Low κL Research Articles

Machine Learning and First-Principle Predictions of Materials with Low Lattice Thermal Conductivity.

We performed machine learning (ML) simulations and density functional theory (DFT) calculations to search for materials with low lattice thermal conductivity, κL. Several cadmium (Cd) compounds containing elements from the alkali metal and carbon groups including A2CdX (A = Li, Na, and K; X = Pb, Sn, and Ge) are predicted by our ML models to exhibit very low κL values (<1.0 W/mK), rendering these materials suitable for potential thermal management and insulation applications. Further DFT calculations of electronic and transport properties indicate that the figure of merit, ZT, for the thermoelectric performance can exceed 1.0 in compounds such as K2CdPb, K2CdSn, and K2CdGe, which are therefore also promising thermoelectric materials.

Enhancing the Thermoelectric Performance of n-Type Mg3.2Sb1.5Bi0.5 by Reducing Lattice Thermal Conductivity through the Incorporation of Chlorine-Containing Compounds.

Mg3Sb2-based thermoelectric materials are characterized by their economic efficiency, nontoxicity, and environmental friendliness and represent a highly promising and eco-friendly functional material for midtemperature applications. To achieve a higher thermoelectric performance, we introduced two compounds, LaCl3 and CeCl3, into Mg3.2Sb1.5Bi0.5 under the guidance of first-principles calculations. The Mg3.2Sb1.5Bi0.5 + 0.03CeCl3 sample reached a maximum ZT value of approximately 1.6 at 723 K. The calculations indicate that two n-type dopants, LaCl3 and CeCl3, can adequately improve the band structure of Mg3Sb2, and the introduction of Cl atoms will also lead to lattice distortion and reduce the lattice thermal conductivity (κL). Experimental results demonstrate that the introduction of Cl atoms efficiently reduces the thermal conductivity while improving the electrical transport properties. Specifically, the Mg3.2Sb1.5Bi0.5 + 0.03CeCl3 sample achieved an exceptionally low κL of 0.3 W m-1 K-1 at 723 K, thereby validating the effectiveness of LaCl3 and CeCl3 doping. This work provides valuable insights into achieving thermoelectric decoupling in Mg3Sb2-based thermoelectric materials.

Antibonding valence states induce low lattice thermal conductivity in metal halide semiconductors

Reduction of phonon mediated thermal transport properties, i.e., lattice thermal conductivity (κL), of semiconductors can strongly affect the performance of thermoelectrics and optoelectronics. Although extrinsic routes to reduce κL have been achieved through selective scattering of phonons via doping, alloying, and hierarchical nano-structuring, semiconductors with intrinsically low κL have recently gained widespread attention due to their ability to decouple electronic and phonon transports. While innate low κL in crystalline semiconductors is a desired requirement to achieve high performance thermoelectrics, the solar upconversion efficiency of photovoltaics based on metal halide perovskites (MHPs) have been shown to increase due to their ultralow κL through the hot-phonon bottleneck effect. Therefore, understanding the microscopic mechanisms underlying ultralow κL in crystalline semiconductors is extremely important. Several structural factors that are intrinsic to a material have been shown to strongly influence the reduction of κL. Among them, the presence of rattling atoms, lone-pair electrons, and large lattice anharmonicity have been widely studied. Here, we bring out yet another largely unexplored intrinsic characteristic of materials related to the filled antibonding valence states (AVS) near the Fermi level, which are shown to induce low κL in crystalline compounds. We focus our review on an emerging class of compounds–metal halide semiconductors including MHPs and investigate the interplay between structures, chemical bonding and κL, carefully curating from literature a list of 33 compounds having different structure dimensionality with known κL. We established a universal connection between the elastic moduli, speeds of sound, and κL with the presence of AVS just below the Fermi level. We found that large peak in the AVS correlates positively with lower values of elastic moduli, speeds of sound, and κL, providing antibonding states based design criteria of low-κL compounds. Furthermore, we discuss different synthesis strategies, which are crucial for experimental realization of ultralow κL through structure manipulation. Additionally, we outline how chemical bonding data can be utilized in machine learning models for predictive modeling of κL. We hope that our approach of understanding low-κL through the viewpoint of chemical bonding theory would encourage exploration of phonon transport properties in other families of materials having filled AVS that can provide further insights on the structure-bonding-property relationships aiding novel materials design approaches.

