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Register a new userAnharmonic phonon spectra of PbTe and SnTe in the self-consistent harmonic approximation
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At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depends on the approximation used for the exchange-correlation kernel in density functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the free energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe, we reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $Gamma$X direction. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high temperature Fm$overline{3}$m structure to the low temperature R3m one.
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Understanding the microscopic processes affecting the bulk thermal conductivity is crucial to develop more efficient thermoelectric materials. PbTe is currently one of the leading thermoelectric materials, largely thanks to its low thermal conductivity. However, the origin of this low thermal conductivity in a simple rocksalt structure has so far been elusive. Using a combination of inelastic neutron scattering measurements and first-principles computations of the phonons, we identify a strong anharmonic coupling between the ferroelectric transverse optic (TO) mode and the longitudinal acoustic (LA) modes in PbTe. This interaction extends over a large portion of reciprocal space, and directly affects the heat-carrying LA phonons. The LA-TO anharmonic coupling is likely to play a central role in explaining the low thermal conductivity of PbTe. The present results provide a microscopic picture of why many good thermoelectric materials are found near a lattice instability of the ferroelectric type.
The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation method. This technique rigorously describes the full thermodyamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the stochastic self-consistent harmonic approximation and its dynamical extension, making particular emphasis on the physical interpretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code.
Two-dimensional (2D) ZrS2 monolayer (ML) has emerged as a promising candidate for thermoelectric (TE) device applications due to its high TE figure of merit, which is mainly contributed by its inherently low lattice thermal conductivity. This work investigates the effect of the lattice anharmonicity driven by temperature-dependent phonon dispersions on thermal transport of ZrS2 ML. The calculations are based on the self-consistent phonon (SCP) theory to calculate the thermodynamic parameters along with the lattice thermal conductivity. The higher- order (quartic) force constants were extracted by using an efficient compressive sensing lattice dynamics technique, which estimates the necessary data based on the emerging machine learning program as an alternative of computationally expensive density functional theory calculations. Resolve of the degeneracy and hardening of the vibrational frequencies of low-energy optical modes were predicted upon including the quartic anharmonicity. As compared to the conventional Boltzmann transport equation (BTE) approach, the lattice thermal conductivity of the optimized ZrS2 ML unit cell within SCP + BTE approach is found to be significantly enhanced (e.g., by 21% at 300 K). This enhancement is due to the relatively lower value of phonon linewidth contributed by the anharmonic frequency renormalization included in the SCP theory. Mainly, the conventional BTE approach neglects the temperature dependence of the phonon frequencies due to the consideration of harmonic lattice dynamics and treats the normal process of three-phonon scattering incorrectly due to the use of quasi-particle lifetimes. These limitations are addressed in this work within the SCP + BTE approach, which signifies the validity and accuracy of this approach.
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We investigate the harmonic and anharmonic contributions to the phonon spectrum of lead telluride, and perform a complete characterization of how the anharmonic effects dominate the phonons in PbTe as temperature increases. This effect is the strongest factor in the favorable thermoelectric properties of PbTe: an optical-acoustic phonon band crossing reduces the speed of sound and the intrinsic thermal conductivity. We present the detailed temperature dependence of the dispersion relation and compare our calculated neutron scattering cross section with recent experimental measurements. We analyze the thermal resistivitys variation with temperature and clarify misconceptions about existing experimental literature. This quantitative prediction opens the way to phonon phase space engineering, to tailor the lifetimes of crucial heat carrying phonons.
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