Witting in own words,

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Write in your own word the following sections of the attached document, do not change the science.

3.1.1 Molecular dynamics

3.1.3 Non-equilibrium Green’s function

Write the equations well like the one attached. Use mendeley(https://www.mendeley.com) to insert all the references correctly in their current positions.

Witting in own words,
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Front. Energy https://doi.org/10.1007/s11708-018-0543-5 REVIEW ARTICLE Kai-Xuan CHEN, Min-Shan LI, Dong-Chuan MO, Shu-Shen LYU Nanostructural thermoelectric materials and their performance © Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract In this review, an attempt was made to introduce the traditional concepts and materials in thermoelectric application and the recent development in searching high-performance thermoelectric materials. Due to the use of nanostructural engineering, thermoelectric materials with a high figure of merit are designed, leading to their blooming application in the energy field. One dimensional nanotubes and nanoribbons, two-dimensional planner structures, nanocomposites, and heterostructures were summarized. In addition, the state-of-the-art theoretical calculation in the prediction of thermoelectric materials was also reviewed, including the molecular dynamics (MD), Boltzmann transport equation, and non-equilibrium Green’s function. The combination of experimental fabrication and first-principles prediction significantly promotes the discovery of new promising candidates in the thermoelectric field. Keywords nanostructural, low-dimensional, thermoelectric material, figure of merit, first-principles 1 Introduction Due to their ability of directly converting waste heat into electricity and vice versa, thermoelectric materials [1–6] have attracted a lot of attention in recent years. It has been considered as one of the effective ways to resolve the severe energy problem using thermoelectric materials. Compared with other methods such as lithium ion Received Aug. 17, 2017; accepted Nov. 12, 2017; online Feb. 10, 2018 ✉), Shu-Shen LYU Kai-Xuan CHEN, Min-Shan LI, Dong-Chuan MO ( ✉ ( ) School of Chemical Engineering and Technology, Sun Yat-sen University, Guangzhou 510275, China; Guangdong Engineering Technology Research Centre for Advanced Thermal Control Material and System Integration (ATCMSI), Guangzhou 510275, China E-mail: modongch@mail.sysu.edu.cn; lvshsh@mail.sysu.edu.cn batteries, solar cells, and supercapacitor, it possesses the advantages of having no moving components, no leakage, and being environmentally friendly [7,8].Generally, the energy conversion efficiency is adopted to evaluate the conversion performance. As is known, the Carnot coefficient hC is considered as the highest reversible energy conversion efficiency under certain circumstances, which is defined as ηC ¼ ΔT T –T ¼ h c, Th Th (1) where DT = Th – Tc denotes the temperature gradient between the heat and cold terminals, which are defined as Th and Tc, respectively. As in the thermoelectric field, the energy generation efficiency of thermoelectric material, hTE, can be expressed as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZT – 1 ΔT ηTE ¼ ⋅ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , (2) Th 1 þ ZT þ Tc =Th where ZT is the so-called thermoelectric figure of merit, which is determined by the intrinsic properties of a certain material. As is known from Eq. (2), in order to obtain a high energy generation efficiency (i.e. to approach the Carnot coefficient), ZT should be large enough, ideally exceeding 3 or even 4, as shown in Fig. 1. The thermoelectric figure of merit [9,10] is defined according to S 2 T , κ (3) κ ¼ κel þ κph , (4) ZT ¼ where s, S, and k are the electrical conductivity, Seebeck coefficient, and thermal conductivity, respectively. The thermal conductivity can be contributed by both electrons and phonons, denoted as kel and kph, respectively [11]. As shown in the definition of ZT, it would require a high electrical conductivity and Seebeck coefficient as well as a 2 Front. Energy 2 Enhancing thermoelectric performance using nanostructural engineering Tables 1 and 2 summarize the ZT obtained in experimental samples in recent years based on Bi2Te3 (working temperature usually at 200–500 K) and IV–VI family (working temperature usually at 600–900 K), respectively. Using nanostructural engineering, the highest ZT of these families can even exceed 2, as illustrated in Fig. 3. For instances, in the work of Venkatasubramanian et al. [15], a figure of merit of 2.4 can be observed in p-type Bi2Te3/ Sb2Te3 at 300 K. Fig. 1 Thermoelectric efficiency (hTE) plotted for different temperature gradient between the hot side and the cold side where the cold side is assumed to be at room temperature (300 K) low thermal conductivity to obtain high-performance thermoelectric materials. However, these transport coefficients are inter-related. It is difficult to alter one parameter without significantly affecting the other transport coefficients. For example, as the carrier concentration increases, both electrical conductivity and thermal conductivity increase but the opposite is true of the Seebeck coefficient, as shown in Fig. 2. Fig. 3 Development of ZT in the past several decades (The reference number of the original data are denoted in the center of the symbol. For Bi2Te3 series, the references sorted by years are Refs. [16–27]. The references for Zn4Sb3, PbTe and SiGe series are Refs. [28–31], [32–39], and [34,40–44], respectively.) Fig. 2 Variation of thermoelectric factors against carrier concentration Due to the inter-relationship among thermoelectric factors, ZT has been around for many years during the last century. Two strategies to design high-performance thermoelectric materials are proposed. The first one is the framework of phonon-glass electron-crystal (PGEC), in which glass-like thermal properties and crystal-like electrical properties are required in one system [12] and only small progress has been made. The other strategy, as pointed out by Hicks and Dressalhaus [13,14], is nanostructural engineering, in which the quantum confinement can weaken the inter-relationship among the transport coefficients and many progresses have been made. Nanostructured engineering can enhance the thermoelectric performance by lowering the thermal conductivity. The reason comes from the stronger phonon scattering induced by the increasing nano-surfaces and interfaces in nano-size samples. It should be mentioned that the effect of nanostructures on reducing thermal conductivity is significant at low temperatures. At a high temperature range, the contribution of short wave phonons to the lattice thermal conductivity will be dominant and therefore point defects will have much stronger effects on the lattice thermal conductivity than nanostructures. 