Dual-channel phonon transport in two-dimensional materials with low thermal conductivity

Searching for compounds with intrinsic low lattice thermal conductivity has been proven a successful strategy for achieving high thermoelectric performance. Herein, employing density functional theory calculations combined with electron and phonon Boltzmann transport theories, we report that Sr3AlSb3 and Ba3AlSb3 within the Zintl 3–1–3 compositional family exhibit record low thermal conductivities of 0.78 and 0.55 W/mK at room temperature, respectively. These low thermal conductivities are rooted in low-energy optical phonon modes with strong anharmonicity and the emergence of high-energy flat optical phonon modes with zero contribution to the lattice thermal conductivity. Heavier cationic atoms are found to soften low-lying optical phonon modes, which enhance phonon scattering and, therefore, favor a lower thermal conductivity. These combined characteristics lead to high and balanced figure of merit values around 2.3 for Zintl Ba3AlSb3 at both optimal p-type and n-type doping and high temperature. Our work highlights the important role of flat optical phonon modes on designing promising thermoelectric materials with intrinsic low thermal conductivity.

After the discovery of graphene, there have been tremendous efforts in exploring various layered two-dimensional (2D) materials for their potential applications in electronics, optoelectronics, as well as energy conversion and storage. One of such 2D materials, SnS2, which is earth abundant, low in toxicity, and cost effective, has been reported to show a high on/off current ratio, fast photodetection, and high optical absorption, thus making this material promising for device applications. Further, a few recent theoretical reports predict high electrical conductivity and Seebeck coefficient in its bulk counterparts. However, the thermal properties of SnS2 have not yet been properly explored, which are important to materialize many of its potential applications. Here, we report the thermal properties of SnS2 measured using the optothermal method and supported by density functional theory (DFT) calculations. Our experiments suggest very low in-plane lattice thermal conductivity (\k{appa} = 3.20 +- 0.57 W m-1 K-1) and cross-plane interfacial thermal conductance per unit area (g = 0.53 +- 0.09 MW m-2 K-1) for monolayer SnS2 supported on a SiO2/Si substrate. The thermal properties show a dependence on the thickness of the SnS2 flake. Based on the findings of our DFT calculations, the very low value of the lattice thermal conductivity can be attributed to low group velocity, a shorter lifetime of the phonons, and strong anharmonicity in the crystal. Materials with low thermal conductivity are important for thermoelectric applications as the thermoelectric power coefficient goes inversely with the thermal conductivity.

Loose bonding induced ultralow lattice thermal conductivity of a metallic crystal KNaRb

Two-dimensional (2D) materials have emerged as a broad platform for exploring promising thermoelectric materials. Motivated by the fabrication of diverse artificially designed Te-based 2D materials with high thermoelectric performance, here, we predicted 2D hexagonal CdTe and pentagonal CdTe2 for potential thermoelectric materials, using the particle swarm optimization (PSO) method combined with density functional theory. CdTe and CdTe2 show predicted direct/indirect band gaps of 1.82 and 1.96 eV, respectively. Chemical bonding analysis revealed that all the Te atoms in CdTe are coupled through uniform ionic bonding. CdTe2 exhibits bonding heterogeneity, arising from weak the Cd–Te ionic bonding and strong Te–Te covalent bonding. Based on Boltzmann transport theory, we found that the bonding heterogeneity in CdTe2 favors low lattice conductivity. The calculated lattice thermal conductivity of CdTe2 is 0.33 Wm–1 K–1 at 300 K, which was contributed by the weaker coupling between acoustic and optical phonon modes, low group velocities of the acoustic modes, and high lattice anharmonicity. On the other hand, the occupied π*5p, π5p, and σ5p bondings in Te–Te pairs significantly facilitate the electrical conductivity and enhance the Seebeck coefficient of p-type CdTe2. The low thermal conductivity and high power factor in CdTe2 give rise to a high thermoelectric performance at low temperature. Our findings should encourage the exploration of 2D materials for thermoelectric applications with strong bonding heterogeneity.