Lone Pair Induced 1D Character and Weak Cation-Anion Interactions: Two Ingredients for Low Thermal Conductivity in Mixed-Anion Metal Chalcohalide CuBiSCl2.

Mixed-anion compounds, which incorporate multiple types of anions into materials, display tailored crystal structures and physical/chemical properties, garnering immense interest in various applications such as batteries, catalysis, photovoltaics, and thermoelectrics. However, detailed studies regarding correlations among crystal structure, chemical bonding, and thermal/vibrational properties are rare for these compounds, which limits the exploration of mixed-anion compounds for associated thermal applications. In this work, we investigate the lattice dynamics and thermal transport properties of the metal chalcohalide, CuBiSCl2. A high-purity polycrystalline CuBiSCl2 sample exhibits a low lattice thermal conductivity (κL) of 0.9-0.6 W/(m·K) from 300 to 573 K. By combining various experimental techniques, including three-dimensional (3D) electron diffraction, with theoretical calculations, we elucidate the origin of low κL in CuBiSCl2. The stereochemical activity of the 6s2 lone pair of Bi3+ favors an asymmetric environment with neighboring anions involving both short and long bond lengths. This particularity often implies weak bonding, low structure dimensionality, and strong anharmonicity, leading to a low κL. In addition, the strong 2-fold linear S-Cu-S coordination with weak Cu···Cl interactions induces a large anisotropic vibration of Cu, which enables strong phonon-phonon scattering and decreases κL. The investigations into lattice dynamics and thermal transport properties of CuBiSCl2 broaden the scope of the existing mixed-anion compounds suitable for the associated thermal applications, offering a new avenue for the search for low thermal conductivity materials in low-cost mixed-anion compounds.

Comparison of ultra-low lattice thermal conductivity of the full-Heusler compound Li2Rb(Cs)Bi after considering strong quartic anharmonicity

This paper conducts a detailed study on the thermal transport and thermoelectric properties of Li2Rb(Cs)Bi and analyzes the optical phonon frequency shift caused by considering anharmonicity. We mainly focus on studying the microscopic mechanism of the difference in lattice thermal conductivity (κL) of the two materials. By calculating the group velocity, scattering rate, scattering phase space and scattering sub-process, it is concluded that κL is mainly dominated by the acoustic branch. Due to its small group velocity and large scattering rate, Li2CsBi has a low κL, which is 0.60 W m−1K−1 at 300 K. Research results show that n-type Li2CsBi has a higher ZT value of about 2.1 at T = 900 K, while p-type Li2RbBi has a higher ZT value of about 1.5 at the same temperature. These results provide an important theoretical basis for the application of Li2Rb(Cs)Bi in the field of thermoelectric conversion.

An interpretable formula for lattice thermal conductivity of crystals

Lattice thermal conductivity (κL) is a crucial physical property of crystals with applications in thermal management, such as heat dissipation, insulation, and thermoelectric energy conversion. However, accurately and rapidly determining κL poses a considerable challenge. In this study, we introduce a formula that achieves high precision (mean relative error = 8.97 %) and provides fast predictions, taking less than 1 min, for κL across a wide range of inorganic binary and ternary materials. Our interpretable, dimensionally aligned and physical grounded formula forecasts κL values for 4601 binary and 6995 ternary materials in the Materials Project database. Notably, we predict undiscovered high κL values for AlBN2 (κL = 101 W m−1 K−1) and the undetected low κL Cs2Se (κL = 0.98 W m−1 K−1) at room temperature. This method for determining κL streamlines the traditionally time-consuming process associated with complex phonon physics. It provides insights into microscopic heat transport and facilitates the design and screening of materials with targeted and extreme κL values through the application of phonon engineering. Our findings offer opportunities for controlling and optimizing macroscopic transport properties of materials by engineering their bulk modulus, shear modulus, and Grüneisen parameter.

