Activated lone-pair electrons lead to low lattice thermal conductivity: a case study of boron arsenide

TL;DR

This study demonstrates that activating lone-pair electrons through bond nanodesigning significantly reduces lattice thermal conductivity in boron arsenide, offering a new strategy for enhancing thermoelectric materials.

Contribution

It introduces a novel approach of using lone-pair electron activation via bond nanodesigning to lower thermal conductivity in materials like boron arsenide.

Findings

Lone-pair electron activation reduces thermal conductivity by over an order of magnitude.

The approach is extendable to other group III-V compounds with similar electronic features.

A correlation between electronegativity difference and thermal conductivity modulation is identified.

Abstract

Reducing thermal conductivity ($\kappa$) is an efficient way to boost the thermoelectric performance to achieve direct solid-state conversion to electrical power from thermal energy, which has lots of valuable applications in reusing waste resources. In this study, we propose an effective approach for realizing low $\kappa$ by introducing lone-pair electrons or making the lone-pair electrons stereochemically active through bond nanodesigning. As a case study, by cutting at the (111) cross section of the three-dimensional cubic boron arsenide (c-BAs), the $\kappa$ is lowered by more than one order of magnitude in the resultant two-dimensional system of graphene-like BAs (g-BAs) due to the stereochemically activated lone-pair electrons. Similar concept can be also extended to other systems with lone-pair electrons beyond BAs, such as group III-V compounds, where a strong correlation between $\kappa$ modulation and electronegativity difference for binary compounds is found. Thus, the lone-pair electrons combined with a small electronegativity difference could be the indicator of lowering $\kappa$ through bond nanodesigning to change the coordination environment. The proposed approach for realizing low $\kappa$ and the underlying mechanism uncovered in this study would largely benefit the design of thermoelectric devices with improved performance, especially in future researches involving novel materials for energy applications.

Equations

$$ZT=S^2\sigma T/\kappa ,$$

$${\omega }_j(\vec{q})\pm {\omega }_{j^{\prime }}(\overrightarrow{q^{\prime }})$$

$$\vec{q}\pm \overrightarrow{q^{\prime }}$$

$$\gamma =-\frac{V}{\omega }\frac{\partial \omega }{\partial V}.$$

$$y=E_0+a_{1}x+a_2{x}^2+a_3{x}^3,$$

Full text

I Introduction

Due to the ability of firsthand solid-state conversion to electrical power from thermal energy, especially for waste heat reusing, thermoelectrics have attracted a lot of attention in recent yearsNature.2012.489..414 . Thermoelectrics have lots of valued applications in recovering resources and thus may make crucial contributions to the crisis of environment by solving energy problemsQINsrep046946 . Moreover, thermoelectrics possess the advantages of having no moving components and being environmentally friendly compared to traditional mechanical heat engines. Generally, the thermoelectric efficiency and performance can be characterized by a dimensionless figure of meritScience.2016.351.6269.141-144

[TABLE]

where $S$, $\sigma$, $T$ and $\kappa$ are thermopower (Seebeck coefficient), electrical conductivity, absolute temperature and total thermal conductivity, respectively. The commercial applications in industry of thermoelectric devices are currently limited by the low ZT merit. To approach the Carnot coefficient as closely as possible, a high energy generation efficiency is necessary, which corresponds to a large ZT merit. Based on the definition [Eq. (1)], lowering the $\kappa$ would be more efficient to boost the ZT merit due to the inversely proportional relationPhysRevB.89.054310 .