2.1 Nanograin/interface effect Both Boukai et al. [68] and Hochbaum et al. [69] investigated the efficient thermoelectric performance of silicon nanowires by varying the nanowire size and their studies indicated that the improved efficiency originates from phonon effects (a three-dimensional to one-dimensional crossover of the phonons participating in phonon drag). Poudel et al. [25] observed a ZT of 1.4 at 373 K in Kai-Xuan CHEN et al. Nanostructural thermoelectric materials 3 Table 1 Thermoelectric materials based on Bi2Te3 Reference Year Samples ZT Temperature/K Chung et al. [22] 2000 p-Type CsBi4Te6 0.8 225 Venkatasubramanian et al. [15] 2001 p-Type Bi2Te3/Sb2Te3 and n-type Bi2Te3/Bi2Te2.83Se0.17 2.4/1.4 300 Polvani et al. [45] 2001 p-Type Bi0.5Sb1.5Te3 alloy under 2GPa >2 300 Sidorenko et al. [46] 2001 Crystals of Bi-Sb alloy under a magnetic field >1 100 Chung et al. [23] 2004 p-Type CsBi4Te6 0.82 225 Zhao et al. [47] 2005 n-Type Bi2Te3 nanocomposite 1.25 420 Tang et al. [48] 2007 Bi2Te3 bulk with layered nanostructure 1.35 300 Cao et al. [49] 2008 Bi2Te3/Sb2Te3 bulk nanocomposites 1.47 440 Poudel et al. [25] 2008 p-Type nanocrystalline BiSbTe bulk alloy 1.2/1.4/0.8 300/373/523 Yan et al. [50] 2010 n-Type Bi2Te2.7Se0.3 1.04 400 Zhang et al. [51] 2011 n-Type Bi2Te3 ultrathin nanowires 0.96 380 Guo et al. [52] 2013 Tl9BiTe6 1/0.86 450/560 Hong et al. [53] 2016 BixSb2 – xTe3 nanoplates 1.2 300 Pan and Li [54] 2016 n-Type Bi2(TeSe)3 alloys 1.1 473 Dharmaiah et al. [55] 2016 p-Type 25%Bi2Te3–75%Sb2Te3 alloys 1.23 350 Table 2 Thermoelectric materials based on IV–VI family Reference Year Samples ZT Temperature/K Hsu et al. [56] 2004 n-Type AgPbmSbTe2m (m = 10/18) 2.2 800 Wang et al. [57] 2006 Ag0.8Pb22SbTe20 1.37 673 Johnsen et al. [58] 2011 PbS 0.94 710 Pei et al. [59] 2011 Polycrystalline Pb0.98Na0.02Te12xSex 1.8 800 Zhang et al. [60,61] 2013 Al0.03PbTe 1.2 700 Zhao et al. [62] 2014 SnSe 2.6 923 Yamini et al. [64] 2014 n-Type (PbTe)0.75(PbS)0.15(PbSe)0.1 composites 1.1 800 Lu et al. [65] 2015 (Ge0.8Pb0.2)0.9Mn0.1Te 1.3 720 Zhao et al. [11] 2016 Hole-doped single-crystal SnSe 2.0 773 Zhao et al. [66] 2016 Counter-doped SnTe with strained endotaxial SrTe 1.2 823 Li et al. [67] 2017 p-Type SnSe doped with Zn 0.96 873 the p-type nanocrystalline BiSbTe bulk alloy and found that the improvement results from the low thermal conductivity were caused by grain boundaries and defects. Miao et al. [70] concluded that the hollow structure of titanate nanotubes was responsible for the ultralow thermal conductivity, which greatly enhanced their thermoelectric properties. Li et al. [71] synthesized SnTe particles with controlled sizes from micro-scale to nano-scale and found that the ZT of the specimen using 165-nm-sized nanoparticles was about 2.3 times that of the SnTe bulk samples due to the enhanced phonon scattering. Yang et al. [72] found that the lattice thermal conductivity of nanoscale three dimensional Si phononic crystals was decreased by 500 times compared with that of porous Si, which led to a 26 times increase in ZT. He et al. [73] showed that YbAl3 from the nanometer to mesoscopic scales can effectively scatter phonons and remarkably decrease the lattice thermal conductivity, which produced a 74% increase in ZT. 2.2 Nano particles/inclusions effect Zhao et al. [74] achieved dual control of phonon- and electron-transport properties by embedding nanoparticles of a soft magnetic material in a thermoelectric matrix and thereby improved the thermoelectric performance of the resulting nanocomposites. Pei el al. [75] found that PbTe with nanoscale Ag2Te precipitates and La doping had a low lattice thermal conductivity. In the work of Johnsen et al. [58], the nanostructuring in (PbS)1–x(PbTe)x samples led to substantial decreases in lattice thermal conductivity 4 Front. Energy relative to pristine PbS. Gahtori et al. [76] reported a ZT of 2.1 at 973 K in Cu2Se with different nanoscale dimensional defect features, in which the low thermal conductivity origined from the enhanced low-to-high wavelength phonon scattering by different kinds of defects. Ahmad et al. [77] reported a ZT of 1.81 at 1100 K in p-type SiGe alloys since YSi2 nanoinclusions formed coherent interfaces with SiGe matrix and facilitated reduction in the grainsize of SiGe, which greatly reduced the thermal conductivity. In addition, many other researchers conducted a lot of research in reducing the thermal conductivity in the systems of grapheme [63,78], carbon nanotubes [61,79], graphynenanoribbons [80,81], PbTe family [37,64,82,83], and Bi2Te3 nanowires [51]. The electrical properties can be tuned as well to enhance the thermoelectric properties. The electrical conductivity can usually be increased by enhancing the electron mobility or altering the electronic structures. Nanostructuring can enhance the density of states near Fermi level via quantum confinement, and therefore, increase the thermopower, which provides a way to decouple the thermopower and electrical conductivity [84]. For example, Ginting et al. [85] synthesized composites with nano-inclusions of ntype (PbTe0.93 – xSe0.07Clx)0.93(PbS)0.07 while the composites with nano-inclusions enhanced the Seebeck coefficient in a dilute Cl- doped compound and led to a ZT of 1.52 at 700 K. 3 Theoretical calculation in low-dimensional thermoelectric materials In recent years, the research into thermoelectric materials has achieved a great success in the combination of theoretical calculations [86]. Based on the start-of-the-art density functional theory, several computational methods have been employed in the prediction of high-performance thermoelectric materials and exploration of the enhancement mechanism. In the heat transport field, there are typically three kinds of methods which are used to study the thermal properties. This section will concentrate on the theoretical method of thermal transport properties using the molecular dynamics (MD) [87,88], Boltzmann transport equation [89–91], and non-equilibrium Green’s function method [92–94], respectively. Generally, these methods adopt the potential data from the first-principles density functional theory. 3.1 3.1.1 Theoretical methods Molecular dynamics Based on Newton’s laws of motion, MD can be used in the study of heat transport. Equilibrium MD adopts the GreenKubo formula to calculate the thermal conductivity, as shown below. 1 καβ ! 1 ¼ hJ α ðtÞ⋅J β ðtÞidt, VkB T 2 (5) 0 where καβ, V, kB, and T are the thermal conductivity tensor, volume, Boltzmann constant, and absolute temperature, respectively. Jα and Jβ are the heat flow along the α and β direction, respectively. Non-equilibrium MD obtains the thermal conductivity of the system according to Fourier’s law. By introducing a gradient of temperature or heat flow density into the system, the heat flow can be calculated as Jα ¼ – 3.1.2 X ∂T : ∂xβ β (6) Boltzmann transport equation The phonon (lattice) thermal conductivity can be calculated by employing the phonon Boltzmann transport equation with relaxation time approximation (RTA) according to the following formula. 1X κph,αβ ¼ C ν ν τ , (7) V l ph,l lα lβ lα where α and β denote the components of the second-order tensor kph. In addition, Cl, ν, and t denote the phonon mode volumetric specific heat, group velocity, and phonon lifetime, respectively [83]. The RTA phonon lifetime can be computed according to the Matthiessen rule where phonon-phonon scattering (tph), isotope scattering (tiso), and boundary scattering (tb) are fully taken into consideration [89]. 1 1 1 1 ¼ ph þ iso þ b : τl τl τl τl (8) The electronic transport coefficients can be computed based on the Boltzmann transport equation. The Seebeck coefficient S and electrical conductivity s can be calculated by   ekB ∂f0 ε– ðεÞ S¼ dε – , (9)  ∂ε kB T ! ¼e where ðεÞ ¼ X k 2  ∂f0 dε – ðεÞ, ∂ε !  (10) νk νk τ k denotes the transport distribu- tion; m, ε, e, and kB are the chemical potential, electron energy, unit charge, and Boltzmann constant, respectively. In addition, f0 is the Fermi distribution function, ν is the group velocity, and t is the relaxation time at the k state [95,96]. Kai-Xuan CHEN et al. Nanostructural thermoelectric materials 3.1.3 Non-equilibrium Green’s function 5 f ðE,,T Þ ¼ When the transport scale is smaller than the mean free path (MFP), the ballistic regime is valid. In such a condition, the non-equilibrium Green’s function method can be effectively used in the study of transport properties. Generally, a typical model of the NEGF can be described as the “left lead-conductor-right lead” (LCR) configuration, as demonstrated in Fig. 4. The conductor can be set to be exactly the same as the leads (in the case of perfect crystal) or totally different from the leads (in the case of interface). 