Ultralow Thermal Conductivity in Vacancy-Ordered Halide Perovskite Cs3Bi2Br9 with Strong Anharmonicity and Wave-Like Tunneling of Low-Energy Phonons.

Halide perovskites are of great interest due to their exceptional optical and optoelectronic properties. However, thermal conductivity of many halide perovskites remains unexplored. In this study, an ultralow lattice thermal conductivity κL (0.24W m-1 K-1 at 300 K) is reported and its weak temperature dependence (≈T-0.27) in an all-inorganic vacancy-ordered halide perovskite, Cs3Bi2Br9. The intrinsically ultralow κL can be attributed to the soft low-lying phonon modes with strong anharmonicity, which have been revealed by combining experimental heat capacity and Raman spectroscopy measurements, and first-principles calculations. It is shown that the highly anharmonic phonons originate from the Bi 6s2 lone pair expression with antibonding states of Bi 6s and Br 4p orbitals driven by the dynamic BiBr6 octahedral distortion. Theoretical calculations reveal that these low-energy phonons are mostly contributed by large Br motions induced dynamic distortion of BiBr6 octahedra and large Cs rattling motions, verified by the synchrotron X-ray pair distribution function analysis. In addition, the weak temperature dependence of κL can be traced to the wave-like tunneling of phonons, induced by the low-lying phonon modes. This work reveals the strong anharmonicity and wave-like tunneling of low-energy phonons for designing efficient vacancy-ordered halide perovskites with intrinsically low κL.

Strong low-energy rattling modes enabled liquid-like ultralow thermal conductivity in a well-ordered solid

ABSTRACT Crystalline solids exhibiting inherently low lattice thermal conductivity (κL) are of great importance in applications such as thermoelectrics and thermal barrier coatings. However, κL cannot be arbitrarily low and is limited by the minimum thermal conductivity related to phonon dispersions. In this work, we report the liquid-like thermal transport in a well-ordered crystalline CsAg5Te3, which exhibits an extremely low κL value of ∼0.18 Wm−1K−1. On the basis of first-principles calculations and inelastic neutron scattering measurements, we find that there are lots of low-lying optical phonon modes at ∼3.1 meV hosting the avoided-crossing behavior with acoustic phonons. These strongly localized modes are accompanied by weakly bound rattling Ag atoms with thermally induced large amplitudes of vibrations. Using the two-channel model, we demonstrate that coupling of the particle-like phonon modes and the heat-carrying wave-like phonons is essential for understanding the low κL, which is heavily deviated from the 1/T temperature dependence of the standard Peierls theory. In addition, our analysis indicates that the soft structural framework with liquid-like motions of the fluctuating Ag atoms is the underlying cause that leads to the suppression of the heat conduction in CsAg5Te3. These factors synergistically account for the ultralow κL value. Our results demonstrate that the liquid-like heat transfer could indeed exist in a well-ordered crystal.

High thermoelectric performance in hollandite-type KxTi8O16-based oxides with complex crystal structure

Thermoelectric (TE) oxides are paid great attention due to their good thermal stability, but the high lattice thermal conductivity (κL) largely impedes their further development. In this paper, a Hollandite-type structure and multiple dopants in KxTi8O16-based oxides are studied to seek for an ultralow κL. Benefited from the complex crystal structure, a relatively low κL (2.13 W m−1 K−1 at 373 K) is obtained in K1.78Ti8O16. The Ba dopant can make the [TiO6] octahedra undistorted and increase the Ti3+ amount, leading to a doubled power factor. Meanwhile, the dual-doping effect of Ba and Nb dopants can further decrease the κL to 0.85 W m−1 K−1. Thus, a competitive zT value of 0.18 is obtained in Ba1.15Ti7.2Nb0.8O16 at 1073 K. This work demonstrates that the TE performance of Hollandite-type oxides deserves to be further studied and a complex crystal structure can be designed to achieve a high zT value.

