Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at 300 K is 30.15 W m⁻¹ K⁻¹ (zigzag) and 13.65 W m⁻¹ K⁻¹ (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relationship with temperature when the temperature is higher than Debye temperature (Θ_D = 278.66 K). In comparison to graphene, the minor contribution around 5% of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.

New classes of two-dimensional (2D) materials beyond graphene, including layered and non-layered, and their heterostructures, are currently attracting increasing interest due to their promising applications in nanoelectronics, optoelectronics and clean energy, where thermal transport is a fundamental physical parameter. In this paper, we systematically investigated the phonon transport properties of the 2D orthorhombic group IV–VI compounds of GeS, GeSe, SnS and SnSe by solving the Boltzmann transport equation (BTE) based on first-principles calculations. Despite their similar puckered (hinge-like) structure along the armchair direction as phosphorene, the four monolayer compounds possess diverse anisotropic properties in many aspects, such as phonon group velocity, Young's modulus and lattice thermal conductivity (κ), etc. Especially, the κ along the zigzag and armchair directions of monolayer GeS shows the strongest anisotropy while monolayer SnS and SnSe show almost isotropy in phonon transport. The origin of the diverse anisotropy is fully studied and the underlying mechanism is discussed in details. With limited size, the κ could be effectively lowered, and the anisotropy could be effectively modulated by nanostructuring, which would extend the applications to nanoscale thermoelectrics and thermal management. Our study offers fundamental understanding of the anisotropic phonon transport properties of 2D materials, and would be of significance for further study, modulation and applications in emerging technologies.

We systematically investigated the geometric, electronic and thermoelectric (TE) properties of bulk black phosphorus (BP) under strain. The hinge-like structure of BP brings unusual mechanical responses such as anisotropic Young's modulus and negative Poisson's ratio. A sensitive electronic structure of BP makes it transform among metal, direct and indirect semiconductors under strain. The maximal figure of merit ZT of BP is found to be 0.72 at 800[emsp14]K that could be enhanced to 0.87 by exerting an appropriate strain, revealing BP could be a potential medium-high temperature TE material. Such strain-induced enhancements of TE performance are often observed to occur at the boundary of the direct-indirect band gap transition, which can be attributed to the increase of degeneracy of energy valleys at the transition point. By comparing the structure of BP with SnSe, a family of potential TE materials with hinge-like structure are suggested. This study not only exposes various novel properties of BP under strain, but also proposes effective strategies to seek for better TE materials.

Two-dimensional (2D) materials with graphene as a representative have been intensively studied for a long time. Recently, monolayer gallium nitride (ML GaN) with honeycomb structure was successfully fabricated in experiments, generating enormous research interest for its promising applications in nano- and opto-electronics. Considering all these applications are inevitably involved with thermal transport, systematic investigation of the phonon transport properties of 2D GaN is in demand. In this paper, by solving the Boltzmann transport equation (BTE) based on first-principles calculations, we performed a comprehensive study of the phonon transport properties of ML GaN, with detailed comparison to bulk GaN, 2D graphene, silicene and ML BN with similar honeycomb structure. Considering the similar planar structure of ML GaN to graphene, it is quite intriguing to find that the thermal conductivity (κ) of ML GaN (14.93 W mK⁻¹) is more than two orders of magnitude lower than that of graphene and is even lower than that of silicene with a buckled structure. Systematic analysis is performed based on the study of the contribution from phonon branches, comparison among the mode level phonon group velocity and lifetime, the detailed process and channels of phonon–phonon scattering, and phonon anharmonicity with potential energy well. We found that, different from graphene and ML BN, the phonon–phonon scattering selection rule in 2D GaN is slightly broken by the lowered symmetry due to the large difference in the atomic radius and mass between Ga and N atoms. Further deep insight is gained from the electronic structure. Resulting from the special sp orbital hybridization mediated by the Ga-d orbital in ML GaN, the strongly polarized Ga–N bond, localized charge density, and its inhomogeneous distribution induce large phonon anharmonicity and lead to the intrinsic low κ of ML GaN. The orbitally driven low κ of ML GaN unraveled in this work would make 2D GaN prospective for applications in energy conversion such as thermoelectrics. Our study offers fundamental understanding of phonon transport in ML GaN within the framework of BTE and further electronic structure, which will enrich the studies of nanoscale phonon transport in 2D materials and shed light on further studies.

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 ($\kappa$) 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 $\kappa$ 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 $\kappa$ 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.

Efficient heat dissipation, which is featured by high thermal conductivity, is one of the crucial issues for the reliability and stability of nanodevices. However, due to the generally fast $1/T$ decrease of thermal conductivity with temperature increase, the efficiency of heat dissipation quickly drops down at an elevated temperature caused by the increase of work load in electronic devices. To this end, pursuing semiconductor materials that possess large thermal conductivity at high temperature, i.e., slower decrease of thermal conductivity with temperature increase than the traditional $\kappa \sim 1/T$ relation, is extremely important to the development of disruptive nanoelectronics. Recently, monolayer gallium nitride (GaN) with a planar honeycomb structure emerges as a promising new two-dimensional material with great potential for applications in nano- and optoelectronics. Here, we report that, despite the commonly established $1/T$ relation of thermal conductivity in plenty of materials, monolayer GaN exhibits anomalous behavior that the thermal conductivity almost decreases linearly over a wide temperature range above 300 K, deviating largely from the traditional $\kappa \sim 1/T$ law. The thermal conductivity at high temperature is much larger than the expected thermal conductivity that follows the general $\kappa \sim 1/T$ trend, which would be beneficial for applications of monolayer GaN in nano- and optoelectronics in terms of efficient heat dissipation. We perform detailed analysis on the mechanisms underlying the anomalously temperature-dependent thermal conductivity of monolayer GaN in the framework of Boltzmann transport theory and further get insight from the view of electronic structure. Beyond that, we also propose two required conditions for materials that would exhibit similar anomalous temperature dependence of thermal conductivity: large difference in atom mass (huge phonon band gap) and electronegativity (LO-TO splitting due to strong polarization of bond). Our study offers fundamental understanding of phonon transport in monolayer GaN, and the insight gained from this study is of great significance for the design and search of materials superior for applications in nano- and optoelectronics in terms of high-performance thermal management.