We examine anharmonic contributions to the optical phonon modes in bulk $T_d$-MoTe$_2$ through temperature-dependent Raman spectroscopy. At temperatures ranging from 100 K to 200 K, we find that all modes redshift linearly with temperature in agreement with the Grüneisen model. However, below 100 K we observe nonlinear temperature-dependent frequency shifts in some modes. We demonstrate that this anharmonic behavior is consistent with the decay of an optical phonon into multiple acoustic phonons. Furthermore, the highest frequency Raman modes show large changes in intensity and linewidth near $T\approx 250$ K that correlate well with the $T_d \to 1T^\prime$ structural phase transition. These results suggest that phonon-phonon interactions can dominate anharmonic contributions at low temperatures in bulk $T_d$-MoTe$_2$, an experimental regime that is currently receiving attention in efforts to understand Weyl semimetals.
Transition metal dichalcogenides (TMDs) are layered materials which show excellent potential for nanoelectronic and optoelectronic applications. However, as many of the exciting features of these materials are controlled by the anharmonic effects, a proper understanding of the phonon properties and anharmonicity associated with these materials is essential for the proposed applications to be realized. We present here a comprehensive study on the phonon properties of two different TMDs; viz., MoS2 and MoTe2, as a function of temperature, laser excitations, and polarization, as well as flake-thi…
We report on the coherent phonon spectroscopy of polymorphic $\mathrm{MoTe_2}$ single crystals using a femtosecond-pulsed laser to investigate the relationship between structural phase transitions and photo-thermal effects induced by high-density laser excitation. Even when a femtosecond pulsed laser was used, which generally induces fewer heat accumulation effects than the case for a CW laser, tellurium segregation was observed in coherent phonon spectra with increasing excitation density, while no structural phase transition among polymorphs of $\mathrm{MoTe_2}$ was observed. The use of high…
Two-dimensional (2D) van der Waals (vdW) materials have extraordinary thermal properties due to the effect of quantum confinement, making them promising for thermoelectric energy conversion and thermal management in microelectronic devices. In this review, the mechanism of phonon anharmonicity originating from three- and four-phonon interactions is derived. The phonon anharmonicity of 2D vdW materials, involving the Grüneisen parameter, phonon lifetime, and thermal conductivity, is summarized and derived in detail. The size-dependent thermal conductivity of representative 2D vdW materials is d…
$N$-layer transition metal dichalcogenides provide a unique platform to investigate the evolution of the physical properties between the bulk (three dimensional) and monolayer (quasi two-dimensional) limits. Here, using high-resolution micro-Raman spectroscopy, we report a unified experimental description of the $Γ$-point optical phonons in $N$-layer $2H$-molybdenum ditelluride (MoTe$_2$). We observe a series of $N$-dependent low-frequency interlayer shear and breathing modes (below $40~\rm cm^{-1}$, denoted LSM and LBM) and well-defined Davydov splittings of the mid-frequency modes (in the ra…
Anharmonic lattice vibrations govern the thermal dynamics in materials and present how the atoms interact and how they conduct heat. An indepth understanding of the microscopic mechanism of phonon anharmonicity in condensed systems is critical for developing better functional and energy materials. In recent years, a variety of novel behaviors in condense matters are driven by phonon anharmonic effects in some way or another, such as soft mode phase transition, negative thermal expansion, multiferroicity, ultralow thermal conductivity or high thermal resistance, and high-temperature superconduc…
An approach to compute the anharmonic peaks of the phonon dispersion curves through the ab initio calculated Hellmann-Feynman forces from a series of supercells with realistic atomic displacements of all atoms, which correspond to a given temperature, is reported. Obtained phonon dispersion bands are able to represent the positions and shapes of the anharmonic peaks. As example, the approach to cubic PbTe and perovskite MgSiO3 crystals is applied.