1 E– e kB T , where f(E, m, T) is the Fermi-Dirac distribution function and m, T, and h are the chemical potential, absolute temperature, and Planck constant, respectively. According to Eqs. (17)–(19), the electronic conductance s, Seebeck coefficient S, and the electronic thermal conductance kel, can be derived, respectively.  ¼ q2 L0 , S¼ (17) 1 L  1, L0 qT (18)   1 L21 κel ¼  L2 – : L0 T Fig. 4 A typical model of non-equilibrium Green’s function To investigate the thermoelectric properties, both electronic and phononic transport should be studied. For ballistic electronic transport, the retarded Green’s function of the central conductor is G ¼ r ½ES C – H C – Σ rL – Σ rR  – 1 , (19) To obtain the ZT, the phononic thermal conductance has to be calculated, which can be determined from the phonon transport part. The calculation of phonon transmittance is similar to that of the electron transmittance in the electronic transport part which has been described above. By replacing the Hamiltonian matrix and electron energy E with the interatomic force constant (FC) matrix and phonon frequency ω, the phonon transmittance T(ω) can be calculated as G r ¼ ½ðω þ iηÞ2 – F C – Σ rL – Σ rR  – 1 , (20) TðωÞ ¼ T rðGr Γ L Ga Γ R Þ: (21) (11) where E, HC, and SC are the electron energy, Hamiltonian and overlap matrix, respectively; and the self-energy term Sr can be obtained as Σ rL ¼ H yLC grL H LC , Σ rR ¼ H CR grR H yCR , (16) þ1 After that, the phononic thermal conductance kph can be calculated by (12) where gr is the retarded surface Green’s function from semi-infinite lead. Besides, HLC (HCR) denotes the Hamiltonian matrix between the left (right) leads and the central conductor. The electronic transmittance matrix T(E), which is significant in electronic transport, can be obtained by κph ðT Þ ¼ ` 2π Þ dω, !0 T ðωÞω ∂gðω,T ∂T 1 gðω,T Þ ¼ 1 `ω e kB T , (22) (23) –1 Γ β ¼ iðΣ rβ – Σ aβ Þ, β ¼ L, R, (13) where g(w, T) is the Bose-Einstein distribution function, while ` and kB denote the reduced Planck constant and Boltzmann constant, respectively. TðEÞ ¼ T rðGr Γ L Ga Γ R Þ, Ga ¼ ðG r Þy : (14) 3.2 For convenience, Lorenz functions Ln are introduced to calculate the thermoelectric factors Ln ð,T Þ ¼ ! 2 dETðEÞ  ðE – Þn h   ∂f ðE,,T Þ  – , ∂E (15) Ballistic thermoelectric transport In the past few years, the research group in Guangdong Engineering Technology Research Centre for Advanced Thermal Control Material and System Integration in Sun Yat-sen University has paid a lot of attention to the theoretical study of ballistic thermoelectric transport by using the density functional theory and non-equilibrium Green’s function method. The emphasis has been laid on the two-dimensional systems including graphyne, transi- 6 Front. Energy tion metal dichalcogenides (TMDs) and the VA group family. 3.2.1 Graphyne Shortly after the discovery of graphene, graphyne, another member of the carbon family, attracted researchers’ attention. In Ref. [97], the thermoelectric transport properties of graphyne nanotubes were investigated by using the non-equilibrium Green’s function method, as implemented in the density functional based tight binding framework. Figure 5 shows the previous study with regard to the thermoelectric properties of new emerging twodimensional materials. Figure 5(a) reveals that both the band gap and thermoelectric figure of merit ZT of graphyne nanotubes show a damped oscillation as the tube diameter increases. In addition, by introducing hydrogenation, the thermoelectric performance is reduced. The thermoelectric performance of graphyne nanotubes is much better than that of graphene according to the theoretical calculation. Fig. 5 3.2.2 TMDs Of all newly proposed two-dimensional materials, TMDs are believed to possess the lowest thermal conductivity. Therefore, these TMDs families were studied as new thermoelectric materials in Ref. [93]. Four kinds of monolayer TMDs (MoS2, MoSe2, WS2, WSe2) were investigated. It was discovered that the monolayer WSe2 harbored the highest thermoelectric figure of merit (ZT = 0.91) at room temperature. The nanotubes that scrolled from these monolayer TMDs were also investigated as a comparison. A degeneration in thermoelectric performance was observed from monolayers to nanotubes, as shown in Fig. 5(b).Following this research, in Ref. [98] the thermoelectric properties of WSe2 nanoribbons were studies since monolayer WSe2 was found to exhibit the most excellent thermoelectric performance. The ZT of WSe2 nanoribbons was higher than that of monolayer WSe2 in both armchair and zigzag ribbons. The highest value of 2.2 could be observed in armchair WSe2 nanoribbons, as depicted in Fig. 5(c). Previous study on the thermoelectric properties of two-dimensional materials (a) Graphyne nanotubes; (b) TMDs; (c) WSe2 nanoribbons; (d) buckled antimonene (Adapted with permission from Ref. [97],Copyright (2013) American Chemical Society; Ref. [93], Copyright (2015) American Chemical Society; Ref. [98], Copyright (2016) Royal Society of Chemistry and Ref. [94], Copyright (2017) American Chemical Society.) Kai-Xuan CHEN et al. Nanostructural thermoelectric materials 3.2.3 VA group family In the framework of 2D systems, the buckled and puckered systems which consist of the VA elements (denoted as arsenene, antimonene and bismuthene) were also studied. The first-principles calculation indicated that buckled antimonene harbored a thermoelectric figure of merit ZT of 2.15 at room temperature. The ZT could even be enhanced to 2.9 at a3% biaxial tensile strain. This is probably the highest value that has ever been reported in pristine 2D materials, as can be seen from Fig. 5(d). The enhancement mainly results from both tuning the electronic structures and reducing the thermal conductance [94]. 4 Low-dimensional thermoelectric materials As pointed out in Section 2, nanostructural engineering is now acting as an effective strategy to enhance the thermoelectric performance [99,100]. Lots of low-dimensional materials have been adopted and studied. Here, the item of low dimensional means the size of the shape or crystal structure. These families can be summarized according to the diverse dimensionality, as are introduced in the following subsections. It should be mentioned that low-dimensional materials are difficult to fabricate precisely due to the high requirement in nanoscale samples. Therefore, many of these results have not yet been realized in experiments. However, the theoretical calculation can provide a valuable guidance to the future research and as the development of nanostructuring technology proceeds, nanoscale materials with atomic accuracy may be prepared. 7 experimental study in carbon nanotubes [105,106], silicon nanowire [68,69], titanate nanotubes [70], Bi2Te3 nanowires [51,107] and the theoretical study in carbon nanotubes [79,92,106,108], InSe nanotubes [109], phosphorene nanoribbons [96], graphyene nanoribbons and nanotubes [80,97], and transition metal dichalcogenide nanoribbons and nanotubes [93,95,98]. 