Thermal Transport Properties of Two-Dimensional Janus MoXSiN2 (X = S, Se, and Te).

The design of Janus materials offers an effective means of regulating both their physical and chemical properties, leading to their application in various fields. However, the underlying mechanism governing the modulation of the thermal transport characteristics through the construction of Janus materials remains unclear. In this work, we introduce VI-group elements into the MoSi2N4 structure, yielding two-dimensional Janus MoXSiN2 (X = S, Se, and Te) and systematically investigate their thermal transport properties based on first-principles calculation methods. Our findings reveal that the lattice thermal conductivities (κl) of MoSSiN2, MoSeSiN2, and MoTeSiN2 are 47.2, 24.3, and 40.6 W/mK at 300 K, respectively, significantly lower than that of MoSi2N4 (224 W/mK). Such low κl values mainly come from the introduction of X atoms, which enhances phonon scattering and reduces phonon vibration frequencies. In addition, MoTeSiN2 exhibits a higher κl compared to MoSeSiN2, contrary to the trend observed in most materials containing VI-group elements, where κl decreases gradually from S to Te. This anomalous behavior can be attributed to the competitive result between its lower phonon vibrational frequency and weaker phonon anharmonicity of MoTeSiN2. This work elucidates the inherent mechanism governing the modulation of thermal transport properties in Janus materials, thereby enhancing the potential application of Janus MoXSiN2 in engineering thermal management.

Effects of Rattling Behavior of K and Cd Atoms along Different Directions in Anisotropic KCdAs on Lattice Thermal Transport and Thermoelectric Properties

We employ advanced first principles methodology, merging self‐consistent phonon theory and the Boltzmann transport equation, to comprehensively explore the thermal transport and thermoelectric properties of KCdAs. Notably, the study accounts for the impact of quartic anharmonicity on phonon group velocities in the pursuit of lattice thermal conductivity and investigates 3ph and 4ph scattering processes on phonon lifetimes. Through various methodologies, including examining atomic vibrational modes and analyzing 3ph and 4ph scattering processes, the article unveils microphysical mechanisms contributing to the low κL within KCdAs. Key features include significant anisotropy in Cd atoms, pronounced anharmonicity in K atoms, and relative vibrations in non‐equivalent As atomic layers. Cd atoms, situated between As layers, exhibit rattling modes and strong lattice anharmonicity, contributing to the observed low κL. Remarkably flat bands near the valence band maximum translate into high PF, aligning with ultralow κL for exceptional thermoelectric performance. Under optimal temperature and carrier concentration doping, outstanding ZT values are achieved: 4.25 (a(b)‐axis, p‐type, 3 × 1019 cm−3, 500 K), 0.90 (c‐axis, p‐type, 5 × 1020 cm−3, 700 K), 1.61 (a(b)‐axis, n‐type, 2 × 1018 cm−3, 700 K), and 3.06 (c‐axis, n‐type, 9 × 1017 cm−3, 700 K).

Structure Low Dimensionality and Lone-Pair Stereochemical Activity: the Key to Low Thermal Conductivity in the Pb-Sn-S System.

Recently, metal sulfides have begun to receive attention as potential cost-effective materials for thermoelectric applications beyond optoelectronic and photovoltaic devices. Herein, based on a comparative analysis of the structural and transport properties of 2D PbSnS2 and 1D PbSnS3, we demonstrate that the intrinsic effects that govern the low lattice thermal conductivity (κL) of these sulfides originate from the combination of the low dimensionality of their crystal structures with the stereochemical activity of the lone-pair electrons of cations. The presence of weak bonds in these materials, responsible for phonon scattering, results in inherently low κL of 1.0 W/m K in 1D PbSnS3 and 0.6 W/m K in 2D PbSnS2 at room temperature. However, the nature of the thermal transport is quite distinct. 1D PbSnS3 exhibits a higher thermal conductivity with a crystalline-like peak at low temperatures, while 2D PbSnS2 demonstrates glassy thermal conductivity in the entire temperature range investigated. First-principles density functional theory calculations reveal that the presence of antibonding states below the Fermi level, especially in PbSnS2, contributes to the very low κL. In addition, the calculated phonon dispersions exhibit very soft acoustic phonon branches that give rise to soft lattices and very low speeds of sounds.