Previous theoretical studies predicted that cubic boron arsenide ($c$-BAs) in the bulk form has an exceptionally high $\kappa$ over 2000 W/mK, which is comparable to the bulk carbon crystals (diamond) with record highest $\kappa$ PhysRevLett.111.025901 . The ultra-high $\kappa$ of $c$-BAs was analyzed to be resulted from the large phonon band gap between acoustic and optical phonon branches together with the bunching of the acoustic phonon branches, which reduce phonon-phonon scattering PhysRevLett.111.025901 . The features of the phonon dispersion of $c$-BAs analyzed based on first-principles calculations are then confirmed by experimental measurements based on inelastic $x$-ray scatteringPhys.Rev.B.2016.94.22.220303 . By considering the phonon-phonon scattering involving four phonons, Feng et al.PhysRevB.2017.96.161201 found that the $\kappa$ of $c$-BAs reduces from 2200 to 1400 W/mK, which was recently confirmed by experimental studies Science.2018.Yongjie.Hu.5522 ; Science.2018.cahill.8982 ; Science.2018.zhifeng.ren.7932 . Experimental measurements reveal that the $\kappa$ of BAs can be suppressed by the arsenic deficiency or vacancy in the BAs sampleAppl.Phys.Lett..2015.106.7.074105 and the phonon-boundary scattering in BAs microstructures PhysRevB.88.214303 ; Appl.Phys.Lett..2016.108.20.201905 . However, the obtained $\kappa$ of BAs is still too high that limits its potential applications in thermoelectrics, despite that the Seebeck coefficient and thermoelectric power factor of BAs is comparable to those of bismuth telluride, Appl.Phys.Lett..2016.108.20.201905 which is one of the most commonly used thermoelectric materials. Thus, it would be meaningful if one can find an effective approach to lower the intrinsic $\kappa$ of BAs to benefit its applications in thermoelectrics. Moreover, the approach that makes such a high $\kappa$ material applicable for thermoelectrics would also largely benefit the design of thermoelectric devices with improved performance by lowering $\kappa$, especially in the future research involving novel materials for energy applications.

In this paper, we propose an effective approach for realizing low $\kappa$ by bond nanodesigning to make the lone-pair electrons stereochemically active. As a result, much lower $\kappa$ can be generally achieved, except the case of graphene (Fig. 1). As a specific case study, when transforming the three-dimensional (3D) $c$-BAs into the two-dimensional (2D) graphene-like BAs ($g$-BAs), the $\kappa$ is found to be lowered by more than one order of magnitude (Fig. 2) due to the stereochemically actived lone-pair electrons. The underlying mechanism is analyzed based on the comparative study on the thermal transport properties of $g$-BAs, $c$-BAs, graphene, and diamond, considering the similarity of the transformation from 3D cubic to 2D honeycomb planar geometry structures ($c$-BAs $\to$ $g$-BAs vs. diamond $\to$ graphene) but the opposite trend for the $\kappa$ modulation. Moreover, deep insight into the electronic origin is gained by performing fundamental analysis on the electronic structures.

II Results and discussions

II.1 The anomalously low $\kappa$ of $g$-BAs

By cutting the 3D cubic structure of $c$-BAs at the (111) cross section, $g$-BAs can be obtained with similar planar honeycomb structure as graphene ($c$-BAs $\to$ $g$-BAs vs. diamond $\to$ graphene). The $\kappa$ of $g$-BAs is obtained to be 137.70 W/mK, which is more than one order of magnitude lower than that of graphene (3094.98 W/mK). Note that only 3-phonons scattering is considered here for simplicity. The $\kappa$ of $g$-BAs could be further lowered if 4-phonons scattering is included. The in-plane longitudinal acoustic (LA), transverse acoustic (TA) and out-pf-plane flexural acoustic (FA) phonon branches contribute 28.5

%

, 43.1

%

 and 26.9

%

, respectively. The $\kappa$ of $g$-BAs are 89.3 and 137.7 W/mK before and after iteration, respectively. The large difference in the RTA and iteration result means that the proportion of N-process could be large and there exists strong phonon hydrodynamics in $g$-BAs.

The lower $\kappa$ of $g$-BAs than graphene is very intriguing considering the similarity of their planar honeycomb geometry structures [Fig. 2(a,b)]. In particular, the $\kappa$ of $c$-BAs is comparable to diamond [Fig. 2(c)]PhysRevLett.111.025901 , both of which share the same cubic structures and are the 3D counterparts of $g$-BAs and graphene, respectively [Fig. 2(a,b)]. However, when transforming from 3D to 2D, huge difference emerges that the $\kappa$ of $g$-BAs (the 2D counterpart of $c$-BAs) is much lower than that of graphene (the 2D counterpart of diamond), despite the comparable $\kappa$ of $c$-BAs and diamond [Fig. 2(c)]. In the following, we perform detailed analysis to achieve fundamental understanding on the anomalously lowered $\kappa$ of $g$-BAs compared to $c$-BAs, diamond, and graphene. With the uncovered underlying mechanism, the generally lower $\kappa$ of systems in 2D than 3D form as shown in Fig. 1 can also be well understood.

