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In crystalline materials, low lattice thermal conductivity is often associated with strong anharmonicity, which can cause significant deviations from the expected Lorentzian lineshape of phonon spectral functions. These deviations, occurring in an overdamped regime, raise questions about the applicability of the Boltzmann transport equation. Furthermore, strong anharmonicity can trigger structural phase transitions with temperature, which cannot be adequately described by the standard harmonic approximation. To address these challenges, we propose a novel approach for computing the lattice thermal conductivity. Our method combines the Green-Kubo linear response theory with the stochastic self-consistent harmonic approximation. The latter allows us to describe the temperature-dependent evolution of the crystal structure, including first- and second-order phase transitions, as well as the vibrational properties in highly anharmonic materials. The Green-Kubo method considers the entire lineshapes of phonon spectral functions in the calculation of the lattice thermal conductivity, thus eliminating the questionable use of phonon lifetimes in the overdamped regime, as well as naturally including coherent transport effects. Additionally, we extend our theory to model complex dynamical lattice thermal conductivity, enhancing our understanding of time-dependent thermoreflectance experiments. As a practical application, we employ this approach to calculate the lattice thermal conductivity of CsPbBr$_3$, a complex crystal known for its anomalous thermal transport behavior with a complex phase diagram. Our method is able to determine the thermal conductivity across different phases in good agreement with experiments.

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

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.

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

We investigated how dimensionality affects heat transport in Si-Ge superlattices by computing the thermal conductivity of planar superlattices and arrays of Ge nanowires and nanodots embedded in Si. We studied superlattices with $\sim$10 nm periods using a fully atomistic Monte Carlo solution of the Boltzmann transport equation in the relaxation time approximation. We found that for periods larger than 4 nm, the room temperature cross-plane conductivity of planar superlattices with equally thick Si and Ge layers is larger than that of their nanowire and dot counterparts of similar sizes (up to 100\%), while the trend is reversed below 4 nm., Comment: 11 pages, 4 figures

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.

Carbon atoms can form structures in one, two, and three dimensions due to its unique chemical versatility. In terms of thermal conductivity, carbon polymorphs cover a wide range from very low values with amorphous carbon to very high values with diamond, carbon nanotubes and graphene. Schwarzites are a class of three-dimensional fully covalent sp$^2$-bonded carbon polymorphs, with the same local chemical environment as graphene and carbon nanotubes, but negative Gaussian curvature. We calculate the thermal conductivity of a (10,0) carbon nanotube, graphene, and two schwarzites with different curvature, by molecular dynamics simulations based on the Tersoff empirical potential. We find that schwarzites present a thermal conductivity two orders of magnitude smaller than nanotubes and graphene. The reason for such large difference is explained by anharmonic lattice dynamics calculations, which show that phonon group velocities and mean free paths are much smaller in schwarzites than in nanotubes and graphene. Their reduced thermal conductivity, in addition to tunable electronic properties, indicate that schwarzites could pave the way towards all-carbon thermoelectric technology with high conversion efficiency.

A density matrix theory of electron transport and optical gain in quantum cascade lasers in an external magnetic field is formulated. Starting from the general quantum kinetic treatment, we describe the intra- and inter-period electron dynamics at the non-Markovian, Markovian and Boltzmann approximation levels. Interactions of electrons with longitudinal optical phonons and classical light field are included in the present description. The non-Markovian calculation for a prototype structure reveals significantly different gain spectra in terms of linewidth and additional polaronic features in comparison to the Markovian and Boltzmann ones. Despite strongly opposed interpretations of the origin of the transport processes in the non-Markovian or Markovian and the Boltzmann approaches, they yield comparable values of the current densities., Comment: 27 pages, 12 figures, to be submitted to Physical Review B