4.2 Two-dimensional mono- and few-layers materials As for two-dimensional systems, much work has been devoted to the study of TMDs. Huang et al. [110,111], Chen et al. [93] and Tahir and Schwingensch lögl [112] studied the monolayer TMDs and found that the monolayer TMDs exhibited a great potential in thermoelectric performance. Huang et al. [111] and Wickramaratne et al. [113] studied the layer dependence of few-layer TMDs and discovered that thermal conductance per thickness approached bulk as the thickness increased. In the work of Lee et al. [114], layer mixing was predicted to be a promising way of improving the thermoelectric properties. Bhattacharyya et al. [115] and Guo [116] studied the stain effect on the thermoelectric performance of TMDs. They observed that the electronic structures of the TMDs family were sensitive to the applied strain and the thermoelectric figure of merit could be tuned by the strain level. Many theoretical workers also devoted their effort to the design of high-performance two-dimensional thermoelectric candidates. Table 3 summarizes the calculated figure of merit for many new emerging two-dimensional materials. It can be seen that the TMDs and the VA group families are both promising candidates for thermoelectric application. Table 3 Theoretical prediction of maximum room-temperature ZT for typical two-dimensional materials 4.1 One-dimensional nanotubes and nanoribbons Much research based on the one-dimensional nanoribbons and nanotubes has been conducted. As is known, the thermoelectric application of graphene has been hampered due to its zero bandgap in the electronic structure. Considerable research has been carried out to open the bandgap of graphene, such as grapheme nanoribbons and nanotubes [101]. Sevinçli et al. [63,102] showed that by geometrical structuring and isotope cluster engineering, the thermal conductance of grapheme nanoribbons could be reduced by 98.8% and the thermoelectric figure of merit could be as high as 3.25 at 800 K. Chang et al. [103] studied the grapheme nanoribbons perforated with an array of nanopores which exhibited a high ZT of ~5 at room temperature. Yeo et al. [104] studied the thermoelectric performance of strained grapheme nanoribbons and discovered that the tensile strain increased the ZT value of certain armchair grapheme nanoribbons. More research focusing on the thermoelectric performance of other family are presented, such as the 2D monolayer ZTmax at RT Graphene 0.0094 [117] Graphyne 0.157 [117] Silicene 0.36 [118] Germanene 0.41 [118] MoS2 0.75 [93], 0.58 [110], 1.35 [113] MoSe2 0.88 [93], 1.39 [113] WS2 0.72 [93], 1.52 [113] WSe2 0.91 [93], 1.88 [113] Black phosphorene > 0.6 [119], 1.44 [120] Puckered arsenene 0.85 [121] Buckled antimonene 2.15 [94] 4.3 Nanocomposites and heterostructures Nanocomposites and heterostructures are also adopted as candidates of thermoelectric materials. Zhang et al. [61] fabricated the Bi2Te3-Te micro-nanoheterostructure and 8 Front. Energy discovered a ZT of ~0.4 at room temperature for such samples, with an enhancement of 40% compared to those without nanoscale heterostructures. Carrete et al. [122] theoretically investigated the thermoelectric transport properties of hybrid thiophene/SiGe superlattices and found that the ZT was twice as those in bulk SiGe. Savelli et al. [123] fabricated the Ti-based silicide quantum dot superlattices by reduced-pressure chemical vapor deposition and observed a trifold increase in the power factor compared with SiGe thin films. Duan et al. [124] observed that the thermoelectric performance of graphene could be significantly enhanced in graphene/hBNvdW device. Yin et al. prepared the Mg2Si1 – xSnx/SiC nano-composites and obtained a ZT of 1.2 at 750 K owing to the introduction of SiC nano-additives. In the work of Luo et al. [125], ZnX acted as a nanoscalehetero structure barrier blocking in CuInTe2, which led to an enhanced Seebeck coefficient and reduced thermal conductivity, with a ZT of 1.52. Yin et al. [126] prepared Mg2Si1 – xSnx/SiC nano-composites with a maximum ZT value of ~1.20 at 750 K. 5 Perspective on the design of highperformance thermoelectric materials With the advancement of nanotstructural technology, the fabrication of nanoscale thermoelectric materials is feasible. In this review, the importance of nanostructural engineering in the design of high-performance thermoelectric materialsis mainly emphasized. High ZT materials can be achieved in nanoscale family due to the quantum confinement effect. The theoretical prediction regarding nanostructural systems has been conducted in recent years, and time will tell whether these systems exhibit excellent performance in experimental testing. Promising thermoelectric candidates may be discovered in the systems which possess heavy elements. Another suggestion for the design of high-performance thermoelectric materials would be the lowering of the dimensionality. For instance, preparing the half-Heusler alloys in nanoscale films or composites with nanoparticle additives might be an effective way to achieve this goal. In addition, research into thermoelectric materials regarding spin needs our attention. The spin Seebeck effect may provide a new opportunity in this field. Moreover, lots of topological insulators are found to be excellent thermoelectric candidates and the mechanism is still unclear. The fast development in state-of-the-art first-principles method in the study of electron and phonon transport has also provided another strategy regarding material design. It is believed that by combining the non-equilibrium Green’s function (adopted in nanoscale systems) and the Boltzmann transport equation (adopted in mesoscale systems), one may effectively predict the properties of newly proposed thermoelectric materials. That would signifi- cantly enhance the explosive growth in excellent thermoelectric candidates. The blooming research into thermoelectric materials will significantly enhance their application in the energy field, which may act as an effective way to resolve the global energy crisis. Acknowledgements Financial support from the National Natural Science Foundation of China (Grant No. 51676212) and the Fundamental Research Funds for the Central Universities are gratefully acknowledged. References 1. Snyder G J, Toberer E S. Complex thermoelectric materials. Nature Materials, 2008, 7(2): 105–114 2. Zebarjadi M, Esfarjani K, Dresselhaus M S, Ren Z F, Chen G. Perspectives on thermoelectrics: from fundamentals to device applications. Energy & Environmental Science, 2012, 5(1): 5147– 5162 3. Tan G, Zhao L D, Kanatzidis M G. Rationally designing highperformance bulk thermoelectric materials. Chemical Reviews, 2016, 116(19): 12123–12149 4. Zhao D L, Tan G. A review of thermoelectric cooling: materials, modeling and applications. Applied Thermal Engineering, 2014, 66(1–2): 15–24 5. Riffat S B, Ma X. Thermoelectrics: a review of present and potential applications. Applied Thermal Engineering, 2003, 23(8): 913–935 6. Ma W, Zhang X. Study of the thermal, electrical and thermoelectric properties of metallic nanofilms. International Journal of Heat and Mass Transfer, 2013, 58(1–2): 639–651 7. Zhang Y, Wang Y, Huang C, Lin G, Chen J. Thermoelectric performance and optimization of three-terminal quantum dot nanodevices. Energy, 2016, 95: 593–601 8. Zhang Y, Huang C, Wang J, Lin G, Chen J. Optimum energy conversion strategies of a nano-scaled three-terminal quantum dot thermoelectric device. Energy, 2015, 85: 200–207 9. Page A, Van der Ven A, Poudeu P F P, Uher C. Origins of phase separation in thermoelectric (Ti, Zr, Hf)NiSn half-Heusler alloys from first principles. Journal of Materials Chemistry. A, Materials for Energy and Sustainability, 2016, 4(36): 13949–13956 10. Sellitto A, Cimmelli V A, Jou D. Thermoelectric effects and size dependency of the figure-of-merit in cylindrical nanowires. International Journal of Heat and Mass Transfer, 2013, 57(1): 109–116 11. Zhao L D, Tan G, Hao S, He J, Pei Y, Chi H, Wang H, Gong S, Xu H, Dravid V P, Uher C, Snyder G J, Wolverton