II.2 Large scattering phase space

Fig. 3(a) shows the phonon dispersion of $g$-BAs, in comparison with $c$-BAs [Fig. 3(b)]. It was claimed in previous studyPhysRevLett.111.025901 that the ultra-high $\kappa$ of $c$-BAs comparable to diamond is resulted from the large phonon band gap between acoustic and optical phonon branches together with the bunching of the acoustic phonon branches. The features of the phonon dispersion of $c$-BAs analyzed based on first-principles calculations are then confirmed by experimental measurements based on inelastic $x$-ray scatteringPhys.Rev.B.2016.94.22.220303 , as reproduced in Fig. 3(b). When transforming from 3D $c$-BAs to 2D $g$-BAs, the phonon dispersions show some different features, which could have remarkable effect on the $\kappa$. ($i$) The phonon band gap in $g$-BAs is 13.00 THz, which is larger than that in $c$-BAs (9.28 THz). The larger phonon band gap is expected to not have a negative effect on the $\kappa$ for the 3-phonons scattering processes considered here. ($ii$) The $z$-direction optical (ZO) phonon branch in $g$-BAs is below the bandgap as highlighted in Fig. 3(a), which could lead to more scattering probability by coupling with acoustic phonon branches (especially LA). See Supplemental Note 1 and Supplemental Figure 2 for more information on the coupling as revealed by phonon-phonon scattering channels. Such coupling is absent in the 3D $c$-BAs. ($iii$) The bunching of acoustic phonon branches in $g$-BAs becomes weak due to the separation of the three phonon branches. The weakened bunching effect for acoustic phonon branches together with the coupling with ZO phonon branch could lead to more phonon-phonon scattering, and thus is probably responsible for the anomalously lower $\kappa$ of $g$-BAs than $c$-BAs.

The ZO phonon branch in $g$-BAs is mainly contributed from the boron (B) atoms, as revealed by the partial density of states ($p$DOS) in Fig. 3(c). In fact, due to the mass difference, the optical phonon branches in both $c$-BAs and $g$-BAs are contributed from the B atoms [Fig. 3(c,d)]. With the geometry structures transformed from 3D ($c$-BAs) to 2D ($g$-BAs), the $z$-direction vibration of B atoms is totally different due to the 2D nature of bondings and structural symmetry, which lowers the frequency of ZO and provides more scattering probability in $g$-BAs by strongly coupling with acoustic phonon branches [Fig. 3(a)] (Supplemental Note 1 and Supplemental Figure 2). Such phonomena is also observed in monolayer GaNNanoscale.2017.9.12.4295-4309 ; Phys.Rev.B.2017.95.19.195416 .

All the possible phonon-phonon scattering events quantified by the scattering phase space are determined based on the phonon dispersions by conserving both energy and crystal momentum with symmetry included PhysRevB.81.085205 ; PhysRevB.80.125203 ; Phys.Rev.B.1996.53.14.9064-9073 ; 0953-8984-20-16-165209

[TABLE]

where $\omega$ is the frequency of phonon modes ($\hbar\omega$ is the corresponding energy), $\vec{q}$ is the wave vector. Normal process corresponds to $\vec{K}=0$, while Umklapp process corresponds to $\vec{K}\neq 0$. Fig. 4 presents the phase space of 3-phonons scattering in $g$-BAs, in comparison with that in $c$-BAs. The scattering phase space in $c$-BAs is small due to the large acoustic-optical phonon band gap, which is responsible for the ultra-high $\kappa$ of $c$-BAs as analyzed in previous studyPhysRevLett.111.025901 . However, the scattering phase space in $g$-BAs is larger than that in $c$-BAs, especially for the frequency range of 5-10 THz (Fig. 4), despite the larger gap in $g$-BAs than $c$-BAs [Fig. 3(a,b)]. The enhanced scattering probability could be attributed to the weakened bunching effect for acoustic phonon branches together with their coupling with ZO phonon branch in $g$-BAs [Fig. 3(a)], which partially explains the anomalously lower $\kappa$ of $g$-BAs than $c$-BAs.

