#### Special topics

SPECIAL TOPIC — Phononics and phonon engineering

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 Select First principles calculations on the thermoelectric properties of bulk Au2S with ultra-low lattice thermal conductivity Y Y Wu(伍义远), X L Zhu(朱雪良), H Y Yang(杨恒玉), Z G Wang(王志光), Y H Li(李玉红), B T Wang(王保田) Chin. Phys. B, 2020, 29 (8): 087202.   DOI: 10.1088/1674-1056/ab973c Abstract （274）   HTML    PDF （3634KB）（139）       Sulfide nanocrystals and their composites have shown great potential in the thermoelectric (TE) field due to their extremely low thermal conductivity. Recently a solid and hollow metastable Au2S nanocrystalline has been successfully synthesized. Herein, we study the TE properties of this bulk Au2S by first-principles calculations and semiclassical Boltzmann transport theory, which provides the basis for its further experimental studies. Our results indicate that the highly twofold degeneracy of the bands appears at the Γ point in the Brillouin zone, resulting in a high Seebeck coefficient. Besides, Au2S exhibits an ultra-low lattice thermal conductivity ( ~0.88 W·m-1·K-1 at 700 K). At 700 K, the thermoelectric figure of merit of the optimal p-type doping is close to 1.76, which is higher than 0.8 of ZrSb at 700 K and 1.4 of PtTe at 750 K. Our work clearly demonstrates the advantages of Au2S as a TE material and would greatly inspire further experimental studies and verifications.
 Select A polaron theory of quantum thermal transistor in nonequilibrium three-level systems Chen Wang(王晨), Da-Zhi Xu(徐大智) Chin. Phys. B, 2020, 29 (8): 080504.   DOI: 10.1088/1674-1056/ab973b Abstract （168）   HTML    PDF （855KB）（118）       We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polaron-transformed Redfield equation combined with full counting statistics. The steady state heat currents are obtained via this unified approach over a wide region of system-bath coupling, and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits, respectively. A giant heat amplification phenomenon emerges in the strong system-bath coupling limit, where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism. Moreover, the heat amplification is also exhibited with moderate coupling strength, which can be properly explained within the polaron framework.
 Select Scaling behavior of thermal conductivity in single-crystalline α-Fe2O3 nanowires Qilang Wang(王啟浪), Yunyu Chen(陈允玉), Adili Aiyiti(阿地力·艾依提), Minrui Zheng(郑敏锐), Nianbei Li(李念北), Xiangfan Xu(徐象繁) Chin. Phys. B, 2020, 29 (8): 084402.   DOI: 10.1088/1674-1056/ab90f0 Abstract （184）   HTML    PDF （1530KB）（94）       Unveiling the thermal transport properties of various one-dimensional (1D) or quasi-1D materials like nanowires, nanotubes, and nanorods is of great importance both theoretically and experimentally. The dimension or size dependence of thermal conductivity is crucial in understanding the phonon-phonon interaction in the low-dimensional systems. In this paper, we experimentally investigate the size-dependent thermal conductivity of individual single crystalline α-Fe2O3 nanowires collaborating the suspended thermal bridge method and the focused electron-beam self-heating technique, with the sample diameter (d) ranging from 180 nm to 661 nm and length (L) changing from 4.84 μm to 20.73 μm. An empirical relationship for diameter-/length-dependent thermal conductivity is obtained, which shows an approximately linear dependence on the aspect ratio (L/(1+Cd)) at T=300 K, where C is a fitting parameter. This is related to the boundary scattering and diameter effect of α-Fe2O3 nanowires although rigorous calculations are needed to confirm the result.
 Select Ultra-low thermal conductivity of roughened silicon nanowires: Role of phonon-surface bond order imperfection scattering Heng-Yu Yang(杨恒玉), Ya-Li Chen(陈亚利), Wu-Xing Zhou(周五星), Guo-Feng Xie(谢国锋), Ning Xu(徐宁) Chin. Phys. B, 2020, 29 (8): 086502.   DOI: 10.1088/1674-1056/ab99af Abstract （164）   HTML    PDF （706KB）（126）       The ultra-low thermal conductivity of roughened silicon nanowires (SiNWs) can not be explained by the classical phonon-surface scattering mechanism. Although there have been several efforts at developing theories of phonon-surface scattering to interpret it, but the underlying reason is still debatable. We consider that the bond order loss and correlative bond hardening on the surface of roughened SiNWs will deeply influence the thermal transport because of their ultra-high surface-to-volume ratio. By combining this mechanism with the phonon Boltzmann transport equation, we explicate that the suppression of high-frequency phonons results in the obvious reduction of thermal conductivity of roughened SiNWs. Moreover, we verify that the roughness amplitude has more remarkable influence on thermal conductivity of SiNWs than the roughness correlation length, and the surface-to-volume ratio is a nearly universal gauge for thermal conductivity of roughened SiNWs.