C, Kanatzidis M G. Ultrahigh power factor and thermoelectric performance in holedoped single-crystal SnSe. Science, 2016, 351(6269): 141–144 12. Mi X Y, Yu X, Yao K L, Huang X, Yang N, Lü J T. Enhancing the thermoelectric figure of merit by low-dimensional electrical transport in phonon-glass crystals. Nano Letters, 2015, 15(8): 5229–5234 13. Hicks L D, Dresselhaus M S. Thermoelectric figure of merit of a one-dimensional conductor. Physical Review B: Condensed Matter and Materials Physics, 1993, 47(24): 16631–16634 Kai-Xuan CHEN et al. Nanostructural thermoelectric materials 14. Hicks L D, Dresselhaus M S. Effect of quantum-well structures on the thermoelectric figure of merit. Physical Review B: Condensed Matter and Materials Physics, 1993, 47(19): 12727–12731 15. Venkatasubramanian R, Siivola E, Colpitts T, O’Quinn B. Thinfilm thermoelectric devices with high room-temperature figures of merit. Nature, 2001, 413(6856): 597–602 16. Goldsmid H J, Douglas R W. The use of semiconductors in thermoelectric refrigeration. British Journal of Applied Physics, 1954, 5(11): 386–390 17. Wright D A. Thermoelectric properties of bismuth telluride and its alloys. Nature, 1958, 181(4612): 834 18. Bergvall P, Beckman O. Thermoelectric properties of nonstoichiometric bismuth-antimony-telluride alloys. Solid-State Electronics, 1963, 6(2): 133–136 19. Champness C H, Chiang P T, Parekh P. Thermoelectric properties of Bi2Te3-Sb2Te3 alloys. Canadian Journal of Physics, 1965, 43(4): 653–669 20. Yim W M, Rosi F D. Compound tellurides and their alloys for peltier cooling—a review. Solid-State Electronics, 1972, 15(10): 1121–1140 21. Sugihara S, Suzuki H, Kawashima S, Fujita M, Kajikawa N, Shiraishi K, Sekine R. Thermoelectric properties and electronic structures for impurity-doped Bi2Te3. In: Proceedings of the 1998 17th International Conference on Thermoelectrics. Nagoya, Japan, 1998, 59–63 22. Chung D Y, Hogan T, Brazis P, Rocci-Lane M, Kannewurf C, Bastea M, Uher C, Kanatzidis M G. CsBi4Te6: a high-performance thermoelectric material for low-temperature applications. Science, 2000, 287(5455): 1024–1027 23. Chung D Y, Hogan T P, Rocci-Lane M, Brazis P, Ireland J R, Kannewurf C R, Bastea M, Uher C, Kanatzidis M G. A new thermoelectric material: CsBi4Te6. Journal of the American Chemical Society, 2004, 126(20): 6414–6428 24. Jiang J, Chen L, Bai S, Yao Q, Wang Q. Thermoelectric properties of textured p-type (Bi,Sb)2Te3 fabricated by spark plasma sintering. Scripta Materialia, 2005, 52(5): 347–351 25. Poudel B, Hao Q, Ma Y, Lan Y, Minnich A, Yu B, Yan X, Wang D, Muto A, Vashaee D, Chen X, Liu J, Dresselhaus M S, Chen G, Ren Z. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science, 2008, 320(5876): 634–638 26. Fan S, Zhao J, Guo J, Yan Q, Ma J, Hng H H. p-Type Bi0.4Sb1.6Te3 nanocomposites with enhanced figure of merit. Applied Physics Letters, 2010, 96(18): 182104 27. Chen S, Logothetis N, Ye L, Liu J. A high performance Ag alloyed nano-scale n-type Bi2Te3 based thermoelectric material. Materials Today: Proceedings, 2015, 2(2): 610–619 28. Caillat T, Fleurial J P, Borshchevsky A. Preparation and thermoelectric properties of semiconducting Zn4Sb3. Journal of Physics and Chemistry of Solids, 1997, 58(7): 1119–1125 29. Jang K W, Kim I H, Lee J I, Choi G S. Thermoelectric properties of Zn4 – xSb3 with x = 0–0.5. Diffusion and Defect Data, Solid State Data. Part B, Solid State Phenomena, 2007, 124–126: 1019–1022 30. Liu Y B, Zhou S M, Yuan X Y, Lou S Y, Gao T, Shi X J, Wu X P. Synthesis and high-performance thermoelectric properties of betaZn4Sb3 nanowires. Materials Letters, 2012, 84: 116–119 31. Zou T, Qin X, Zhang Y, Li X, Zeng Z, Li D, Zhang J, Xin H, Xie 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 9 W, Weidenkaff A. Enhanced thermoelectric performance of βZn4Sb3 based nanocomposites through combined effects of density of states resonance and carrier energy filtering. Scientific Reports, 2015, 5(1): 17803 Loffe A F. Semiconductor Thermoelements and Thermoelectric Cooling.London: Infosearch, Ltd, 1957 Fritts R W. Lead telluride alloys and junctions. In: Cadoff I B, Miller E, eds. Thermoelectric Materials and Devices. New York: Reinhold Publishing Corporation, 1960, 143–162 Mahan G D. Good thermoelectrics. Solid State Physics, 1998, 51: 81–157 Wang H, Li J F, Nan C W, Zhou M, Liu W, Zhang B P, Kita T. High-performance Ag0.8Pb18 + xSbTe20 thermoelectric bulk materials fabricated by mechanical alloying and spark plasma sintering. Applied Physics Letters, 2006, 88(9): 092104 Heremans J P, Jovovic V, Toberer E S, Saramat A, Kurosaki K, Charoenphakdee A, Yamanaka S, Snyder G J. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science, 2008, 321(5888): 554–557 Biswas K, He J, Blum I D, Wu C I, Hogan T P, Seidman D N, Dravid V P, Kanatzidis M G. High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature, 2012, 489 (7416): 414–418 Wu D, Zhao L D, Tong X, Li W, Wu L, Tan Q, Pei Y, Huang L, Li J F, Zhu Y, Kanatzidis M G, He J. Superior thermoelectric performance in PbTe-PbS pseudo-binary: extremely low thermal conductivity and modulated carrier concentration. Energy & Environmental Science, 2015, 8(7): 2056–2068 Chen Z, Jian Z, Li W, Chang Y, Ge B, Hanus R, Yang J, Chen Y, Huang M, Snyder G J, Pei Y. Lattice dislocations enhancing thermoelectric PbTe in addition to band convergence. Advanced Materials, 2017, 29(23): 1606768 Dismukes J P, Ekstrom L, Steigmeier E F, Kudman I, Beers D S. Thermal and electrical properties of heavily doped Ge-Si alloys up to 1300°K. Journal of Applied Physics, 1964, 35(10): 2899–2907 Fleurial J P, Vandersande J, Scoville N, Bajgar C, Beaty J. Progress in the optimization of n-type and p-type SiGe thermoelectric materials. AIP Conference Proceedings, 1993, 271: 759–764 Kleint C A, Heinrich A, Muehl T, Hecker J. Structural properties of strain symmetrized silicon/germanium (111) superlattices. In: IEEE International Symposium on Circuits and Systems (ISCAS 2001). Sydney, NSW, Australia, 2001, Z8131–Z8136 Joshi G, Lee H, Lan Y, Wang X, Zhu G, Wang D, Gould R W, Cuff D C, Tang M Y, Dresselhaus M S, Chen G, Ren Z. Enhanced thermoelectric figure-of-merit in nanostructured p-type silicon germanium bulk alloys. Nano Letters, 2008, 8(12): 4670–4674 Bathula S, Jayasimhadri M, Gahtori B, Singh N K, Tyagi K, Srivastava A K, Dhar A. The role of nanoscale defect features in enhancing the thermoelectric performance of p-type nanostructured SiGe alloys. Nanoscale, 2015, 7(29): 12474–12483 Polvani D A, Meng J F, Chandra Shekar N V, Sharp J, Badding J V. Large improvement in thermoelectric properties in pressuretuned p-type Sb1.5Bi0.5Te3. Chemistry of Materials, 2001, 13(6): 2068–2071 Sidorenko N A, Ivanova L D. Bi-Sb solid solutions: potential materials for high-efficiency thermoelectric cooling to below 10 Front. Energy 180 K. Inorganic Materials, 2001, 37(4): 331–335 47. Zhao X B, Ji X H, Zhang Y H, Zhu T J, Tu J P, Zhang X B. Bismuth telluride nanotubes and the effects on the thermoelectric properties of nanotube-containing nanocomposites. Applied Physics Letters, 2005, 86(6): 062111 48. Tang X, Xie W, Li H, Zhao W, Zhang Q, Niino M. Preparation and thermoelectric transport properties of high-performance p-type Bi2Te3 with layered nanostructure. Applied Physics Letters, 2007, 90(1): 012102 49. Cao Y Q, Zhao X B, Zhu T J, Zhang X B, Tu J P. Syntheses and thermoelectric properties of Bi2Te3/Sb2Te3 bulk nanocomposites with laminated nanostructure. Applied Physics Letters, 2008, 92 (14): 143106 50. Yan X, Poudel B, Ma Y, Liu W S, Joshi G, Wang H, Lan Y, Wang D, Chen G, Ren Z F. Experimental studies on anisotropic thermoelectric properties and structures of n-type Bi2Te2.7Se0.3. Nano