The Tamura model is a particular type of 1$^{\text{st}}$ Born approximation of the phonon-isotope scattering problem. The expression for the mode-resolved phonon-isotope scattering rates in this model, derived in 1983, is still widely used in ab initio transport calculations. While the original work emphasized its applicability to low-energy acoustic phonons only, it has, nevertheless, been also applied to optical phonons in the field of phonon transport. The model has the salient feature of being a perturbation theory on top of a virtual crystal background. As such, this approach does not correspond to the proper methodology for solving the phonon-substitution defect problem in the respective limit. Here, we explore three avenues to go beyond the Tamura model and carry out calculations on a set of common materials to compare the different approaches. This work allows a systematic improvement of the treatment of phonon-isotope scattering in ab initio phonon transport, while unifying it with the general phonon-substitution scattering problem.
Thermal transport in single layer molybdenum disulfide (MoS2) is critical to advancing its applications. In this paper, we use molecular dynamics (MD) simulations with first-principles force constants to study the isotope effect on the thermal transport of single layer MoS2. Through phonon modal analysis, we found that isotopes can strongly scatter phonons with intermediate frequencies, and the scattering behavior can be radically different from that predicted by conventional scattering model based on perturbation theory (Tamura's formula). Such a discrepancy becomes smaller for low isotope co…
Recent studies reveal that four-phonon scattering is generally important in determining thermal conductivities of solids. However, these studies have been focused on materials where thermal conductivity $κ$ is dominated by acoustic phonons, and the impact of four phonon scattering, although significant, is still generally smaller than three-phonon scattering. In this work, taking AlSb as example, we demonstrated that four-phonon scattering is even more critical to three-phonon scattering as it diminishes optical phonon thermal transport, and therefore significantly reduces the thermal conducti…
The isotopic mass of constituent elements of materials has a well-known effect on the energy of vibrational modes. By means of monochromated scanning transmission electron microscopy we have experimentally studied the phonon bandstructure of hexagonal BN, where a phonon band gap appears between in-plane optical phonon modes and the lower energy part of the phonon spectrum. The size of the phonon band gap can be manipulated by the isotopic mass of the boron. While in $^{11}$BN the phonon band gap is about 7 meV wide, in $^{10}$BN the gap nearly closes, being an order of magnitude smaller (below…
Boron arsenide (c-BAs) is at the forefront of research on ultrahigh thermal conductivity materials. We present a Raman scattering study of isotopically tailored cubic boron arsenide single crystals for 11 isotopic compositions spanning the range from nearly pure c-$^{10}$BAs to nearly pure c-$^{11}$BAs. Our results provide insights on the effects of strong mass disorder on optical phonons and the appearance of two-mode behavior in the Raman spectra of mixed crystals. Strong isotope disorder also relaxes the one-phonon Raman selection rules, resulting in disorder-activated Raman scattering by a…
Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution
ISIS Neutron and Muon Source, STFC, Rutherford Appleton Laboratory（STFC拉瑟福德阿普尔顿实验室中子与μ子源）；University of Bath（巴斯大学）；United Kingdom Atomic Energy Authority（英国原子能管理局）
We present a theory of the isotope effect of the Curie temperature $T_{\rm c}$ in itinerant ferromagnets. The isotope effect in ferromagnets occurs via the electron-phonon vertex correction and the effective attractive interaction mediated by the electron-phonon interaction. The decrease of the Debye frequency increases the relative strength of the Coulomb interaction, which results in a positive isotope shift of $T_{\rm c}$ when the mass $M$ of an atom increases. Following this picture, we evaluate the isotope effect of $T_{\rm c}$ by using the Stoner theory and a spin-fluctuation theory. Whe…
Zirconium hydride is an important material for storage of hydrogen isotopes. Here we report the structural, electronic, vibrational and thermodynamic properties of ZrH2, ZrD2 and ZrT2 using density functional theory (DFT). The structural optimization was carried out by the plane-wave based pseudo-potential method under the generalized gradient approximation (GGA) scheme. The electronic structure of the ZrH2 compound was illustrated in terms of the electronic density of states, charge density distribution and the electron localization function. The phonon dispersion curves, phonon density of st…
Based on Zhang and Li's molecular dynamics calculations, the heat conductivity ($κ$) of metallic single-wall Carbon nanotubes (SNTs) was incorrectly concluded as mainly influenced by the radius. Apart from that, their isotope effect interpretation on $κ(T)$ for the metallic SNTs using solely the phonon scattering mechanism is also highlighted to be incorrect.
