Anharmonic Phonon-phonon Interactions Research Articles

Twist Angle-Dependent Phonon Hybridization in WSe2/WSe2 Homobilayer.

The emerging moiré superstructure of twisted transition metal dichalcogenides (TMDs) leads to various correlated electronic and optical properties compared to those of twisted bilayer graphene. In such a versatile architecture, phonons can also be renormalized and evolve due to atomic reconstruction, which, in turn, depends on the twist angle. However, observing this reconstruction and its relationship to phonon behavior with conventional, cost-effective imaging methods remains challenging. Here, we used noninvasive Raman spectroscopy on twisted WSe2/WSe2 (t-WSe2) homobilayers to examine the evolution of phonon modes due to interlayer coupling and atomic reconstruction. Unlike in the natural bilayer (NB), ∼0° as well as ∼60° t-WSe2 samples, the nearly degenerate A1g/E2g mode in the twisted samples (1-7°) split into a doublet in addition to the nondegenerate B2g mode, and the maximum splitting is observed around 2-3°. Our detailed theoretical calculations qualitatively capture the splitting and its dependence as a function of the twist angle and highlight the role of the moiré potential in phonon hybridization. Additionally, we found that around the 2° twist angle, the anharmonic phonon-phonon interaction is higher than the natural bilayer and decreases for larger twist angles. Interestingly, we observed anomalous Raman frequency softening and line-width increase with the decreasing temperature below 50 K, pointing to the combined effect of enhanced electron-phonon coupling and cubic anharmonic interactions in moiré superlattice.

Full-landscape selection rules of electrons and phonons and temperature-induced effects in 2D silicon and germanium allotropes

The electron-phonon (el-ph) and phonon-phonon interactions play crucial roles in determining the electronic and thermal transport properties of materials. Using the group theory and ab-initio calculations, we have derived the full-landscape selection rules for intravalley and intervalley scattering for carriers in 2D silicon and germanium allotropes with low buckled (LB) and large honeycomb dumbbell (LHD) structures, showing dominant role of optical modes in total el-ph coupling in LHD Si/Ge due to most el-ph scattering channels via acoustic modes blocked by symmetries. Remarkably, we show that due to the relatively large optical phonon bandwidth and “bunching effect" of acoustic phonon bands, the selection rules of three-phonon interactions reveal the dominant ooo and aoo channels in LHD and LB Si/Ge, respectively, and the temprature-induced effects significantly increase the ratio between mode-resolved four-phonon interactions and three-phonon interactions in most of the phonon-frequency region, finally leading to the low thermal conductivities in both LB and LHD Si/Ge. Furthermore, we observe the anomalous temperature-dependent thermal conductivities in LHD Ge, resulted from the vanishing quasi-acoustic-optical phonon gap under the temperature-induced effects. By considering full el-ph coupling and higher-order anharmonic phonon-phonon interactions, the maximal thermoelectric figures of merits in LHD Si and LB Ge are found to reach 1.06 and 0.66 at 700 K, respectively, significantly surpassing their bulk counterparts. Our work is poised to stimulate wide-ranging exploration into phonon transport across diverse materials, and benefits both fundamental knowledge and advanced technologies of 2D Si/Ge allotropes.

Experimental and theoretical study of anomalous temperature dependence of phonons in Y2Ti2O7 pyrochlore

We present Raman spectroscopic as well as first-principles theoretical studies of the temperature dependence of phonon spectra in the pyrochlore ${\mathrm{Y}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. Our experimental results show that the frequencies of several phonons display anomalous softening upon cooling. Our theoretical calculations of the temperature dependence, via phonon self-energy corrections arising from cubic anharmonic interactions, lead to such anomalies but only for a couple of high-frequency phonon modes. Our work strongly supports the suggestion that anharmonic phonon-phonon interactions are strong in the pyrochlore titanates and that they are responsible for the phonon anomalies observed. The strong anharmonic effects are likely due to the presence of the vacant Wyckoff sites and the shifts of the oxygen atoms from their actual positions in the pyrochlore lattice. However, the theoretical calculations fail to explain the anomalous behavior of low and intermediate frequency modes observed in our experiments. It seems likely that a much more sophisticated, perhaps nonperturbative, treatment of the anharmonic interactions will be required for a full explanation of the anomalies.