 Select Lattice thermal conductivity of β12 and χ3 borophene Jia He(何佳), Yulou Ouyang(欧阳宇楼), Cuiqian Yu(俞崔前), Pengfei Jiang(蒋鹏飞), Weijun Ren(任卫君), and Jie Chen(陈杰) Chin. Phys. B, 2020, 29 (12): 126503.   DOI: 10.1088/1674-1056/abbbe6 Abstract （78）   HTML    PDF （3830KB）（73）       Borophene allotropes have many unique physical properties due to their polymorphism and similarity between boron and carbon. In this work, based on the density functional theory and phonon Boltzmann transport equation, we investigate the lattice thermal conductivity $\kappa$ of both β 12 and χ3 borophene. Interestingly, these two allotropes with similar lattice structures have completely different thermal transport properties. β12 borophene has almost isotropic $\kappa$ around 90 W/(mK) at 300 K, while $\kappa$ of χ3 borophene is much larger and highly anisotropic. The room temperature $\kappa$ of χ 3 borophene along the armchair direction is 512 W/(mK), which is comparable to that of hexagonal boron nitride but much higher than most of the two-dimensional materials. The physical mechanisms responsible for such distinct thermal transport behavior are discussed based on the spectral phonon analysis. More interestingly, we uncover a unique one-dimensional transport feature of transverse acoustic phonon in χ3 borophene along the armchair direction, which results in a boost of phonon relaxation time and thus leads to the significant anisotropy and ultrahigh thermal conductivity in χ3 borophene. Our study suggests that χ 3 borophene may have promising application in heat dissipation, and also provides novel insights for enhancing the thermal transport in two-dimensional systems.
 Select Reduction of interfacial thermal resistance of overlapped graphene by bonding carbon chains Yuwen Huang(黄钰文), Wentao Feng(冯文韬), Xiaoxiang Yu(余晓翔), Chengcheng Deng(邓程程), and Nuo Yang(杨诺) Chin. Phys. B, 2020, 29 (12): 126303.   DOI: 10.1088/1674-1056/abc677 Abstract （118）   HTML    PDF （919KB）（75）       Exploring the mechanism of interfacial thermal transport and reducing the interfacial thermal resistance are of great importance for thermal management and modulation. Herein, the interfacial thermal resistance between overlapped graphene nanoribbons is largely reduced by adding bonded carbon chains as shown by molecular dynamics simulations. And the analytical model (phonon weak couplings model, PWCM) is utilized to analyze and explain the two-dimensional thermal transport mechanism at the cross-interface. An order of magnitude reduction of the interfacial thermal resistance is found as the graphene nanoribbons are bonded by just one carbon chain. Interestingly, the decreasing rate of the interfacial thermal resistance slows down gradually with the increasing number of carbon chains, which can be explained by the proposed theoretical relationship based on analytical model. Moreover, by the comparison of PWCM and the traditional simplified model, the accuracy of PWCM is demonstrated in the overlapped graphene nanoribbons. This work provides a new way to improve the interfacial thermal transport and reveal the essential mechanism for low-dimensional materials applied in thermal management.
 Select A phononic rectifier based on carbon schwarzite host-guest system Zhongwei Zhang(张忠卫), Yulou Ouyang(欧阳宇楼), Jie Chen(陈杰), and Sebastian Volz Chin. Phys. B, 2020, 29 (12): 124402.   DOI: 10.1088/1674-1056/abbbf9 Abstract （76）   HTML    PDF （1624KB）（59）       Thermal rectification is a promising way to manipulate the heat flow, in which thermal phonons are spectrally and collectively controlled. As phononic devices are mostly relying on monochromatic phonons, in this work we propose a phononic rectifier based on the carbon schwarzite host-guest system. By using molecular dynamic simulations, we demonstrate that the phononic rectification only happens at a specific frequency of the hybridized mode for the host-guest system, due to its strong confinement effect. Moreover, a significant rectification efficiency, ∼ 134 %, is observed, which is larger than most of the previously observed efficiencies. The study of length and temperature effects on the phononic rectification shows that the monochromaticity and frequency of the rectified thermal phonons depend on the intrinsic anharmonicity of the host-guest system and that the on-center rattling configuration with weak anharmonicity is preferable. Our study provides a new perspective on the rectification of thermal phonons, which would be important for controlling monochromatic thermal phonons in phononic devices.