Two-dimensional materials, such as graphene, boron nitride and transition metal dichalcogenides, have attracted increased interest due to their potential applications in electronics and optoelectronics. Thermal transport in two-dimensional materials could be quite different from three-dimensional bulk materials. This article reviews the progress on experimental measurements and theoretical modeling of phonon transport and thermal conductivity in two-dimensional materials. We focus our review on a few typical two-dimensional materials, including graphene, boron nitride, silicene, transition metal dichalcogenides, and black phosphorus. The effects of different physical factors, such as sample size, strain and defects, on thermal transport in Two-dimensional materials are summarized. We also discuss the environmental effect on the thermal transport of two-dimensional materials, such as substrate and when two-dimensional materials are presented in heterostructures and intercalated with inorganic components or organic molecules.

Understanding the origins of low lattice thermal conductivity in a novel two-dimensional monolayer NaCuS for achieving medium-temperature thermoelectric applications

Two-dimensional (2D) phosphorene, which possesses fascinating physical and chemical properties distinctively different from other 2D materials, calls for a fundamental understanding of thermal transport properties for its rapidly growing applications in nano- and optoelectronics and thermoelectrics. However, even the basic phonon property, for example, the exact value of the lattice thermal conductivity ($\ensuremath{\kappa}$) of phosphorene reported in the literature, can differ unacceptably by one order of magnitude. More importantly, the fundamental physics underlying its unique properties such as strong phonon anharmonicity and unusual anisotropy remains largely unknown. In this paper, based on the analysis of electronic structure and lattice dynamics from first principles, we report that the giant phonon anharmonicity in phosphorene is associated with the soft transverse optical (TO) phonon modes and arises from the long-range interactions driven by the orbital governed resonant bonding. We also provide a microscopic picture connecting the anisotropic and low $\ensuremath{\kappa}$ of phosphorene to the giant directional phonon anharmonicity and long-range interactions, which are further traced back to the asymmetric resonant orbital occupations of electrons and characteristics of the hinge-like structure. The unambiguously low $\ensuremath{\kappa}$ of phosphorene obtained consistently by three independent ab initio methods confirms the phonon anharmonicity to a large extent and is expected to end the confusing huge deviations in previous studies. This work further pinpoints the necessity of including van der Waals interactions to accurately describe the interatomic interactions in phosphorene. We propose in 2D material that resonant bonding leads to low thermal conductivity, despite that it is originally found in three-dimensional (3D) thermoelectric and phase-change materials. Our study offers insights into phonon transport from the view of orbital states, which would be of great significance to the design of emerging phosphorene-based nanodevices.

We calculate the lattice thermal conductivities of the pyrite-type ZnSe2 at pressures of 0 and 10 GPa using the linearized phonon Boltzmann transport equation. We obtain a very low value [0.69 W/(mK) at room temperature at 0 GPa], comparable to the best thermoelectric materials. The vibrational spectrum is characterized by the isolated high-frequency optical phonon modes due to the stretching of Se-Se dimers and low-frequency optical phonon modes due to the rotation of Zn atoms around these dimers. The low-frequency optical phonon modes are characterized by a strong anharmonicity and will substantially increase the three-phonon scattering space which suppress the thermal conductivity. Interestingly, two transverse acoustic phonon modes with similar frequencies and wave vectors have very different degrees of anharmonicity depending on their polarization. We relate this to the low thermal conductivity and show that the anharmonicities of the transverse acoustic phonon modes are connected to the corresponding change in the pyrite parameter, which can be interpreted as a descriptor for the local volume change. To determine the thermoelectric performance of ZnSe2, we also investigate its electrical transport properties. The results show that both p-type or n-type ZnSe2 can show promising electrical transport properties. We trace this back to the complex energy isosurfaces of both valence and conduction bands. The low thermal conductivities and promising electrical transport properties lead to a large thermoelectric figure of merit of ZnSe2 for both p-type and n-type doping.

Thermal transport in graphene

Extremely strong four-phonon scattering and ultra-low lattice thermal conductivity due to quartic anharmonicity in fluoride perovskites XHgF3 (X = K, Rb)

Germanium telluride (GeTe) and its variants are promising compounds as high figure of merit thermoelectric materials due to their low lattice thermal conductivity. The strong anharmonicity and the intrinsic Ge vacancies are shown to be the origin of the low thermal conductivity. While the anharmonic effect on the lattice thermal conductivity has been systematically studied using the perturbation theory, the vacancy disorder has been treated perturbatively mostly as an extreme case of phonon-isotope scattering. This simplification ignores realistic features such as the nonbonding character and the detailed local environments near the vacancies. In this study, we calculate the lattice thermal conductivity of the cubic GeTe by considering the anharmonicity and the vacancy disorder on the same footing using the machine-learning potential molecular dynamics. We obtain the spectral function via the nonperturbative approaches, the velocity autocorrelation function, and the phonon unfolding scheme to investigate the effect of the vacancies on the lattice thermal conductivity. We find that the reduction in the lattice thermal conductivity by the vacancies originates from the momentum-dependent scattering of the acoustic phonon modes and the momentum-independent scattering of the optical phonon modes as determined by the strength of the anharmonicity.