Electrical and thermal transport properties of medium-entropy SiyGeySnx alloys

Electrical and thermal transport properties of disordered materials have long been of both theoretical interest and engineering importance. As a new class of materials with an intrinsic compositional disorder, high/medium-entropy alloys (HEAs/MEAs) are being immensely studied mainly for their excellent mechanical properties. By contrast, electrical and thermal transport properties of HEAs/MEAs are less well studied. Here we investigate these two properties of silicon (Si)-germanium (Ge)-tin (Sn) MEAs, where we keep the same content of Si and Ge while increasing the content of Sn from 0 to 1/3 to tune the configurational entropy and thus the degree of compositional disorder. We predict all SiyGeySnx MEAs to be semiconductors with a wide range of band gaps from near-infrared (0.28 eV) to visible (1.11 eV) in the light spectrum. We find that the band gaps and effective carrier masses decrease with increasing Sn content. As a result, increasing the compositional disorder in SiyGeySnx MEAs enhances their electrical conductivity. For the thermal transport properties of SiyGeySnx MEAs, our molecular dynamics simulations show an opposite trend in the thermal conductivity of these MEAs at room temperature, which decreases with increasing compositional disorder, owing to enhanced Anderson localization and strong phonon-phonon anharmonic interactions. The enhanced electrical conductivity and weakened thermal conductivity make SiyGeySnx MEAs with high Sn content promising functional materials for thermoelectric applications. Our work demonstrates that HEAs/MEAs not only represent a new class of structural alloys but also a novel category of functional alloys with unique electrical and thermal transport properties.

Correlations between the structural, magnetic, and ferroelectric properties of BaMO3: M = Ti1-x(Mn/Fe)x compounds: A Raman study

Multiferroics possess two or more switchable states such as polarization, magnetization, etc. Phonon excitations in multiferroic phase are strongly modified by magnetoelectric coupling, spin-phonon coupling, and anharmonic phonon-phonon interactions. Here, we have investigated the correlation between phonons and multiferroic order parameters in hexagonal BaMO3: M = Ti1-x(Mn/Fe)x systems using powder x-ray diffraction (PXRD), Raman spectroscopic, and magnetic measurements. The structural transformation from a polar tetragonal to a non-polar 6H-type hexagonal phase is observed as a function of doping (Mn/Fe). Magnetic measurements reveal that the BaTi1-xMnxO3 is paramagnetic while BaTi1-xFexO3 exhibits composition-dependent ferromagnetic order. Importantly, Anomalous temperature-dependence is observed for two phonons (E1g at ∼ 152 cm−1 and A1g at ∼ 636 cm−1) in both the systems exhibiting similar trend with the doping (Mn/Fe) irrespective of the differences in their magnetic ground state. Hence, we attribute the phonon anomalies in both the (Fe/Mn doped) systems to strong anharmonic phonon-phonon interactions arising from large atomic displacements involved in the vibrations. In addition, we have also observed signatures of correlation of phonons with ferroelectric phase as well as magnetically ordered state suggesting the presence of a strain-induced magnetoelectric coupling in the doped compounds.

Coupled transport of phonons and carriers in semiconductors: A case study of n -doped GaAs

We present a general coupled electron-phonon Boltzmann transport equations (BTEs) scheme designed to capture the mutual drag of the two interacting systems. By combining density functional theory based first principles calculations of anharmonic phonon-phonon interactions with physical models of electron-phonon interactions, we apply our implementation of the coupled BTEs to calculate the thermal conductivity, mobility, Seebeck and Peltier coefficients of n-doped gallium arsenide. The measured low temperature enhancement in the Seebeck coefficient is captured using the solution of the fully coupled electron-phonon BTEs, while the uncoupled electron BTE fails to do so. This work gives insights into the fundamental nature of charge and heat transport in semiconductors and advances predictive ab initio computational approaches. We discuss possible extensions of our work.

X-site aliovalent substitution decoupled charge and phonon transports in XYZ half-Heusler thermoelectrics