We also compare the phase spaces between $g$-BAs and graphene. It is found that the overall scattering phase space in $g$-BAs is larger than that in graphene. Thus, the anomalously lower $\kappa$ of $g$-BAs than graphene is understandable despite their similar structures. However, it should be noted that the difference in the scattering phase space is much less than one order of magnitude, which cannot fully explain the large difference in the scattering rate (Inset of Fig. 4) and further the more than one order of magnitude lower $\kappa$ of $g$-BAs (137.70 W/mK) than graphene (3094.98 W/mK). Therefore, there should be some other mechanism also responsible for the anomalously low $\kappa$ of $g$-BAs beyond the scattering phase space.

II.3 Strong phonon anharmonicity

It is well known that the phonon lifetime is governed by two factors: phonon-phonon scattering phase space and strength. The phonon-phonon scattering strength describes how strong is the phonon-phonon scattering process, which is governed by the anharmonic nature of the system. The Grüneisen parameter that describes the phonon anharmonicity can be calculated based on the change of phonon frequency with respect to the volume change

[TABLE]

Fig. 5(a) shows the obtained Grüneisen parameter of $g$-BAs, in comparison with graphene. The FA phonon branch possess the largest magnitude of Grüneisen parameter for both $g$-BAs and graphene, and the magnitude is larger in $g$-BAs than in graphene, revealing the stronger phonon anharmonicity in $g$-BAs. Thus, the more than one order of magnitude lower $\kappa$ of $g$-BAs than graphene can be well understood by combining the larger scattering phase space (Fig. 4) and the stronger phonon anharmonicity in $g$-BAs.

The phonon anharmonicity can also be intuitively revealed by the potential energy well. To have an explicit look at the anharmonicity, the potential energy wells (potential energy changes per atom due to the atomic displacement) of $g$-BAs and graphene are plotted in Fig. 5(b) for comparison. Both the potential wells are asymmetric with respect to the positive and negative atomic displacements, indicating the asymmetry in the ability of an atom vibrating around its equilibrium position and the nonlinear dependence of restoring forces on atomic displacement amplitudes, which is the direct evidence of the anharmonicityPhys.Rev.B.2016.94.16.165445 ; Angew.Chem.Int.Ed..2016.55..2-18 ; EnergyEnviron.Sci..2016.SnSe.Zhao . We further fit the calculated points for $g$-BAs and graphene, respectively, with the polynomial

[TABLE]

where $y$ is the relative energy change per atom, and $x$ is the relative movement of atom. The fitted parameters for $g$-BAs and graphene are listed in the table as inset in Fig. 5(b). The fitted quadric ($a_{2}$) and cubic ($a_{3}$) terms correspond to the harmonicity and anharmonicity, respectively. The relatively smaller harmonic term in $g$-BAs reveals the weaker bonding strength of B-As bond than C-C band in graphene, and the relatively larger magnitude of the anharmonic term reveals stronger phonon anharmonicity in $g$-BAs.

II.4 Lone-pair electrons

To gain deep insight into the origin of the strong phonon anharmonicity in $g$-BAs, we further perform fundamental analysis on the electronic structures to uncover the underlying mechanism. We will show that the strong phonon anharmonicity in $g$-BAs is fundamentally driven by the stereochemically active lone-pair electrons due to the special orbital hybridization.