 Select Nonequilibrium reservoir engineering of a biased coherent conductor for hybrid energy transport in nanojunctions "Bing-Zhong Hu(胡柄中), Lei-Lei Nian(年磊磊), and Jing-Tao Lü(吕京涛) Chin. Phys. B, 2020, 29 (12): 120505.   DOI: 10.1088/1674-1056/abb3ee Abstract （99）   HTML    PDF （730KB）（86）       We show that a current-carrying coherent electron conductor can be treated as an effective bosonic energy reservoir involving different types of electron-hole pair excitations. For weak electron-boson coupling, hybrid energy transport between nonequilibrium electrons and bosons can be described by a Landauer-like formula. This allows for unified account of a variety of heat transport problems in hybrid electron-boson systems. As applications, we study the non-reciprocal heat transport between electrons and bosons, thermoelectric current from a cold-spot, and electronic cooling of the bosons. Our unified framework provides an intuitive way of understanding hybrid energy transport between electrons and bosons in their weak coupling limit. It opens the way of nonequilibrium reservoir engineering for efficient energy control between different quasi-particles at the nanoscale.
 Select Tuning thermal transport via phonon localization in nanostructures Dengke Ma(马登科), Xiuling Li(李秀玲), and Lifa Zhang(张力发) Chin. Phys. B, 2020, 29 (12): 126502.   DOI: 10.1088/1674-1056/abb7fa Abstract （129）   HTML    PDF （3019KB）（113）       Localization, one of the basic phenomena for wave transport, has been demonstrated to be an effective strategy to manipulate electronic, photonic, and acoustic properties of materials. Due to the wave nature of phonons, the tuning of thermal properties through phonon localization would also be expected, which is beneficial to many applications such as thermoelectrics, electronics, and phononics. With the development of nanotechnology, nanostructures with characteristic length about ten nanometers can give rise to phonon localization, which has attracted considerable attention in recent years. This review aims to summarize recent advances with theoretical, simulative, and experimental studies toward understanding, prediction, and utilization of phonon localization in disordered nanostructures, focuses on the effect of phonon localization on thermal conductivity. Based on previous researches, perspectives regarding further researches to clarify this hectic-investigated and immature topic and its exact effect on thermal transport are given.
 Select Anti-parity-time symmetric phase transition in diffusive systems Pei-Chao Cao(曹培超) and Xue-Feng Zhu(祝雪丰) Chin. Phys. B, 2021, 30 (3): 030505.   DOI: 10.1088/1674-1056/abd694 Abstract （120）   HTML （8）    PDF （2107KB）（110）       Parity-time (PT) symmetry/anti-parity-time (APT) symmetry in non-Hermitian systems reveal profound physics and spawn intriguing effects. Recently, it has been introduced into diffusive systems together with the concept of exceptional points (EPs) from quantum mechanics and the wave systems. With the aid of convection, we can generate complex thermal conductivity and imitate various wavelike dynamics in heat transfer, where heat flow can be "stopped" or moving against the background motion. Non-Hermitian diffusive systems offer us a new platform to investigate the heat wave manipulation. In this review, we first introduce the construction of APT symmetry in a simple double-channel toy model. Then we show the phase transition around the EP. Finally, we extend the double-channel model to the four-channel one for showing the high-order EP and the associated phase transition. In a general conclusion, the phase difference of adjacent channels is always static in the APT symmetric phase, while it dynamically evolves or oscillates when the APT symmetry is broken.