Understanding the origin of the high thermoelectric figure of merit of Zintl-phase KCaBi.

Herein, we have investigated the unexplored thermoelectric properties of Zintl-phase KCaBi using first-principles calculation and the solution of the Boltzmann transport equation. KCaBi shows intrinsically very low lattice thermal conductivities (κl) along the (x(y), and z)-directions of (1.78, 0.68) and (1.15, 0.43) W m-1 K-1 at 300 and 800 K, respectively. Along with the effect of very low κl, the high figure of merit (ZT) for p-type KCaBi results from the high Seebeck coefficients (S) and optimal electrical conductivities (σ), which originate from the high and steep total density of state (TDOS) at the valence band edge and the less dispersed multi-valley nature of the valence band edge in the band structure. On the other hand, large ZT for n-type KCaBi results from moderate S and high σ caused by the sloped TDOS at the conduction band edge and the highly dispersed nature of the conduction band edge in the band structure, and very low values of κl. The highest ZT of KCaBi that we obtained at 800 K along the (x(y), and z)-directions was (1.83, 0.80) for the p-type case at a hole concentration of 1021 cm-3 and (1.36, 1.22) for the n-type case at electron concentration 7 × 1018 cm-3. Our study demonstrates that both p-type and n-type KCaBi have the potential to be promising thermoelectric materials.

Anomalous thermal transport and high thermoelectric performance of Cu-based vanadate CuVO3

Thermoelectric (TE) conversion technology, capable of transforming heat into electricity, is critical for sustainable energy solutions. Many promising TE materials contain rare or toxic elements, so the development of cost-effective and eco-friendly high-performance TE materials is highly urgent. Herein, we explore the thermal transport and TE properties of transition metal vanadate CuVO3 by using first-principles calculation. On the basis of the unified theory of heat conduction, we uncover the hierarchical thermal transport feature in CuVO3, where wave-like tunneling makes a significant contribution to the lattice thermal conductivity (κl) and results in the anomalously weak temperature dependence of κl. This is primarily attributable to the complex phononic band structure caused by the heterogeneity of Cu–O and V–O bonds. Simultaneously, we report a high power factor of 5.45 mW·K−2·m−1 realized in hole-doped CuVO3, which arises from a high electrical conductivity and a large Seebeck coefficient enabled by the multiple valleys and large electronic density of states near the valence band edge. Impressively, the low κl and the high power factor make p-typed CuVO3 have ZT of up to 1.39, with the excellent average ZT above 1.0 from 300 to 600 K, which is superior to most reported Cu-based TE materials. Our findings suggest that the CuVO3 compound is a promising candidate for energy conversion applications in innovative TE devices.

Revisiting lattice thermal conductivity of CsCl: The crucial role of quartic anharmonicity

Thermal conductivity (κL) plays a critical role in thermal management applications. Usually, crystals with simpler structures exhibit higher κL due to fewer phonon scatterings. However, cesium chloride (CsCl) presents an anomaly, demonstrating an unexpectedly low κL of 1.0 W m−1 K−1 at 300 K, as observed in Professor Iversen's experimental measurement despite its simple structure. This prompts a need for understanding anomalous low κL and matching theory with experimental observations. Our study brings forth several findings for CsCl: (i) relying solely on three-phonon scattering inadequately captures κL. (ii) Anharmonic phonon renormalization significantly contributes to increased κL. (iii) Coherent phonons align temperature-dependent κL closely with the experiment. This work not only enhances understanding of anomalous κL in CsCl but also provides an approach to bridge the gap between experiment and theory in other crystals.