Opposite impact of thermal expansion and phonon anharmonicity on the phonon-limited resistivity of elemental metals from first principles
European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Université catholique de Louvain（欧洲理论光谱设施，凝聚态物质与纳米科学研究所，天主教鲁汶大学）；Scientific Computing Department, Science and Technology Facilities Council, UK Research and Innovation, Daresbury Laboratory（科学与工程设施理事会英国研究与创新达尔斯伯里实验室科学计算部）；Département de Physique et Institut Courtois, Université de Montréal（蒙特利尔大学物理系与库瓦托瓦研究所）；Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science（魏茨曼科学研究所分子化学与材料科学系）；WEL Research Institute（WEL研究所）
Lattice vibrations in CH$_3$NH$_3$PbI$_3$ are strongly interacting, with double well instabilities present at the Brillouin zone boundary. Analysis within a first-principles lattice dynamics framework reveals anharmonic potentials with short phonon quasi-particle lifetimes and mean-free paths. The phonon behaviour is distinct from the inorganic semiconductors GaAs and CdTe where three-phonon interaction strengths are three orders of magnitude smaller. The implications for the applications of hybrid halide perovskites arising from thermal conductivity, band-gap deformation, and charge-carrier s…
The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "$2n+1$" theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron scattering spectra …
We report on the dynamics of coherent phonons in semimetal 1T'-MoTe2 using femtosecond pump-probe spectroscopy. On an ultrafast sub-picosecond time scale at room temperature, a low frequency and long-lifetime shear phonon mode was observed at 0.39 THz, which was previously reported in the form of a characteristic phonon only in the low temperature Td-MoTe2 phase. Unlike the other optical phonon modes, the shear phonon mode was found to strongly couple with photoexcited carriers. Moreover, the amplitude of the shear mode surprisingly decreased with increasing excitation density, a phenomenon wh…
The dynamics of band-gap renormalization and gain build-up in monolayer MoTe$_2$ is investigated by evaluating the non-equilibrium Dirac-Bloch equations with the incoherent carrier-carrier and carrier-phonon scattering treated via quantum-Boltzmann type scattering equations. For the case where an approximately $300$ fs-long high intensity optical pulse generates charge-carrier densities in the gain regime, the strong Coulomb coupling leads to a relaxation of excited carriers on a few fs time scale. The pump-pulse generation of excited carriers induces a large band-gap renormalization during th…
Investigating the competition between ferroelectric ordering and quantum fluctuations is essential to tailor the desired functionalities of mixed ferroelectric and incipient ferroelectric systems, like, (Ba,Sr)TiO3 and (Eu,Ba)TiO3. Recently, it has been shown that suppression of quantum fluctuations increases ferroelectric ordering in (Eu,Ba)TiO3 and since these phenomena are coupled to crystallographic phase transitions it is essential to understand the role of phonons. Here, we observe that the unusual temperature dependence of phonons in BaTiO3 gets suppressed when Ba2+ is replaced by Eu2+.…
The microscopic origin of the large negative thermal expansion of cubic scandium trifluorides (ScF3) is investigated by performing a set of anharmonic free-energy calculations based on density functional theory. We demonstrate that the conventional quasiharmonic approximation (QHA) completely breaks down for ScF3 and the quartic anharmonicity, treated nonperturbatively by the self-consistent phonon theory, is essential to reproduce the observed transition from negative to positive thermal expansivity and the hardening of the R4+ soft mode with heating. In addition, we show that the contributio…
Phonon-phonon anharmonic effects have a strong influence on the phonon spectrum; most prominent manifestation of these effects are the softening (shift in frequency) and broadening (change in FWHM) of the phonon modes at finite temperature. Using Raman spectroscopy, we studied the temperature dependence of the FWHM and Raman shift of $\mathrm{E_{2g}^1}$ and $\mathrm{A_{1g}}$ modes for single-layer and natural bilayer MoS$_2$ over a broad range of temperatures ($8 < $T$ < 300$ K). Both the Raman shift and FWHM of these modes show linear temperature dependence for $T>100$ K, whereas they become …
The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions (EPI) in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in our suspended graphene sample at a wide temperature range. Four-phonon scattering contr…
Materials with ultralow thermal conductivity are of great interest for efficient energy conversion and thermal barrier coating. Copper-based semiconductors such as copper chalcogenides and copper halides are known to possess extreme low thermal conductivity, whereas the fundamental origin of the low thermal conductivity observed in the copper-based materials remains elusive. Here, we reveal that s-d coupling induced giant phonon anharmonicity is the fundamental mechanism responsible for the ultralow thermal conductivity of copper compounds. The symmetry controlled strong coupling of high-lying…
Analytical theory of large size intrinsic localized modes (ILMs) in anharmonic two-atomic chain is presented. It is shown that ILMs with frequencies close to the borders of phonon gap are govern by quartic anharmonicity while the effect of cubic anharmonicity is essentially reduced. This reduction effect is a consequence of small amplitude of vibrations of every second atom. As a result, an ILM cannot split down from the optical phonon band, in contradiction with the commonly accepted point of view. But it can spit up from the top of the acoustic phonon band making possible the existence of th…