 Select Designing thermal demultiplexer: Splitting phonons by negative mass and genetic algorithm optimization Yu-Tao Tan(谭宇涛), Lu-Qin Wang(王鲁钦), Zi Wang(王子), Jiebin Peng(彭洁彬), and Jie Ren(任捷) Chin. Phys. B, 2021, 30 (3): 036301.   DOI: 10.1088/1674-1056/abd68b Abstract （100）   HTML （0）    PDF （1321KB）（107）       We propose the concept of thermal demultiplexer, which can split the heat flux in different frequency ranges into different directions. We demonstrate this device concept in a honeycomb lattice with dangling atoms. From the view of effective negative mass, we give a qualitative explanation of how the dangling atoms change the original transport property. We first design a two-mass configuration thermal demultiplexer, and find that the heat flux can flow into different ports in corresponding frequency ranges roughly. Then, to improve the performance, we choose the suitable masses of dangling atoms and optimize the four-mass configuration with genetic algorithm. Finally, we give out the optimal configuration with a remarkable effect. Our study finds a way to selectively split spectrum-resolved heat to different ports as phonon splitter, which would provide a new means to manipulate phonons and heat, and to guide the design of phononic thermal devices in the future.
 Select Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit-phonon hybrid system Chen Wang(王晨), Lu-Qin Wang(王鲁钦), and Jie Ren(任捷) Chin. Phys. B, 2021, 30 (3): 030506.   DOI: 10.1088/1674-1056/abcfa8 Abstract （93）   HTML （2）    PDF （4726KB）（87）       Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system-bath dissipation. Here by exemplifying in a nonequilibrium qubit-phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system-bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit-phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.
 Select First-principles analysis of phonon thermal transport properties of two-dimensional WS2/WSe2 heterostructures Zheng Chang(常征), Kunpeng Yuan(苑昆鹏), Zhehao Sun(孙哲浩), Xiaoliang Zhang(张晓亮), Yufei Gao(高宇飞), Xiaojing Gong(弓晓晶), and Dawei Tang(唐大伟) Chin. Phys. B, 2021, 30 (3): 034401.   DOI: 10.1088/1674-1056/abd2a6 Abstract （102）   HTML （4）    PDF （3103KB）（104）       The van der Waals (vdW) heterostructures of bilayer transition metal dichalcogenide obtained by vertically stacking have drawn increasing attention for their enormous potential applications in semiconductors and insulators. Here, by using the first-principles calculations and the phonon Boltzmann transport equation (BTE), we studied the phonon transport properties of WS2/WSe2 bilayer heterostructures (WS2/WSe2-BHs). The lattice thermal conductivity of the ideal WS2/WSe2-BHs crystals at room temperature (RT) was 62.98 W/mK, which was clearly lower than the average lattice thermal conductivity of WS2 and WSe2 single layers. Another interesting finding is that the optical branches below 4.73 THz and acoustic branches have powerful coupling, mainly dominating the lattice thermal conductivity. Further, we also noticed that the phonon mean free path (MFP) of the WS2/WSe2-BHs (233 nm) was remarkably attenuated by the free-standing monolayer WS2 (526 nm) and WSe2 (1720 nm), leading to a small significant size effect of the WS2/WSe2-BHs. Our results systematically demonstrate the low optical and acoustic phonon modes-dominated phonon thermal transport in heterostructures and give a few important guidelines for the synthesis of van der Waals heterostructures with excellent phonon transport properties.
 Select Enhanced thermoelectric properties in two-dimensional monolayer Si2BN by adsorbing halogen atoms Cheng-Wei Wu(吴成伟), Changqing Xiang(向长青), Hengyu Yang(杨恒玉), Wu-Xing Zhou(周五星), Guofeng Xie(谢国锋), Baoli Ou(欧宝立), and Dan Wu(伍丹) Chin. Phys. B, 2021, 30 (3): 037304.   DOI: 10.1088/1674-1056/abd163 Abstract （96）   HTML （0）    PDF （2497KB）（53）       Using the first principles calculation and Boltzmann transport theory, we study the thermoelectric properties of Si2BN adsorbing halogen atoms (Si2BN-4X, $X=\textF$, Cl, Br, and I). The results show that the adsorption of halogen atoms can significantly regulate the energy band structure and lattice thermal conductivity of Si2BN. Among them, Si2BN-4I has the best thermoelectric performance, the figure of merit can reach 0.50 K at 300 K, which is about 16 times greater than that of Si2BN. This is because the adsorption of iodine atoms not only significantly increases the Seebeck coefficient due to band degeneracy, but also rapidly reduces the phonon thermal conductivity by enhancing phonon scattering. Our work proves the application potential of Si2BN-based crystals in the field of thermoelectricity and the effective method for metal crystals to open bandgaps by adsorbing halogens.