The orbital projected electronic structures [band structure and density of states (DOS)] of $g$-BAs are depicted in Fig. 6(a,b,c). Direct band gap ($\sim$0.75 eV) emerges in $g$-BAs, which is different from the indirect band gap in $c$-BAs [Fig. 6(d,e)]. As shown in Fig. 6(a,b,c), the bonding states in $g$-BAs are governed by the B-$s/p$ and As-$p$ orbitals. As for B atom, all the 3 valence electrons are involved in the formation of B-As $\sigma$ bonds due to the $sp^{2}$-hybridization [Fig. 6(a)]. The situation is totally different for As atom which possesses 5 valence electrons. The As-$s$ orbital is largely ($\sim$10 eV) confined below the valence band, forming an isolated band [Fig. 6(b)]. Consequently, only the As-$p$ orbitals contribute to the B-As $\sigma$ bonds. Thus, the $s^{2}$ electrons in the $s^{2}p^{3}$ valence configuration of As atom do not participate in the bonding and thus form lone-pair around the As atoms. To have an intuitive view on the lone-pair As-$s$ electrons, we plot the electron localization function (ELF) in Fig. 7. The ELF displays the location and size of bonding and lone-pair electron, which is powerful in interpreting chemical bonding patternsPhys.Rev.B.2016.94.16.165445 . The ELF values range from 0 to 1, where 0 means no electron, 0.5 corresponds to the electron-gas-like pair probability, and 1 corresponds to perfect localization. It is well known that in graphene the C-C $\sigma$ bonds are contributed from the hybridized C-$s/p_{x}/p_{y}$ orbitals and the solo C-$p_{z}$ orbital forms the $\pi$ bonds and the electronic Dirac cone (Supplemental Figure 3) Balandin2012266 . Thus, there is no lone-pair electrons formed in graphene. By comparing the side views of the ELF between $g$-BAs [Fig. 7(b)] and graphene [Fig. 7(a)], it can be clearly seen that there are electrons localized around As atom that are not bonded, which are the lone-pair electrons.

It was proposed that lone-pair electrons could lead to low $\kappa$lone-pair1962 . The principle underlying the concept is that the overlapping wave functions of lone-pair electrons with valence (bonding) electrons from adjacent atoms would induce nonlinear electrostatic forces upon thermal agitation, leading to increased phonon anharmonicity in the lattice and thus reducing the $\kappa$lone-pair1962 ; Phys.Rev.Lett..2008.101.3.035901 ; Phys.Rev.Lett..2011.107.23.235901 ; EnergyEnviron.Sci..2013.6.2.570-578 ; NatPhys.2015.11.12.990-991 ; Angew.Chem.Int.Ed..2016.55.27.7792-7796 ; Phys.Rev.B.2016.94.12.125203 . Due to the orbital distribution in the same energy range and wave functions overlap as shown in Figs. 6(a,b,c) and 7(b), the non-bonding lone-pair As-$s$ electrons interact with the covalently bonding electrons of adjacent B atoms in $g$-BAs. The interactions induce nonlinear electrostatic force among atoms when they thermally vibrate around the equilibrium positions2018_NE_50_425_Guangzhao_Lonepair . The nonlinear electrostatic force originates from the asymmetric change of the hybridization between As-$s$ and B-$s/p$ for the atomic motion, as revealed by the $p$DOS evolution in Supplemental Figure 4. A more asymmetric potential energy well is induced together with the additional nonlinear electrostatic force [Fig. 5(b)], which leads to the strong phonon anharmonicity in $g$-BAs [Fig. 5(a)] and significantly reduces the $\kappa$ of $g$-BAs [Fig. 2(c)].

The form of orbital hybridizations in $c$-BAs are highly consistent with those in $g$-BAs as shown in Fig. 6, which means that lone-pair As-$s$ electrons also emerge around As atoms in $c$-BAs. However, no strong phonon anharmonicity is induced in $c$-BAs by the lone-pair As-$s$ electrons despite the similar orbital hybridization form as $g$-BAs, which is due to the different bonding nature and coordination environment between 3D and 2D geometry structures. Due to the perfect octahedral coordination of As atoms in $c$-BAs resulted from its cubic structure [Fig. 2(b)], four equivalent valence bonds are formed. Thus, the lone-pair electrons in $c$-BAs are stereochemically inactive, which has no effect on the phonon anharmonicity. In contrast, for $g$-BAs possessing planar structure, no pyramidal geometry is formed for the B-As bonds. Consequently, lone-pair As-$s$ electrons are located at both sides of the 2D structure plane in $g$-BAs [Fig. 7(b)], which is different from that in 3D bulk systems of $c$-BAs. Thus, strong phonon anharmonicity exist in $g$-BAs due to the stereochemical activity of the lone-pair As-$s$ electrons in the geometric form of planar structure.