Phonons are essential for understanding the thermal properties in monolayer transition metal dichalcogenides, which limit their thermal performance for potential applications. We investigate the lattice dynamics and thermodynamic properties of MoS2, MoSe2, and WS2 by first principles calculations. The obtained phonon frequencies and thermal conductivities agree well with the measurements. Our results show that the thermal conductivity of MoS2 is highest among the three materials due to its much lower average atomic mass. We also discuss the competition between mass effect, interatomic bonding …
The binary compound SnSe exhibits record high thermoelectric performance, largely because of its very low thermal conductivity. The origin of the strong phonon anharmonicity leading to the low thermal conductivity of SnSe is investigated through first-principles calculations of the electronic structure and phonons. It is shown that a Jahn-Teller instability of the electronic structure is responsible for the high-temperature lattice distortion between the Cmcm and Pnma phases. The coupling of phonon modes and the phase transition mechanism are elucidated, emphasizing the connection with hybrid …
Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well-understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100-1500K on a single-crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmoni…
The layered semiconductor SnSe is one of the highest-performing thermoelectric materials known. We demonstrate, through a first-principles lattice-dynamics study, that the high-temperature Cmcm phase is a dynamic average over lower-symmetry minima separated by very small energetic barriers. Compared to the low-temperature Pnma phase, the Cmcm phase displays a phonon softening and enhanced three-phonon scattering, leading to an anharmonic damping of the low-frequency modes and hence the thermal transport. We develop a renormalisation scheme to quantify the effect of the soft modes on the calcul…
In this work, we performed temperature-dependent Raman spectroscopy studies on three layered metal thiophosphates: CuInP2S6, CuCrP2S6, and CuInP2S6-In4/3P2S6 heterostructures. These materials are emerging multiferroics, with CuInP2S6 and CuInP2S6-In4/3P2S6 exhibiting room temperature ferrielectric polarization while CuCrP2S6 is both anti-ferroelectric and antiferromagnetic at low temperatures (<145 and <30 K, respectively). We studied two prominent peaks in the Raman spectra of these compounds, namely their P-P and P-S stretching modes. First order linear fits to the mode softening yielded coe…
In this work we explore the phase diagram of the binary Nb-S system from ambient pressures up to 250 GPa using $ab$ $initio$ evolutionary crystal structure prediction. We find several new stable compositions and phases, especially in the high-pressure regime, and investigate their electronic, vibrational, and superconducting properties. Our calculations show that all materials, besides the low-pressure phases of pure sulfur, are metals with low electron-phonon coupling strengths and critical superconducting temperatures below 15 K. Furthermore, we investigate the effects of phonon anharmonicit…
The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the …
Motivated by the excellent electronic and optoelectronic properties of two-dimensional (2D) tin oxides, we systematically investigated the thermal conductivity of monolayer SnO and SnO2by the first-principles calculations. The room-temperature thermal conductivity of monolayer SnO and SnO2reaches 9.6 W/(mK) and 98.8 W/(mK), respectively. The size effect is much weaker for monolayer SnO than for monolayer SnO2, due to the coexistence of size dependent and independent component in the thermal conductivity of monolayer SnO. The large difference between the thermal conductivity of 2D tin oxides ca…
The thermal properties of materials are critically important to various technologies and are increasingly the target of materials design efforts. However, it is only relatively recent advances in first-principles computational techniques that have enabled researchers to explore the microscopic mechanisms of thermal properties, such as thermal expansion. We use the Grüneisen theory of thermal expansion in combination with density functional calculations and the quasiharmonic approximation to uncover mechanisms of thermal expansion in PbTiO$_3$ thin-films in terms of elastic and vibrational cont…
We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral molecular dynamics simulations. Our method enjoys a remarkably low variance, which allows one to compute accurate phonon frequencies after a few picoseconds of nuclear dynamics, and it is further stabilized by the use of appropriate constrained displacement operators. We applied it to solid hydrogen at high pressure. For phase III, our predicted infrared (I…
Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate \textit{ab initio} investigations of lattice anharmonicity encounter difficulties owing to the cumbersome computations. Here we introduce the phonon quasiparticle approach and review its application to various materials. This method efficiently and reliably addresses lattice anharmonicity by combining \textit{ab initio} molecular dynamics and lattice dynamics calculations. Thus, in principle, it accounts for full anharmonic effects and overcomes finite-size effects t…