Thermal transport in two-dimensional (2D) materials has attracted great attention since the discovery of high thermal conductivity in graphene, which is closely related to the hydrodynamic phonon transport. In this Perspective, we briefly summarize the recent progresses in studying hydrodynamic phonon transport in 2D materials, including both theoretical and experimental works. First, the criterion and numerical methods for studying hydrodynamic phonon transport are reviewed. We then discuss the physical mechanism and peculiar phenomena related to hydrodynamic phonon transport in 2D materials and finally present the challenge for future studies. This Perspective aims to provide the physical understanding of the hydrodynamic phonon transport, which might be beneficial to the exploration of novel thermal transport behaviors in 2D materials.

Confinement or dimensionality reduction is a novel strategy to reduce the lattice thermal conductivity and, consequently, to improve the thermoelectric conversion performance. Bismuth and tellurium based low-dimensional materials have great potential in this regard. The phonon transport and thermoelectric properties of Bi2Te2X (X = S, Se, Te) monolayers are systematically investigated by employing density functional theory and the Boltzmann transport equation. The calculated lattice thermal conductivity of these 2D systems ranges from ∼1.3 W m-1 K-1 (Bi2Te2Se) to ∼1.5 W m-1 K-1 (Bi2Te3) for a 10 μm system size at room temperature and considering spin-orbit coupling in harmonic force constants. This remarkably low lattice thermal conductivity is attributed to small group velocities and enhanced anharmonic phonon scattering rates. A detailed analysis is presented in terms of mode-level phonon group velocities, anharmonic scattering rates and phonon mean free paths. Our results reveal that the thermal transport in these 2D systems is dominated by in-plane transverse acoustic modes. Additionally, the thermal conductivity can be further reduced by decreasing the sample size due to phonon-boundary scattering. The thermoelectric properties including the Seebeck coefficient, power factor and electrical conductivity are calculated using the semi-classical Boltzmann transport equation within the rigid band approximation. The low thermal conductivities coupled with their high carrier mobilities lead to good thermoelectric power factors. With optimal carrier doping, a figure of merit ∼0.6 can be achieved at room temperature, which increases to ∼0.8 at 700 K, thus making them promising candidates for thermoelectric applications.

Various two-dimensional (2D) materials with a graphene-like buckled structure have emerged, and the β-phase AsP monolayer has been recently proposed to be thermodynamically stable from first-principles calculations. The studies of thermal transport are very useful for these 2D materials-based nano-electronics devices. Motivated by this, a comparative study of strain-dependent phonon transport of AsP monolayers is performed by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). It is found that the lattice thermal conductivity () of the AsP monolayer is very close to the one of As monolayer with a similar buckled structure, which is due to neutralization between the reduction of phonon lifetimes and group velocity enhancement from As to AsP monolayer. The corresponding room-temperature sheet thermal conductance of AsP monolayer is 152.5 . It is noted that the increasing tensile strain can harden a long wavelength out-of-plane (ZA) acoustic mode, and soften the in-plane longitudinal acoustic (LA) and transversal acoustic (TA) modes. Calculated results show that of AsP monolayer presents a nonmonotonic up-and-down behavior with increased strain. The unusual strain dependence is due to the competition among the reduction of phonon group velocities, improved phonon lifetimes of ZA mode and nonmonotonic up-and-down phonon lifetimes of TA/LA mode. It is found that acoustic branches dominate the in the considered strain range, and the contribution from ZA branch increases with increased strain, while it is opposite for TA/LA branch. By analyzing cumulative with respect to phonon mean free path, tensile strain can modulate effectively the size effects on in the AsP monolayer. Our work enriches the studies of thermal transports of 2D materials with graphene-like buckled structures, and strengthens the idea to engineer thermal transport properties by simple mechanical strain, and stimulates further experimental works to synthesize AsP monolayers.

Abnormal enhancement of thermal conductivity by planar structure: A comparative study of graphene-like materials