II.5 Extention to other systems

It was shown above that bond nanodesigning by changing the coordination environment is an effective approach for realizing low $\kappa$, which would benefit the design of thermoelectric devices with improved performance. The approaches can also be applied to other materials beyond the BAs systems studied here, for instance, the class of group III-V compounds (e.g. BN, AlN, GaN, etc), where lone-pair electrons also exist (Fig. 1). Strong phonon anharmonicity and low $\kappa$ could be achieved with the stereochemically activated lone-pair electrons, which can be realized by breaking the perfect octahedral coordination [Fig. 2(a,b)]. Note that the 2D structures of the systems presented in Fig. 1 are all planar except silicene. For the systems with buckled structures in 2D form, such as silicon vs. silicene, the situation will be different due to the broken symmetry-based selection rule for phonon-phonon scatteringPhysRevB.82.115427 ; Nanoscale.2017.9.12.4295-4309 ; Phys.Rev.B.2017.95.19.195416 . It is found that there exists a strong correlation between the electronegativity difference and the $\kappa$ modulation for binary compounds (Fig. 1). The effect of $\kappa$ modulation by stereochemically activating the lone-pair electrons is weaker with a larger electronegativity difference. The reason may lie in the contribution to phonon anharmonicity of the electronegativity differenceNanoscale.2017.9.12.4295-4309 . Other approaches could also have the same effects on the $\kappa$ modulation that make the lone-pair electrons stereochemically active, such as nanostructuring. Alternatively, it would be also possible by substituting the atoms in ordinary materials with special atoms that can form non-bonding lone-pair electrons, such as nitrogen, phosphorus, arsenic, etc.

Note that the $\kappa$ of the studied systems here does not achieve an ultralow value, which may limit their direct applications in thermoelectrics. However, if the approach of activating lone-pair electrons is combined with the commonly used strategy of nanostructuring, ultralow $\kappa$ desirable for thermoelectrics could be effectively achieved. For example, experimental measurements have already demonstrated that the $\kappa$ of BAs can be suppressed by the arsenic deficiency or vacancy in the BAs sampleAppl.Phys.Lett..2015.106.7.074105 and the phonon-boundary scattering in BAs microstructures PhysRevB.88.214303 ; Appl.Phys.Lett..2016.108.20.201905 . However, the obtained $\kappa$ of BAs is still too high, which limits its potential applications in thermoelectrics, despite its quite large Seebeck coefficient and thermoelectric power factorAppl.Phys.Lett..2016.108.20.201905 . If the lone-pair electrons in the BAs system can be stereochemically activated, the $\kappa$ could be further reduced, which would improve the thermoelectric performance in the experimental setup. Besides, due to the intrinsic high $\kappa$, BAs also shows promising applications in efficient heat dissipation of electronics. When incorporating it into conventional semiconducting devices for heat dissipation, special attention should be paid to avoid activating the lone-pair electrons in BAs based nanostructures for keeping the high $\kappa$.

III Conclusions

In summary, by cutting the 3D cubic structure of $c$-BAs at the (111) cross section, more than one order of magnitude lowered $\kappa$ is achieved in the resultant 2D system of $g$-BAs with similar structure as graphene, which shows that bond nanodesigning by transforming the materials into nanoscale with the broken coordination environment could be an effective approach for realizing low $\kappa$. Based on the systematic study on the thermal transport properties of $g$-BAs comparing with $c$-BAs, diamond, and graphene ($c$-BAs $\to$ $g$-BAs vs. diamond $\to$ graphene), the underlying mechanism for the substantially lowered $\kappa$ in the case of ‘$c$-BAs $\to$ $g$-BAs’ lies in two aspects: 1) Resulted from mass difference and 2D nature of bondings and structural symmetry, the weakened bunching effect for acoustic phonon branches together with their coupling with ZO phonon branch play a key role in driving large probability of phonon-phonon scattering. 2) Strong phonon anharmonicity is fundamentally driven by the stereochemically actived lone-pair electrons in $g$-BAs. Due to the special orbital hybridization, the $s^{2}$ electrons in the $s^{2}p^{3}$ valence configuration of As atom do not participate in the bonding but form lone-pair instead. When transforming from the 3D cubic structure of $c$-BAs to 2D planar structure of $g$-BAs, the lone-pair As-$s$ electrons become stereochemically actived due to the break of the perfect octahedral coordination of As atoms in $c$-BAs, which leads to strong phonon anharmonicity in $g$-BAs. Similar concept can be also extended to other systems with lone-pair electrons beyond BAs, such as group III-V compounds (e.g. BN, AlN, GaN, etc), where a strong correlation between $\kappa$ modulation and electronegativity difference for binary compounds is found. Thus, the lone-pair electrons combined with a small electronegativity difference could be the indicator of lowering $\kappa$ through bond nanodesigning to change the coordination environment. The proposed approach for realizing low $\kappa$ and the underlying mechanism uncovered in this study would shed light on future research involving novel materials for energy applications.