Letters, 2010, 10(9): 3373–3378 51. Zhang G, Kirk B, Jauregui L A, Yang H, Xu X, Chen Y P, Wu Y. Rational synthesis of ultrathin n-type Bi2Te3 nanowires with enhanced thermoelectric properties. Nano Letters, 2012, 12(1): 56– 60 52. Guo Q, Chan M, Kuropatwa B A, Kleinke H. Enhanced thermoelectric properties of variants of Tl9SbTe6 and Tl9BiTe6. Chemistry of Materials, 2013, 25(20): 4097–4104 53. Hong M, Chen Z G, Yang L, Zou J. BixSb2 – xTe3 nanoplates with enhanced thermoelectric performance due to sufficiently decoupled electronic transport properties and strong wide-frequency phonon scatterings. Nano Energy, 2016, 20: 144–155 54. Pan Y, Li J F. Thermoelectric performance enhancement in n-type Bi2(TeSe)3 alloys owing to nanoscale inhomogeneity combined with a spark plasma-textured microstructure. NPG Asia Materials, 2016, 8(6): e275 55. Dharmaiah P, Kim H S, Lee C H, Hong S J. Influence of powder size on thermoelectric properties of p-type 25%Bi2Te3–75%Sb2Te3 alloys fabricated using gas-atomization and spark-plasma sintering. Journal of Alloys and Compounds, 2016, 686: 1–8 56. Hsu K F, Loo S, Guo F, Chen W, Dyck J S, Uher C, Hogan T, Polychroniadis E K, Kanatzidis M G. Cubic AgPbmSbTe2 + m: bulk thermoelectric materials with high figure of merit. Science, 2004, 303(5659): 818–821 57. Wang H, Li J F, Nan C W, Zhou M, Liu W, Zhang B P, Kita T. High-performance Ag0.8Pb18 + xSbTe20 thermoelectric bulk materials fabricated by mechanical alloying and spark plasma sintering. Applied Physics Letters, 2006, 88(9): 092104 58. Johnsen S, He J, Androulakis J, Dravid V P, Todorov I, Chung D Y, Kanatzidis M G. Nanostructures boost the thermoelectric performance of PbS. Journal of the American Chemical Society, 2011, 133(10): 3460–3470 59. Pei Y, Shi X, LaLonde A, Wang H, Chen L, Snyder G J. Convergence of electronic bands for high performance bulk thermoelectrics. Nature, 2011, 473(7345): 66–69 60. Zhang Q, Yang S, Zhang Q, Chen S, Liu W, Wang H, Tian Z, Broido D, Chen G, Ren Z. Effect of aluminum on the thermoelectric properties of nanostructured PbTe. Nanotechnology, 2013, 24(34): 345705 61. Zhang Y, Wang H, Kräemer S, Shi Y, Zhang F, Snedaker M, Ding 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. K, Moskovits M, Snyder G J, Stucky G D. Surfactant-free synthesis of Bi2Te3-Te micro-nano heterostructure with enhanced thermoelectric figure of merit. ACS Nano, 2011, 5(4): 3158–3165 Zhao L D, Lo S H, Zhang Y, Sun H, Tan G, Uher C, Wolverton C, Dravid V P, Kanatzidis M G. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature, 2014, 508(7496): 373–377 Sevinçli H, Sevik C, Çağın T, Cuniberti G. A bottom-up route to enhance thermoelectric figures of merit in graphene nanoribbons. Scientific Reports, 2013, 3(1): 1228 Yamini S A, Wang H, Ginting D, Mitchell D R, Dou S X, Snyder G J. Thermoelectric performance of n-type (PbTe)0.75(PbS)0.15(PbSe)0.1 composites. ACS Applied Materials & Interfaces, 2014, 6(14): 11476–11483 Lu Z W, Li J Q, Wang C Y, Li Y, Liu F S, Ao W Q. Effects of Mn substitution on the phases and thermoelectric properties of Ge0.8Pb0.2Te alloy. Journal of Alloys and Compounds, 2015, 621: 345–350 Zhao L D, Zhang X, Wu H, Tan G, Pei Y, Xiao Y, Chang C, Wu D, Chi H, Zheng L, Gong S, Uher C, He J, Kanatzidis M G. Enhanced thermoelectric properties in the counter-doped SnTe system with strained endotaxial SrTe. Journal of the American Chemical Society, 2016, 138(7): 2366–2373 Li J C, Li D, Qin X Y, Zhang J. Enhanced thermoelectric performance of p-type SnSe doped with Zn. Scripta Materialia, 2017, 126: 6–10 Boukai A I, Bunimovich Y, Tahir-Kheli J, Yu J K, Goddard W A III, Heath J R. Silicon nanowires as efficient thermoelectric materials. Nature, 2008, 451(7175): 168–171 Hochbaum A I, Chen R, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A, Yang P. Enhanced thermoelectric performance of rough silicon nanowires. Nature, 2008, 451(7175): 163–167 Miao L, Tanemura S, Huang R, Liu C Y, Huang C M, Xu G. Large Seebeck coefficients of protonated titanate nanotubes for hightemperature thermoelectric conversion. ACS Applied Materials & Interfaces, 2010, 2(8): 2355–2359 Li Z, Chen Y, Li J F, Chen H, Wang L, Zheng S, Lu G. Systhesizing SnTe nanocrystals leading to thermoelectric performance enhancement via an ultra-fast microwave hydrothermal method. Nano Energy, 2016, 28: 78–86 Yang L, Yang N, Li B. Thermoelectric properties of nanoscale three dimensional Si phononic crystals. International Journal of Heat and Mass Transfer, 2016, 99: 102–106 He D, Zhao W, Mu X, Zhou H, Wei P, Zhu W, Nie X, Su X, Liu H, He J, Zhang Q. Enhanced thermoelectric performance of heavyfermion YbAl3 via multi-scale microstructures. Journal of Alloys and Compounds, 2017, 725: 1297–1303 Zhao W, Liu Z, Sun Z, Zhang Q, Wei P, Mu X, Zhou H, Li C, Ma S, He D, Ji P, Zhu W, Nie X, Su X, Tang X, Shen B, Dong X, Yang J, Liu Y, Shi J. Superparamagnetic enhancement of thermoelectric performance. Nature, 2017, 549(7671): 247–251 Pei Y, Lensch-Falk J, Toberer E S, Medlin D L, Snyder G J. High thermoelectric performance in PbTe due to large nanoscale Ag2Te precipitates and La doping. Advanced Functional Materials, 2011, 21(2): 241–249 Kai-Xuan CHEN et al. Nanostructural thermoelectric materials 76. Gahtori B, Bathula S, Tyagi K, Jayasimhadri M, Srivastava A K, Singh S, Budhani R C, Dhar A. Giant enhancement in thermoelectric performance of copper selenide by incorporation of different nanoscale dimensional defect features. Nano Energy, 2015, 13: 36–46 77. Ahmad S, Singh A, Bohra A, Basu R, Bhattacharya S, Bhatt R, Meshram K N, Roy M, Sarkar S K, Hayakawa Y, Debnath A K, Aswal D K, Gupta S K. Boosting thermoelectric performance of p-type SiGe alloys through in-situ metallic YSi2 nanoinclusions. Nano Energy, 2016, 27: 282–297 78. Kim G H, Hwang D H, Woo S I. Thermoelectric properties of nanocomposite thin films prepared with poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) and graphene. Physical Chemistry Chemical Physics, 2012, 14(10): 3530–3536 79. Tan X J, Liu H J, Wen Y W, Lv H Y, Pan L, Shi J, Tang X F. Thermoelectric properties of ultrasmall single-wall carbon nanotubes. Journal of Physical Chemistry C, 2011, 115(44): 21996– 22001 80. Ouyang T, Xiao H P, Xie Y E, Wei X L, Chen Y P, Zhong J X. Thermoelectric properties of gamma-graphyne nanoribbons and nanojunctions. Journal of Applied Physics, 2013, 114(7): 073710 81. Wang C, Ouyang T, Chen Y, Zhou B, Zhong J. Thermoelectric properties of gamma-graphyne nanoribbon incorporating diamond-like quantum dots. Journal of Physics. D, Applied Physics, 2016, 49(13): 135303 82. Yang D, Lu C, Yin H, Herman I P. Thermoelectric performance of PbSe quantum dot films. Nanoscale, 2013, 5(16): 7290–7296 83. Guo R Q, Wang X J, Kuang Y D, Huang B L. First-principles study of anisotropic thermoelectric transport properties of IV–VI semiconductor compounds SnSe and SnS. Physical Review B: Condensed Matter and Materials Physics, 2015, 92(11): 115202 84. Chen Z G, Han G, Yang L, Cheng L, Zou J. Nanostructured thermoelectric materials: current research and future challenge. Progress in Natural Science: Materials International, 2012, 22(6): 535–549 85. Ginting D, Lin C C, Rathnam L, Yun J H, Yu B K, Kim S J, Rhyee J S. High thermoelectric performance due to nanoinclusions and randomly distributed interface potentials in n-type (PbTe0.93 – xSe0.07Clx)0.93(PbS)0.07 composites. Journal of Materials Chemistry. A, Materials for Energy and Sustainability, 2017, 5(26): 13535–13543 86. Zhang D, Yang J, Jiang Q, Zhou Z, Li X, Xin J, Basit A, Ren Y, He X. Multi-cations compound Cu2CoSnS4: DFT calculating, band engineering and thermoelectric performance regulation. Nano Energy, 2017, 36: 156–165 87. Volz S