Highly Anisotropic to Isotropic Nature and Ultralow Out-of-Plane Lattice Thermal Conductivity of Layered PbClF-Type Materials.

Materials with an extreme lattice thermal conductivity (κl) are indispensable for thermal energy management applications. Layered materials provide an avenue for designing such functional materials due to their intrinsic bonding heterogeneity. Therefore, a microscopic understanding of the crystal structure, bonding, anharmonic lattice dynamics, and phonon transport properties is critically important for layered materials. Alkaline-earth halofluorides exhibit anisotropy from their layered crystal structure, which is strongly determined by axial bond(s), and it is attributed to the large axial ratio (c/a > 2) for CaBrF, CaIF, and SrIF, in which Br/I acts as a rattler, as evidenced from potential energy curves and phonon density of states. The low axial (c/a) ratio leads to relatively isotropic κl values in the BaXF (X = Cl, Br, I) series. MXF (M = Ca, Sr, Ba) compounds exhibit highly anisotropic (a large phonon transport anisotropy ratio of 10.95 for CaIF) to isotropic (a small phonon transport anisotropy ratio of 1.49 for BaBrF) κl values despite their iso-structure. Moreover, ultralow κl (<1 W/m K) values have been predicted for CaBrF, CaIF, and SrIF in the out-of-plane direction due to weak van der Waals (vdWs) bonding. Overall, this comprehensive study on MXF compounds provides insights into designing low κl layered materials with a large axial ratio by fine-tuning out-of-plane bonding from ionic to vdWs bonding.

Low Thermal Conductivity and High Thermoelectric Performance of Nb-Doped Quarternary Mixed Crystal Nb0.05W0.95-xMox(Se1-xSx)2.

Transition-metal dichalcogenide WSe2 has attracted increasing interest due to its large thermopower (S), low-cost, and environment-friendly constituents. However, its thermoelectric figure of merit, ZT, of WSe2 is limited due to its large lattice thermal conductivity (κL) and low electrical conductivity. In view of WSe2 and MoS2 having the same crystal structure, here we designed and prepared Nb-doped quarternary mixed crystal (MC) Nb0.05W0.95-xMox(Se1-xSx)2 (0 ≤ x ≤ 0.095). The results indicate that the κL of the MC can reach as low as 0.12 W m K-1 at 850 K, being 93% smaller than that of WSe2. Our analysis reveals that its low κL originates chiefly from intense scattering of both high-frequency phonons from point defects (mainly alloying elements) and mid/low-frequency phonons from MoS2 inclusions residual within MC. In addition, the alloying of WSe2 with MoS2 causes a 5-fold increase in cation vacancies (VW‴'), leading to a large increase in hole concentration and electrical conductivity, which gives rise to a ∼7.5 times increase in power factor (reaching 4.2 μ W cm-1 K-2 at 850 K). As a result, a record high ZTmax = 0.63 is achieved at 850 K for the MC sample with x = 0.076, which is 20 times larger than that of WSe2, demonstrating that MC Nb0.05W0.95-xMox(Se1-xSx)2 is a promising thermoelectric material.

Self-consistent phonon calculations and quartic anharmonic lattice thermal conductivity in 2D InS monolayer

Low lattice thermal conductivity (κl) is a crucial factor for higher figure-of merit and hence the efficiency of thermoelectric generators. There are several reports on intrinsically low κl values in two-dimensional (2D) van der Waals materials using density functional theory and molecular dynamics simulations. In general, phonon dispersions are studied at absolute zero temperature using the finite-displacement approach within harmonic approximations. In addition, the κlis calculated using the third-order cubic interatomic force constants (IFCs) by solving the Boltzmann transport equation for phonons. In these calculations, we use quartic IFCs to solve self-consistent phonon equations to obtain dynamical dispersion relations at a finite temperature of 300 K using finite-temperature Green’s function for Bosonic systems in 2D indium sulfide (InS) monolayer. The cubic and quartic IFCs are calculated using machine learning algorithms, namely, the ordinary least square fitting and the least absolute shrinkage and selection operator. It was found that there is a lowering of the renormalized anharmonic phonon frequencies in the dispersion relations at 300 K upon the inclusion of quartic IFCs and anharmonic terms in the case of the InS monolayer. Thus, the κlvalue is reduced to 0.6 W/mK as compared to 0.9 W/mK obtained using cubic IFCs.