IV Computational Details

All the first-principles calculations are performed based on the density functional theory (DFT) as implemented in the Vienna ab initio simulation package (vasp)PhysRevB.54.11169 . The Perdew-Burke-Ernzerhof (PBE)PhysRevLett.77.3865 of generalized gradient approximation (GGA) is chosen as the exchange-correlation functional for describing boron arsenide (BAs) systems, which is produced using the projector augmented wave (PAW) methodPhysRevB.59.1758 . Based on careful convergence test, the kinetic energy cutoff of wave function is set as 800 eV for all the DFT calculations. For the 2D systems, a large vacuum spacing is necessary to hinder the interactions arising from the employed periodic boundary conditions, which is set as 20 Å along the out-of-plane direction. The Monkhorst-Pack PhysRevB.13.5188 $k$-meshes of $15\times 15\times 1$ and $2\times 2\times 1$ are used to sample the Brillouin zone (BZ) for the structure optimizations and supercell force calculations, respectively, with the energy convergence threshold set as $10^{-8}$ eV. The structure optimization is fully conducted with no limitation until the maximal Hellmann-Feynman force acting on each atom is less than $10^{-9}$ eV/Å.

For the supercell force calculations to obtain interatomic force constants (IFCs), a $5\times 5\times 1$ supercell is constructed based on the convergence of the phonon dispersion with respect to the supercell size. The cutoff radius ($r^{\mathrm{cutoff}}$) introduced during the calculations of the anharmonic IFCs is also fully tested, which is used to discard the interactions between atoms with distance larger than a certain value for practical purposes. The $r^{\mathrm{cutoff}}$ of 10th nearest neighbors ($\sim$0.94 nm) is found to be large enough to obtain converged and reliable $\kappa$npjCM.2018.4.1.3 . The space group symmetry properties are used to reduce the computational cost and the translational and rotational invariance of IFCs are enforced using the Lagrange multiplier method phonopy ; PhysRevB.77.144112 ; PhysRevB.86.174307 . With the anharmonic IFCs, the scattering matrix can be constructed, based on which one can calculate all the three-phonon scattering rates and then obtain phonon lifetime. The Born effective charge ($Z^{*}$) and dielectric constant ($\epsilon$) obtained based on the density functional perturbation theory (DFPT) are included for taking into account of long-range electrostatic interactions. The thickness for calculating $\kappa$ is chosen as the van der Walls diameter (3.7 Å). The $\kappa$ is obtained by solving the linearized phonon BTE using an iterative procedure as implemented in the ShengBTE package based on the IFCs Li20141747 ; PhysRevB.86.174307 . More information can be found in Supplemental Note 2.

V Acknowledgments

Simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0366. M.H. acknowledges the start-up fund from the University of South Carolina. Z.Q. is supported by the National Natural Science Foundation of China (Grant No. 11847158) and the China Postdoctoral Science Foundation (2018M642776).

VI Supplemental Information

Supplemental Table for the specific $\kappa$ of the typical systems in 3D and 2D forms;

Supplemental Figures for 1) the phonon dispersion showing quadratic behavior of FA, 2) phonon-phonon scattering channels of FA, 3) oribitals projected electronic structures for graphene, 4) $p$DOS evolution for $g$-BAs due to atomic motion, and 5) normalized $\kappa$ for several typical 2D materials;

Supplemental Notes for 1) phonon-phonon scattering channels and 2) more information on computational methods.

VII Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.