We have carried out temperature-dependent x-ray diffraction and Raman scattering experiments on powder $Cs_3Bi_2Br_9$. Trigonal to monoclinic structural transition at around 95 K is discussed and shown to be driven by the softening of the soft mode. We propose a model to describe the dynamics of the incomplete soft-mode. Raman scattering experiments demonstrate the origin of the soft mode to the rocking motions of Br atoms that participate to form $BiBr_6$ octahedra, which correlates the reported theoretical calculations. Some of the Raman mode frequencies exhibit anomalous temperature depende…
All phonons in a single crystal of NaBr were measured by inelastic neutron scattering at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal-optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. Ab initio computations were first performed with the quasiharmonic approximation (QHA), in which the phonon frequencies depend only on $V$, and on $T$ only insofar as it alters $V$ by thermal expansion. This QHA was an unqualified failure for predicting the temperature dependence of phonon frequenci…
We report on time-resolved broadband transient reflectivity (tr-bb-TR) measurements performed on a bulk single crystal of T$_d$-MoTe$_2$ as a function of the incident pump fluence (F). Tr-bb-TR data unveil photoinduced electronic changes progressing on the sub-picosecond timescale as well as the dynamics of the coherent low-frequency $^1A_1$ interlayer shear phonon. Our results indicate a gradual evolution of both the TR and the $^1A_1$ Fourier intensity spectra as a function of F, ruling out the threshold-like change that has been associated with the ultrafast photoinduced $T_d \to 1T'$ phase…
We determine the frequency dependence of four independent CdWO$_4$ Cartesian dielectric function tensor elements by generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Single crystal surfaces cut under different angles from a bulk crystal, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long wavelength active transverse and longitudinal optic phonon modes with $A_u$ and $B_u$ symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate t…
A Weyl semimetal is a new type of topological quantum phase with intriguing physics near the Weyl nodes. Although the equilibrium state of Weyl semimetals has been investigated, the ultrafast dynamics near the Weyl node in the nonequilibrium state is still missing. Here by performing time and angle resolved photoemission spectroscopy on type-II Weyl semimetal MoTe$_2$, we reveal the dispersion of the unoccupied states and identify the Weyl node at 70 meV above E$_F$. Moreover, by tracking the ultrafast relaxation dynamics near the Weyl node upon photo-excitation with energy, momentum and tempo…
Graphene+, a novel carbon monolayer with sp2-sp3 hybridization, is recently reported to exhibit graphene-like Dirac properties and unprecedented out-of-plane half-auxetic behavior [Yu et al, Cell Reports Physical Science, 3 100790 (2022)]. Herein, from comprehensively state-of-the-art first-principles studies, we report the exceptional lattice thermal transport properties of graphene+ driven by the unique sp2-sp3 crystal configuration. At room temperature, the thermal conductivity of graphene+ is calculated to be ~170 W/mK, which is much lower than that of graphene (~3170 W/mK) Despite the buc…
A theory of superconductivity is presented where the effect of anharmonicity, as entailed in the acoustic, or optical, phonon damping, is explicitly considered in the pairing mechanism. The gap equation is solved including diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping for optical phonons, with a damping coefficient which, in either case, can be directly related to the Gruneisen parameter and hence to the anharmonic coefficients in the interatomic potential. The results show that the increase of anharmonicity has a strikingly non-monotonic effect on the critica…
The temperature-dependent effective potential (TDEP) method for anharmonic phonon dispersion is generalized to the full potential case by combining with path integral formalism. This extension naturally resolves the intrinsic difficulty in the original TDEP at low temperature. The new method is applied to solid metallic hydrogen at high pressure. A colossal nuclear quantum effect (NQE) and subsequent anharmonicity are discovered, which not only leads to unexpectedly large drift of protons, but also slows down the convergence rate substantially when computing the phonon dispersions. By employin…
Roadmap for electronic structure, anharmonicity, and electron-phonon calculations in locally disordered inorganic and hybrid halide perovskites
Univ Rennes, INSA Rennes, CNRS, Institut FOTON - UMR 6082（雷恩大学，雷恩国立应用科学学院，法国国家科学研究中心，FOTON研究所）；Computation-based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究院计算科学与技术研究中心）；Univ Rennes, ENSCR, INSA Rennes, CNRS, ISCR - UMR 6226（雷恩大学，雷恩高等师范学院，雷恩国立应用科学学院，法国国家科学研究中心，ISCR研究所）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）
Interfacial thermal transport is critical for many thermal-related applications such as heat dissipation in electronics. While the total interfacial thermal conductance (ITC) can be easily measured or calculated, the ITC spectral mapping has been investigated only recently and is not fully understood. By combining nonequilibrium molecular dynamics simulations and atomistic Green's function method, we systematically investigate the ITC spectrum across an ideal interface, i.e., the argon-heavy argon interface. Our results show that the ITC spectrum increases gradually with temperature as more ph…
