2016挑戰(zhàn)杯附件的熱電性能nanoen

1、Nano Energy 30 (2016) 225234High thermoelectric performance of Weyl semimetal TaAsBo Penga, Hao Zhanga, Hezhu Shaob, Hongliang Luc, David Wei Zhangc, Heyuan Zhuaa Shanghai Ultra-precision Optical Manufacturing Engineering Research Center and Key Laboratory of Micro and Nano Photonic Structures (Mini

2、stry of Education), Department of Optical Science and Engineering, Fudan University, Shanghai 200433,b Ningbo Institute of Materials Technology and Engineering,Academy of Sciences, Ningbo 315201,c State Key Laboratory of ASIC and System, Institute of Advanced Nanodevices, School of Microelectronics,

3、 Fudan University, Shanghai 200433,A R T I C L E I N F O A B S T R A C T The existence of Weyl nodes predicted in TaAs has been conrmed by angle-resolved photoemission spectroscopy, which provides potential applications in thermoelectric devices due to the extraordinary transport properties of TaAs.

4、 By using rst-principles calculations and semiclassical Boltzmann transport theory, we study the electrical transport properties of TaAs. High anisotropy is observed in the electrical transport of TaAs. The obtained Seebeck coecients are in good agreement with experimental values. The lattice dynami

5、cs properties of TaAs are also investigated and the obtained phonon frequencies agree well with the measurements. The lattice thermal conductivity is calculated using the self-consistent iterative approach. Anisotropic lattice thermalKeywords:Weyl semimetal TaAs ThermoelectricsAb initio calculations

6、44conductivity is observed as well.um thermoelectric gure of merit zT of 0.63 at 900 K is found for n-doTaAs along zz direction. Finally, the size dependence of lattice thermal conductivity and correspondingthermoelectric properties are investigated for designing thermoelectric nanostructures. The w

7、ork sheds light on the nature of the thermoelectric response of Weyl semimetal.good conductor for electrons, which often conict with each other as well 4,5.Materials with non-trivial electronic topology such as Bi2Se3 and Bi2Te3 have been found to exhibit high thermoelectric performance 6 8. These m

8、aterials usually comprise heavy atoms and possess small band gaps 9, since heavy atoms lead to low vibrational frequencies that result in a low lattice thermal conductivity 10, and heavy atoms also imply large spin-orbit coupling (SOC) necessary for certain nontrivial topological materials 11,12. In

9、 addition, zT of these materials can be further improved by optimizing the geometry size to ize the contribution of the gapless edge states and to reduce thelattice thermal conductivity 1315.Recently, TaAs, a newly predicted Weyl semimetal 1618, has been conrmed by a number of experiments 1923, and

10、the key features of the Weyl semimetal such as the negative magnetohave been observed in TaAs 2426. The compounds hosting Weyl fermions are called as Weyl semimetal, with and only with Weyl nodes1. IntroductionThermoelectric materials can convert wasted heat into electrical energy (known as the Seeb

11、eck eect) and vice versa (known as the Peltier eect), which provide an environmentally friendly alternative to increase energy-consumption eciency for a sustainable energy future. A key challenge to improving thermoelectric properties is to obtainecient energy conversion. The thermoelectric temperat

12、ure T is dened as 13gureofmeritatzT = S2T ,where S is(1)potentialSeebeck coecient measuring theelectricaldierence created from a temperature gradient, is electrical con-ductivity, and = el + l is thermal conductivity consisting of electro- nic and lattice contributions, which is a standard approxima

13、tion. The optimization of the thermoelectric performance of materials is dicult since the three transport parameters S, and are usually conicting to each other. For instance, increasing the electrical conductivity usually indicates lowering the Seebeck coecient S, while the electro- nic thermal cond

14、uctivity el is proportional to T according to the Wiedemann-Franz relation. Furthermore, high thermoelectric perfor- mance requires the system to be a bad conductor for phonons but aformed by crossing of two non-degenerate bandsly enough to thechemical potential 2734. Besides being of great interest

15、 to funda- mental physics, TaAs has been shown to exhibit high carrier mobilities26. Thus TaAs may nd substal applications in electronics,spintronics and quantum computation 23,26. The structural, elastic, dielectric, lattice vibrational, and electronic properties of TaAs have Corresponding author.a

16、ddress: zhangh (H. Zhang).Received 19 July 2016; Received in revised form 5 October 2016; Accepted 7 October 2016Available online 10 October 20162211-2855/ © 2016 Elsevier.Contents lists available at ScienceDirectNano Energyjournal homepage:B. Peng et al.Nano Energy 30 (2016) 225234also been in