In this work, the effects of niobium (Nb) doping on thermoelectric properties of n-type half-Heusler (Hf0.25Zr0.25Ti0.5)1-xNbxNiSn (x = 0, 0.005, 0.01, 0.015, 0.02, and 0.025) compounds were investigated. The samples were synthesized by arc-melting method and followed by annealing, mechanical grinding and spark plasma sintering (SPS) process. The electrical conductivity, the Seebeck coefficient, the thermal conductivity, and the Hall coefficient measurements were performed in the range of temperature from room temperature to 923 K. By changing Nb-doping amount, the electrical conductivity increased with increasing the doping level, while the Seebeck coefficient relatively less decreased at high temperatures, resulting in the highest power factor of 36 × 10−4 (W/K2m) at 773 K with x = 0.02 sample. Furthermore, a significant reduction in the lattice thermal conductivity is attributed to anharmonic phonon-phonon interactions by aliovalent substitution into multi-element site and higher degree of phase separation, which was achieved through the synthesis process of these compounds. The enhancement of the power factor combined to low thermal conductivity leads to ∼20% increase of the dimensionless figure of merit (ZT, ∼1.0 at 773 K) in comparison to the parent Hf0.25Zr0.25Ti0.5NiSn compound. It is believed that this is attributed to a decoupling between the electrical conductivity, thermopower, and phonon transport by Nb-doping. The Nb-doped compounds also showed high stability of the power factor up to 873 K.

X-Site Aliovalent Substitution Decoupled Charge and Phonon Transports in XYZ Half-Heusler Thermoelectrics

In this work, the effects of niobium (Nb) doping on thermoelectric properties of n-type half-Heusler (Hf0.25Zr0.25Ti0.5)1-xNbxNiSn (x = 0, 0.005, 0.01, 0.015, 0.02, and 0.025) compounds were investigated. The samples were synthesized by arc-melting method and followed by annealing, mechanical grinding and spark plasma sintering (SPS) process. The electrical conductivity, the Seebeck coefficient, the thermal conductivity, and the Hall coefficient measurements were performed in the range of temperature from room temperature to 923 K. By changing Nb doping amount, the electrical conductivity increased with increasing the doping level, while the Seebeck coefficient relatively less decreased at high temperatures, resulting in the highest power factor of 36 x 10-4 (W/K2m) at 773 K with x = 0.02 sample. Furthermore, a significant reduction in the lattice thermal conductivity is attributed to anharmonic phonon-phonon interactions by aliovalent substitution into multi-element site and higher degree of phase separation, which was achieved through the synthesis process of these compounds. The enhancement of the power factor combined to low thermal conductivity leads to ~ 20% increase of the dimensionless figure of merit (ZT, ~1.0 at 773 K) in comparison to the parent Hf0.25Zr0.25Ti0.5NiSn compound. The Nb-doped compounds also showed high stability of the power factor up to 873 K.

Anharmonic phonon properties in Eu0.5Ba0.5TiO3

Abstract Phonon properties have been studied using reduced sound velocity of Eu0.5Ba0.5TiO3 (EBTO). To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced sound velocity of multiferroic EBTO exhibits a kink at TN = 1.9 K. This anomalously reduced sound velocity can be interpreted as an effect of vanishing magnetic ordering above TN. What’s more, the ferroelectric subsystem cannot be influenced by the magnetic subsystem above TN for TN ≪TC in the EBTO. It was found that the reduced sound velocity decreases as T increases near ferroelectric transition TC. That is to say, the sound velocity softens near ferroelectric transition TC. It is also noteworthy that the reduced sound velocity softens when the RE (the coupling between the ferroelectric pseudo-spins and phonons), V(3) and |V(4)| (the third- and fourth-order atomic force constants of the anharmonic phonons, respectively) increase. These conclusions are all in good accordance with the experimental data and theoretical results.

Anomalous reduced sound velocity of multiferroic TbMn2O5

The anomalous reduced sound velocity of multiferroic TbMn2O5 (TMO) has been studied using Green's function technique. To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced velocity of sound of TMO exhibits a kink at the ferroelectric phase transition temperature TC. This can be explained as an effect of vanishing ferroelectric ordering above TC. It was found that the reduced sound velocity increases with increasing V(3) (the third-order atomic force constants of the anharmonic phonons) in the interval T < TC, whereas the reduced sound velocity remains unchanged in the interval TC < T < TN. It was also found that the reduced sound velocity increases with the increase of V(4) (the fourth-order atomic force constants of the anharmonic phonons) in the interval T < TN. In addition, the ferroelectric phase transition temperature TC decreases when V(4) increases in the interval T < TN. Those theoretical results are in agreement with the experimental data.

Influence of thermal losses at the gate contact of Si nanowire transistors: A phenomenological treatment in quantum transport theory

A quantum mechanical simulation approach relying on the non-equilibrium Green's function formalism, combining atomistic electron and phonon transport, and accounting for phonon losses at the gate contact is presented in this paper. To correctly capture self-heating effects in ultra-scaled gate-all-around nanowire field-effect transistors, it is necessary to go beyond electron-phonon and anharmonic phonon-phonon interactions. A phenomenological self-energy derived from Fourier's law is therefore introduced to model heat flows through oxide layers. It is found that in an NWFET with a channel length of 15 nm turning on thermal losses at the gate contact leads to a decrease in the maximum lattice temperature by more than 100 K and to a 10% increase in the device current in the ON-state.

