to be approximately homogeneous and isotropic over all ranges of electron separation, but exhibit some inhomogeneity at short- and intermediate-range, whereas those in graphite are found to be homogeneous at short-range, but inhomogeneous and anisotropic at intermediate- and long-range electron separation., Comment: 23 pages, 15 figures, 1 table, REVTeX4, submitted to PRB

The effect of the electron-electron cusp on the convergence of configuration interaction (CI) wave functions is examined. By analogy with the pseudopotential approach for electron-ion interactions, an effective electron-electron interaction is developed which closely reproduces the scattering of the Coulomb interaction but is smooth and finite at zero electron-electron separation. The exact many-electron wave function for this smooth effective interaction has no cusp at zero electron-electron separation. We perform CI and quantum Monte Carlo calculations for He and Be atoms, both with the Coulomb electron-electron interaction and with the smooth effective electron-electron interaction. We find that convergence of the CI expansion of the wave function for the smooth electron-electron interaction is not significantly improved compared with that for the divergent Coulomb interaction for energy differences on the order of 1 mHartree. This shows that, contrary to popular belief, description of the electron-electron cusp is not a limiting factor, to within chemical accuracy, for CI calculations., Comment: 11 pages, 6 figures, 3 tables, LaTeX209, submitted to The Journal of Chemical Physics

A quantum Monte Carlo method of determining Jastrow-Slater wave functions for which the energy is stationary with respect to variations in the single-particle orbitals is presented. A potential is determined by a least-squares fitting of fluctuations in the energy with a linear combination of one-body operators. This potential is used in a self-consistent scheme for the orbitals whose solution ensures that the energy of the correlated wave function is stationary with respect to variations in the orbitals. The method is feasible for atoms, molecules, and solids and is demonstrated for the carbon and neon atoms., Comment: 4 pages, Revtex, 3 postscript figures