The observation of the local - mode vibration, the two - mode behavior of the LO phonons at large isotope concentration, as well as large line broadening in LIH - D mixed crystals directly evidence strong additional phonon scattering due to the isotope - induced disorder.
We reconsider the long-standing problem of the effect of spin fluctuations on the critical temperature and isotope effect in a phonon-mediated superconductor. Although the general physics of the interplay between phonons and paramagnons had been rather well understood, the existing approximate formulas fail to describe the correct behavior of $% T_{c}$ for general phonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formula for $T_{c}$ which agrees well with exact numerical solutions of the Eliashberg equations for a broad range of parameters. Based on bot…
The intermetallic compound ZrCo and its hydrides are important materials for their use in hydrogen isotope storage. The dynamical, thermodynamic and elastic properties of ZrCo and its hydrides ZrCoX3 (X= H, D and T) are reported. While the electronic structure calculations are performed using plane wave pseudopotential approach, the effect of isotopes on the vibrational and thermodynamic properties has been demonstrated through frozen phonon approach. The results reveal significant difference between the ZrCoH3 and its isotopic analogs in terms of phonon frequencies and zero point energies. Fo…
Recently, three-component new fermions in topological semimetal MoP are experimentally observed, which may have potential applications like topological qubits, low-power electronics and spintronics. These are closely related to thermal transport properties of MoP. In this work, the phonon transport of MoP is investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). The calculated room-temperature lattice thermal conductivity is 18.41 $\mathrm{W m^{-1} K^{-1}}$ and 34.71 $\mathrm{W m^{-1} K^{-1}}$ along the in- and cross-plane d…
We report ab initio calculations of the electronic band structure, the corresponding optical spectra, and the phonon dispersion relations of trigonal alpha-HgS (cinnabar). The calculated dielectric functions are compared with unpublished optical measurements by Zallen and coworkers. The phonon dispersion relations are used to calculate the temperature and isotopic mass dependence of the specific heat which has been compared with experimental data obtained on samples with the natural isotope abundances of the elements Hg and S (natural minerals and vapor phase grown samples) and on samples prep…
In an electron system coupled with anharmonic phonons, i.e., {\it rattling}, inverse isotope effect on the Kondo temperature $T_{\rm K}$ is found to occur by the numerical evaluation of the Sommerfeld constant $γ$ of the Anderson-Holstein model. For the anharmonic potential of an oscillator with mass $M$ in which large $γ$ has been found to be almost independent of an applied magnetic field, $γ$ is significantly suppressed when $M$ is increased, i.e., $T_{\rm K}$ is enhanced due to the relation of $γ$$\sim$$T_{\rm K}^{-1}$ in the Kondo problem, leading to the inverse isotope effect on $T_{\rm …
We have simulated the ultra-high-temperature ceramic zirconium carbide (ZrC) in order to predict electron and phonon scattering properties, including lifetimes and transport. Our predictions of heat and charge conductivity, which extend to 3000 K, are relevant to extreme temperature applications of ZrC. Mechanisms are identified on a first principles basis that considerably enhance or suppress heat transport at high temperature, including strain and anharmonicity. The extent to which boundary confinement and isotope scattering effects lower thermal conductivity is predicted.