G, Chen G. Molecular-dynamics simulation of thermal conductivity of silicon crystals. Physical Review B: Condensed Matter and Materials Physics, 2000, 61(4): 2651–2656 88. Volz S G, Chen G. Molecular dynamics simulation of thermal conductivity of silicon nanowires. Applied Physics Letters, 1999, 75(14): 2056–2058 89. Xie H, Ouyang T, Germaneau É, Qin G, Hu M, Bao H. Large tunability of lattice thermal conductivity of monolayer silicene via mechanical strain. Physical Review B: Condensed Matter and Materials Physics, 2016, 93(7): 075404 90. Turney J E, Landry E S, McGaughey A J H, Amon C H. Predicting 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 11 phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations. Physical Review B: Condensed Matter and Materials Physics, 2009, 79(6): 064301 Li W, Carrete J, Katcho N A, Mingo N. ShengBTE: a solver of the Boltzmann transport equation for phonons. Computer Physics Communications, 2014, 185(6): 1747–1758 Jiang J W, Wang J S, Li B W. A nonequilibrium Green’s function study of thermoelectric properties in single-walled carbon nanotubes. Journal of Applied Physics, 2011, 109(1): 014326 Chen K X, Wang X M, Mo D C, Lyu S S. Thermoelectric properties of transition metal dichalcogenides: from monolayers to nanotubes. Journal of Physical Chemistry C, 2015, 119(47): 26706–26711 Chen K X, Lyu S H, Wang X M, Fu Y X, Heng Y, Mo D C. Excellent thermoelectric performance predicted in two-dimensional buckled antimonene: a first-principles study. Journal of Physical Chemistry C, 2017, 121(24): 13035–13042 Fan D D, Liu H J, Cheng L, Jiang P H, Shi J, Tang X F. MoS2 nanoribbons as promising thermoelectric materials. Applied Physics Letters, 2014, 105(13): 133113 Zhang J, Liu H J, Cheng L, Wei J, Liang J H, Fan D D, Shi J, Tang X F, Zhang Q J. Phosphorene nanoribbon as a promising candidate for thermoelectric applications. Scientific Reports, 2014, 4(1): 6452 Wang X M, Lu S S. Thermoelectric transport in graphyne nanotubes. Journal of Physical Chemistry C, 2013, 117(38): 19740–19745 Chen K X, Luo Z Y, Mo D C, Lyu S S. WSe2 nanoribbons: new high-performance thermoelectric materials. Physical Chemistry Chemical Physics, 2016, 18(24): 16337–16344 He W, Zhang G, Zhang X, Ji J, Li G, Zhao X. Recent development and application of thermoelectric generator and cooler. Applied Energy, 2015, 143: 1–25 Gou X, Xiao H, Yang S. Modeling, experimental study and optimization on low-temperature waste heat thermoelectric generator system. Applied Energy, 2010, 87(10): 3131–3136 Wang L. Thermopower and thermoconductance properties of zigzag edged graphene nanoribbon based thermoelectric module. Physics Letters, 2013, 377(21–22): 1486–1490 Sevinçli H, Cuniberti G. Enhanced thermoelectric figure of merit in edge-disordered zigzag graphene nanoribbons. Physical Review B: Condensed Matter and Materials Physics, 2010, 81(11): 113401 Chang P H, Nikolić B K. Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high-ZT thermoelectrics. Physical Review B: Condensed Matter and Materials Physics, 2012, 86(4): 041406 Yeo P S E, Sullivan M B, Loh K P, Gan C K. First-principles study of the thermoelectric properties of strained graphene nanoribbons. Journal of Materials Chemistry. A, Materials for Energy and Sustainability, 2013, 1(36): 10762–10767 Yu C, Choi K, Yin L, Grunlan J C. Light-weight flexible carbon nanotube based organic composites with large thermoelectric power factors. ACS Nano, 2011, 5(10): 7885–7892 Avery A D, Zhou B H, Lee J, Lee E S, Miller E M, Ihly R, Wesenberg D, Mistry K S, Guillot S L, Zink B L, Kim Y H, 12 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. Front. Energy Blackburn J L, Ferguson A J. Tailored semiconducting carbon nanotube networks with enhanced thermoelectric properties. Nature Energy, 2016, 1(4): 16033 Hsin C L, Wingert M, Huang C W, Guo H, Shih T J, Suh J, Wang K, Wu J, Wu W W, Chen R. Phase transformation and thermoelectric properties of bismuth-telluride nanowires. Nanoscale, 2013, 5(11): 4669–4672 Jiang J W, Wang J S. Joule heating and thermoelectric properties in short single-walled carbon nanotubes: electron-phonon interaction effect. Journal of Applied Physics, 2011, 110(12): 124319 Si H G, Wang Y X, Yan Y L, Zhang G B. Structural, electronic, and thermoelectric properties of InSe nanotubes: first-principles calculations. Journal of Physical Chemistry C, 2012, 116(6): 3956–3961 Huang W, Da H, Liang G. Thermoelectric performance of MX2 (M = Mo, W; X = S, Se) monolayers. Journal of Applied Physics, 2013, 113(10): 104304 Huang W, Luo X, Gan C K, Quek S Y, Liang G. Theoretical study of thermoelectric properties of few-layer MoS2 and WSe2. Physical Chemistry Chemical Physics, 2014, 16(22): 10866–10874 Tahir M, Schwingenschlögl U. Tunable thermoelectricity in monolayers of MoS2 and other group-VI dichalcogenides. New Journal of Physics, 2014, 16(11): 115003 Wickramaratne D, Zahid F, Lake R K. Electronic and thermoelectric properties of few-layer transition metal dichalcogenides. Journal of Chemical Physics, 2014, 140(12): 124710 Lee C, Hong J, Whangbo M H, Shim J H. Enhancing the thermoelectric properties of layered transition-metal dichalcogenides 2H–MQ2 (M = Mo, W; Q = S, Se, Te) by layer mixing: density functional investigation. Chemistry of Materials, 2013, 25(18): 3745–3752 Bhattacharyya S, Pandey T, Singh A K. Effect of strain on electronic and thermoelectric properties of few layers to bulk MoS2. Nanotechnology, 2014, 25(46): 465701 Guo S D. Biaxial strain tuned thermoelectric properties in monolayer PtSe2. Journal of Materials Chemistry. C, Materials for Optical and Electronic Devices, 2016, 4(39): 9366–9374 Wang X M, Mo D C, Lu S S. On the thermoelectric transport 118. 119. 120. 121. 122. 123. 124. 125. 126. properties of graphyne by the first-principles method. Journal of Chemical Physics, 2013, 138(20): 204704 Yang K, Cahangirov S, Cantarero A, Rubio A, D’Agosta R. Thermoelectric properties of atomically thin silicene and germanene nanostructures. Physical Review B: Condensed Matter and Materials Physics, 2014, 89(12): 125403 Fei R, Faghaninia A, Soklaski R, Yan J A, Lo C, Yang L. Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Letters, 2014, 14(11): 6393– 6399 Lv H Y, Lu W J, Shao D F, Sun Y P. Enhanced thermoelectric performance of phosphorene by strain-induced band convergence. Physical Review B: Condensed Matter and Materials Physics, 2014, 90(8): 085433 Medrano Sandonas L, Teich D, Gutierrez R, Lorenz T, Pecchia A, Seifert G, Cuniberti G. Anisotropic thermoelectric response in twodimensional puckered structures. Journal of Physical Chemistry C, 2016, 120(33): 18841–18849 Carrete J, Mingo N, Tian G, Ågren H, Baev A, Prasad P N. Thermoelectric properties of hybrid organic-inorganic superlattices. Journal of Physical Chemistry C, 2012, 116(20): 10881– 10886 Savelli G, Silveira Stein S, Bernard-Granger G, Faucherand P, Montès L, Dilhaire S, Pernot G. Titanium-based silicide quantum dot superlattices for thermoelectrics applications. Nanotechnology, 2015, 26(27): 275605 Duan J, Wang X, Lai X, Li G, Watanabe K, Taniguchi T, Zebarjadi M, Andrei E Y. High thermoelectric power factor in graphene/hBN devices. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(50): 14272–14276 Luo Y, Jiang Q, Yang J, Li W, Zhang D, Zhou Z, Cheng Y, Ren Y, He X, Li X. Simultaneous regulation of electrical and thermal transport properties in CuInTe2 by directly incorporating excess ZnX (X = S, Se). Nano Energy, 2017, 32: 80–87 Yin K, Su X, Yan Y, Tang H, Kanatzidis M G, Uher C, Tang X. Morphology modulation of SiC nano-additives for mechanical robust high thermoelectric performance Mg2Si1 – xSnx/SiC nanocomposites. Scripta Materialia, 2017, 126: 1–5