Anharmonicity and weak bonding-driven extraordinary thermoelectric performance in wrinkled SnSe monolayer with low lattice thermal conductivity

SnSe compound (Nature, 2014, 508, 373–377) has become the star in the field of thermoelectric (TE) materials owing to the environmental friendliness, abundant reserves, and excellent performance. In the present work, the electronic structures, thermal and electronic transport, as well as TE properties of a two-dimensional (2D) wrinkled SnSe monolayer are comprehensively investigated in combination with first-principles calculations and Boltzmann transport theory. The SnSe monolayer is an indirect semiconductor with a bandgap of 2.88 eV using Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. The “multivalley” band structure of SnSe monolayer is not only beneficial for maximizing the power factor, but also leads to low lattice thermal conductivity (κl) (1.37/1.42 W/mK @ 300 K armchair-/zigzag-direction). The further crystal orbital Hamilton population (COHP) analysis shows that the low κl in SnSe monolayer is attributed to weak antibonding state below the Fermi level, which in turn weakens the chemical bonding and leads to the mutual exclusion of Sn and Se atoms. As a consequence, the softening of phonon modes and a significant reduction in the phonon group velocity are discovered for the SnSe monolayer, which is beneficial for strong anharmonicity and significant phonon scatterings. Additionally, the electronic transport properties of the 2D SnSe monolayer are evaluated by taking into account the electron-phonon interactions, and the optimal ZTs of 2.13 (armchair-direction) and 3.01 (zigzag-direction) are achieved for n-type and p-type SnSe monolayer at 900 K, respectively. Our present work can not only provide fundamental understanding of thermal and electronic transport properties of wrinkled SnSe monolayer, but also shed some light on the theoretical design of low dimensional SnSe-layered material in thermoelectric applications.

Lone-pair electron-induced low lattice thermal conductivity and excellent thermoelectric performance of AuX (X = S, Se, Te) monolayers

We present a detailed study on the phonon thermal transport and thermoelectric (TE) properties of gold monochalcogenide AuX (X = S, Se, Te) monolayers via first-principles calculations and the Boltzmann transport theory. At room temperature, the calculated lattice thermal conductivity (κl) values in the x-direction (y-direction) were determined to be 12.66 (3.59), 6.06 (1.23), and 3.02 (0.40) W/(m·K) for the AuS, AuSe, and AuTe monolayers, respectively. The analysis of scattering matrix elements and anharmonic scattering rates suggested that the presence of strong bond anharmonicity leads to low κl values. This anharmonicity was induced by the nonlinear electrostatic repulsive force between lone-pair electrons (LPEs) surrounding the chalcogen atom and adjacent bonding electron. Furthermore, the AuS monolayer exhibited the highest bond anharmonicity among the three monolayers. This can be attributed to the reduced strength of the electrostatic repulsive force when electronegativity decreased from S to Se and Te. Although the AuS monolayer exhibited the strongest bond anharmonicity, its κl was still the largest, demonstrating that among the factors that influence κl, harmonic factors have a greater effect than anharmonic parameters. When the atomic mass was increased, the phonon frequencies, phonon group velocities, and κl decreased. Benefiting from low κl induced by LPEs, the maximum ZT values of p-type doped AuSe and AuTe monolayers exceeded 1.0 and 2.0 at T = 800 K, respectively. These results not only confirmed that the introduction of LPEs can reduce the lattice thermal conductivity and enhance the TE performance of 2D materials, but also demonstrated the promising potential of the 2D AuX family for applications in high-temperature TE devices.