Materials with high thermal conductivities (k) is valuable to solve the challenge of waste heat dissipation in highly integrated and miniaturized modern devices. Herein, we report the first synthesis of atomically thin isotopically pure hexagonal boron nitride (BN) and its one of the highest k among all semiconductors and electric insulators. Single atomic layer (1L) BN enriched with 11B has a k up to 1009 W/mK at room temperature. We find that the isotope engineering mainly suppresses the out-of-plane optical (ZO) phonon scatterings in BN, which subsequently reduces acoustic-optical scatterin…
The equilibrium ground-state structure of LiNbO3 in the paraelectric and ferroelectric phases is fully optimized in a first-principles calculation using the full-potential linearized augmented plane wave method. The equilibrium volume, c/a ratio and all (four, in the ferroelectric phase) internal parameters are found to be in good agreement with the experimental data. Frozen phonon calculations are performed for TO-Gamma phonons corresponding to the A1 and A2 irreducible representations of the R3c space group in the ferroelectric phase. The comparison with available experimental frequencies fo…
We report the Raman spectroscopy of 12C/13C graphene isotope superlattices synthesized by chemical vapour deposition. At large periods the Raman spectra corresponds to the sum of the bulk 12C and 13C contributions. However, at small periods we observe the formation of mixed 12C/13C modes for Raman processes that involve two phonons, which results in the tripling of the 2D and 2D' Raman peaks. This tripling can be well understood in the framework of real space Raman spectroscopy, where the two emitted phonons stem from different regions of the superlattice. The intensity of the mixed peak incre…
The numerical calculations of the standard Eliashberg-Nambu strong coupling theory and a formula of isotope effect derived in this paper provide direct evidences that an-harmonic vibrations of lattice enhance isotope effect with anomalous coefficient $α>1/2$. The results in this paper explain very well the wide distributed $α$ values for the samples with different ratios of substitutions of $^{12}$C by $^{13}$C of fulleride superconductor Rb$_{3}$C$_{60}$. The calculations of isotope effects indicate that the intra-molecule radial modes have more important contributions to superconductivity th…
We propose systems that allow a tuning of the phonon transmission function T($ω$) in graphene nanoribbons by using C$^{13}$ isotope barriers, antidot structures, and distinct boundary conditions. Phonon modes are obtained by an interatomic fifth-nearest neighbor force-constant model (5NNFCM) and T($ω$) is calculated using the non-equilibrium Green's function formalism. We show that by imposing partial fixed boundary conditions it is possible to restrict contributions of the in-plane phonon modes to T($ω$) at low energy. On the contrary, the transmission functions of out-of-plane phonon modes c…
Effects of coupling between phonon distortions and stripe-like spin waves in the CuO plane of HgBa$_2$CuO$_4$ are studied by band calculations. Local exchange enhancements depend sensitively on the local structure around Cu sites. Interactions where spin waves have twice as long wave length as phonon waves can lead to a 'dip' in the density of states (DOS) below the Fermi energy, $E_F$. This type of interaction is compatible with several seemingly contradictory observations among high-$T_C$ cuprates, like the isotope effect, anti-ferromagnetic fluctuations, stripes and pseudogaps. It can also …
Structural manipulation at the nanoscale breaks the intrinsic correlations among different energy carrier transport properties, achieving high thermoelectric performance. However, the coupled multifunctional (phonon and electron) transport in the design of nanomaterials makes the optimization of thermoelectric properties challenging. Machine learning brings convenience to the design of nanostructures with large degree of freedom. Herein, we conducted comprehensive thermoelectric optimization of isotopic armchair graphene nanoribbons (AGNRs) with antidots and interfaces by combining Green's fun…
The silicon-vacancy centre (SiV) in diamond has interesting vibronic features. We demonstrate that the zero phonon line position can be used to reliably identify the silicon isotope present in a single centre. This is of interest for quantum information applications since only the silicon 29 isotope has nuclear spin. In addition, we demonstrate that the 64 meV line is due to a local vibrational mode of the silicon atom. The presence of a local mode suggests a plausible origin of the isotopic shift of the zero phonon line.
The possibility of propagation of second sound waves in diamond single crystals depending on their dimensions, concentrations of isotopes and temperature is studied. At this correct account of phonon scattering on boundaries is important. The calculation of phonon collision frequencies is carried out in the reduced isotropic crystal model using second and third modules of elasticity and in Callaway model on the basis of experimental data on diamond thermal conductivity. Both models give us the consistent values of parameters under which the propagation of SSW is possible. It is discovered that…
A discovery of the unusual thermal properties of graphene stimulated experimental, theoretical and computational research directed at understanding phonon transport and thermal conduction in two-dimensional material systems. We provide a critical review of recent results in the graphene thermal field focusing on phonon dispersion, specific heat, thermal conductivity, and comparison of different models and computational approaches. The correlation between the phonon spectrum in graphene-based materials and the heat conduction properties is analyzed in details. The effects of the atomic plane ro…