The role of phonon-phonon and electron-phonon scattering in thermal transport in PdCoO2.

The layered metal oxide PdCoO2 is of fundamental interest in solid-state physics due to its unique nature as a two-dimensional electron gas. It is well known that electron-phonon scattering plays the leading role in the electrical transport of lots of materials; however, the influence of electron-phonon coupling on the thermal transport in PdCoO2 is rarely studied. Herewith we employ ab initio calculations to study the phonon lifetimes of PdCoO2 due to electron-phonon scattering and anharmonic phonon-phonon interactions. It is found that electron-phonon scattering has a large correction to the lattice thermal conductivity of PdCoO2 for both the in-plane and cross-plane directions, which is reduced by 21% and 27%, respectively. Moreover, the correction becomes larger and is more significant for the in-plane direction with decreasing temperature. As a result, the cross-plane lattice thermal transport overwhelms the in-plane value at low temperatures. This study provides useful guidance for the development of relevant devices involving two-dimensional electron gas systems.

Low-temperature anharmonic phonon properties of supported graphene

Temperature-dependent Raman studies of anharmonic phonon-phonon processes in supported graphene are presented. Different G peak position temperature dependencies for graphene on glass and copper substrates were observed. Having calculated graphene-substrate total interaction energy taking into account substrate-induced strain, we estimated E2g mode energy changes due to anharmonic phonon-phonon interaction as the temperature decreases from room temperature to a value close to absolute zero for both substrates. For graphene on glass, the obtained value was about 1.8 times greater than the theoretical one for suspended graphene. For graphene on copper, the value was about 2.9 times greater. This result demonstrates a strong substrate influence on anharmonic phonon-phonon processes in graphene.

Effect of ferromagnetic and ferroelectric properties on the sound velocity anomaly in BiFeO3

The effect of ferromagnetic and ferroelectric properties on the sound velocity in multiferroic BiFeO3 (BFO) is studied with using Green’s function method on the basis of the magnetoelectric coupling, the spin-phonon interaction and the anharmonic phonon-phonon interaction. The Heisenberg-like model is employed to describe the magnetic subsystem, and the transverse Ising model is used to explain the ferroelectric subsystem. The reduced velocity is obtained in the limit of zero wave vectors. It is shown that the reduced velocity of sound of BiFeO3 exhibits a cusp-like at the magnetic phase transition temperature TN. This anomaly in reduced velocity can be explained as an influence of vanishing magnetic ordering above TN and the ferroelectric subsystem can not be influenced by the magnetic subsystem above TN due to TN ≪ TC in the BFO. The reduced velocity and TN increase with increasing of the J1, J2 and g, whereas reduced velocity decreases with I increases. The achieved conclusion is in accordance with the experimental results.

The Origin of Ultralow Thermal Conductivity in InTe: Lone-Pair-Induced Anharmonic Rattling.

Understanding the origin of intrinsically low thermal conductivity is fundamentally important to the development of high-performance thermoelectric materials, which can convert waste-heat into electricity. Herein, we report an ultralow lattice thermal conductivity (ca. 0.4 W m(-1) K(-1) ) in mixed valent InTe (that is, In(+) In(3+) Te2 ), which exhibits an intrinsic bonding asymmetry with coexistent covalent and ionic substructures. The phonon dispersion of InTe exhibits, along with low-energy flat branches, weak instabilities associated with the rattling vibrations of In(+) atoms along the columnar ionic substructure. These weakly unstable phonons originate from the 5s(2) lone pair of the In(+) atom and are strongly anharmonic, which scatter the heat-carrying acoustic phonons through strong anharmonic phonon-phonon interactions, as evident in anomalously high mode Grüneisen parameters. A maximum thermoelectric figure of merit (z T) of about 0.9 is achieved at 600 K for the 0.3 mol % In-deficient sample, making InTe a promising material for mid-temperature thermoelectric applications.