Tutor Answer

mikewinter3
School: Duke University

Attached.

1

Paraphrasing

Student name:
Institutional affiliation:

2
Paraphrasing
The attached word document addresses the question “Witting in own words” by answering the
following:
Write in your own word the following sections of the attached document, do not change the science:

3.1.1 Molecular dynamics
3.1.3 Non-equilibrium Green’s function


1

Running Head: Theoretical calculation in low-dimensional thermoelectric materials

Paraphrasing: Theoretical calculation in low-dimensional thermoelectric materials

Student name:
Institutional affiliation:

2

Theoretical calculation in low-dimensional thermoelectric materials

Paraphrasing: Theoretical calculation in low-dimensional thermoelectric materials

3.1.1. Molecular dynamics
According to the laws of Newton motion, heat transport is studied using MD. The thermal
conductivity calculated using the Green Kubo formula as follows:

Where T= absolute temperature, KB= Boltzmann constant, V=volume, J𝛼 and J𝛽 represts heat
flow along direction 𝛼 and 𝛽 respectively. Moreover, the non-equilibrium MD achieves thermal
conductivity based on the law of Fourier. The heat flow density or temperature gradient introduced
so that heat flow is obtain as follows:

3.1.3 Non-equilibrium Green’s function
The ballistic regime is only v...

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Anonymous
Good stuff. Would use again.

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