Structure, dynamical stability, and electronic properties of phases inTaS2from a high-level quantum mechanical calculation

${\mathrm{TaS}}_{2}$ is a transition-metal dichalcogenide having an exceptionally rich phase diagram, which includes exotic phenomena such as a charge density wave. We analyzed the structure, bonding, ground state, and dynamical stability of $1T, 2H$, and $3R$ phases of ${\mathrm{TaS}}_{2}$, and a commensurate charge density wave phase from the first principles. Van der Waals interaction among layers and strong electron-electron interactions were included by using the exact exchange plus random phase approximation, a high-level quantum mechanical approach. The calculated structural parameters agree well with the available experimental data. The individual sheets of ${\mathrm{TaS}}_{2}$ are bound by dispersive forces, which are stronger than dispersive forces in graphite and fluorographite. $1T\ensuremath{-}{\mathrm{TaS}}_{2}$ is dynamically unstable at low temperature, which leads to the formation of charge density wave and opening of the in-plane band gap. Anharmonic phonon-phonon interactions stabilize the $1T$ structure at elevated temperatures. The calculated phase diagram of ${\mathrm{TaS}}_{2}$ reveals that the $1T$ phase is the ground state at temperatures above 1300 K, $2H$ below this point, and the charge density wave phase becomes more stable than the perfect $1T$ structure below 480 K.

Ab initiostudy of the anharmonic lattice dynamics of iron at theγ−δphase transition

We report calculations of phonon dispersions of iron (Fe) at its $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\delta}$ phase transition using a self-consistent ab initio lattice dynamical method in conjunction with an effective magnetic force approach via the antiferromagnetic approximation. Our results show that anharmonic phonon-phonon interactions play a crucial role in stabilizing the $\ensuremath{\delta}$-Fe phase in the open bcc lattice. In contrast, the lattice dynamics of the close-packed fcc $\ensuremath{\gamma}$-Fe phase are dominated by magnetic interactions. Simultaneous considerations of the lattice anharmonic and magnetic interactions produced temperature-dependent phonon dispersions for $\ensuremath{\delta}$-Fe and $\ensuremath{\gamma}$-Fe phases in excellent agreement with recent experimental measurements. The present results highlight the key role of lattice anharmonicity in determining the structural stability of iron at high temperatures, which has significant implications for other high-temperature paramagnetic metals like Ce and Pu.

Anharmonic stabilization and band gap renormalization in the perovskiteCsSnI3

Amongst the X(Sn,Pb)Y$_3$ perovskites currently under scrutiny for their photovoltaic applications, the cubic B-$\alpha$ phase of CsSnI$_3$ is arguably the best characterized experimentally. Yet, according to the standard harmonic theory of phonons, this deceptively simple phase should not exist at all due to rotational instabilities of the SnI$_6$ octahedra. Here, employing self-consistent phonon theory we show that these soft modes are stabilized at experimental conditions through anharmonic phonon-phonon interactions between the Cs ions and their iodine cages. We further calculate the renormalization of the electronic energies due to vibrations and find an unusual opening of the band gap, estimated as 0.24 and 0.11 eV at 500 and 300 K, which we attribute to the stretching of Sn-I bonds. Our work demonstrates the important role of temperature in accurately describing these materials.

Significant reduction of lattice thermal conductivity by the electron-phonon interaction in silicon with high carrier concentrations: a first-principles study.

The electron-phonon interaction is well known to create major resistance to electron transport in metals and semiconductors, whereas fewer studies are directed to its effect on phonon transport, especially in semiconductors. We calculate the phonon lifetimes due to scattering with electrons (or holes), combine them with the intrinsic lifetimes due to the anharmonic phonon-phonon interaction, all from first principles, and evaluate the effect of the electron-phonon interaction on the lattice thermal conductivity of silicon. Unexpectedly, we find a significant reduction of the lattice thermal conductivity at room temperature as the carrier concentration goes above 10(19) cm(-3) (the reduction reaches up to 45% in p-type silicon at around 10(21) cm(-3)), a range of great technological relevance to thermoelectric materials.

A Theoretical Study of the Variation in the Curie Temperature of the La and Zr Doped BaTiO3when External Electric Field Is Applied

As Barium Titanate (BaTiO3) is a noble ferroelectric material and has enormous applications in various electrical and electronics applications. Different properties of BaTiO3 depend on the Curie temperature of the material and the Curie temperature varies with the introduction of different impurities and the concentration of that impurity. In the present study an expression has been derived for the variation in the Curie Temperature Tc, by using double time temperature dependent Green’s function and a modified Joseph Hamiltonian. In the formalism the fourth order anharmonic phonon-phonon interaction is considered. The variation of the Tc is also studied under the effect of applied electric field and the results are compared with the previous studies achieved by different researchers.