17、vestigated in35,36. Moreover, a recent study hasfound that theum of the thermoelectric power factor P of TaAsis comparable to that of PbTe, a promising thermoelectric material 9. Therefore, TaAs might have a great potential for ecient thermo- electric response. An accurate treatment of the lattice t

18、hermal con- ductivity of TaAs is required for predicting the thermoelectric perfor-mance precisely. In addition, the phonon and electron meanpath,which are also crucial when designing thermoelectric nanostructures, remain uninvestigated.Here, by using rst-principles calculations and semiclassical Bo

19、ltzmann transport theory, we study the electrical transport proper- ties of TaAs. The lattice thermal conductivity is calculated using the self-consistent iterative approach. Anisotropic transport properties are observed in TaAs, indicating orientation-dependent applications in the design of nanodev

20、ices. Although high electronic and lattice thermal conductivities are observed, TaAs can still be a high-performance thermoelectric material. Finally, the size dependence of zT is investi- gated at dierent temperatures, which provides new opportunities to realize high thermoelectric performance in T

21、aAs.Fig. 1. (a) Body-centered tetragonal structure, (b) side and (c) top view for conventional cell of TaAs, and (d) primitive unit cell of TaAs.3. Results and discussions3.1. Electrical transport properties2. Computational methodsTantalum arsenide is a body-centered tetragonal lattice system withAl

22、l the calculations are performed using the Vienna ab-initiosimulation package (VASP) based on density functional theory (DFT)space groupI41md(#109, C4v), as shown in Fig. 1(a)(c). Theoptimized lattice constants are a=3.462 and c=11.708 , which are in good agreements with previous results 16,17,36. A

23、s shown in37. We choose teralized gradient approximation (GGA) in thePerdew-Burke-Ernzerhof (PBE) parametrization for the exchange- correlation functional with eleven valence electrons for Ta atom and ve valence electrons for As atom. A plane-wave basis set is employed with kinetic energy cuto of 80

24、0 eV. A 15 × 15 × 15 k-mesh is used during structural relaxation for the unit cell until the energy dierencesare converged within 106 eV, with a Hellman-Feynman force conver- gence threshold of 104 eV/.The thermoelectric properties are obtained using semiclassical Boltzmann transport theor

25、y and the rigid band approach as imple- mented in the BoltzTraP code 38,39. The constant relaxation time approximation is employed, which is valid when the relaxation time does not vary strongly with the energy scale of kBT 2,40. This approximation has described the thermoelectric properties of many

26、 materials accurately 4143,2. A dense 41×41×41 k-mesh is intro- duced for TaAs to enable accurate Fourier interpolation of the Kohn- Sham eigenvalues. The initial k-mesh is interpolated up to a mesh ve times denser than the original.Using the ShengBTE code, the lattice thermal conductivity

27、 can be calculated iteratively from the Boltzmann transport equation for phonons with harmonic and anharmonic interatomic force constants (IFCs) as input 4447. The harmonic IFCs are obtained by density functional perturbation theory (DFPT) using the supercell approach, which calculates the dynamical

28、 matrix through the linear response of electron density 48. A 3 × 3 × 3 supercell with 5 × 5 × k-mesh is used. Using the harmonic IFCs, the phonon dispersion relation can be obtained, which determines the group velocity and specic heat C. The third-order anharmonic IFCs play an i

29、mportant role in calculatingFig. 2(d), there are two Ta atoms and two As atoms in each primitive unit cell.The electronic structures of TaAs obtained by the PBE functional and the HSE functional are similar and the trends of the band structures are the same 36. Therefore, we discuss the PBE results

30、for TaAs in the following. Fig. 2(a) shows the band structure of TaAs along high-symmetry directions in the absence of SOC. The valence and conduction band cross each other along -N-1, indicating that TaAs is a semimetal. Including SOC in the rst-principles calculation leads to adramatic change of t

31、he band structure near the Fervel, as shown inFig. 2(b). The band structure is fully gapped along high-symmetry directions. Excellent consistency is observed between calculated elec- tronic structure and angle-resolved photoemission spectroscopy (ARPES) measurements 1922.The total and partial densit

32、y of states (DOS) N () are shown inFig. 3(a). The electronic states near the valence-bandum andconduction-band minimum mainly consist of Ta 5d orbitals. The enhanced DOS due to 5d electrons of Ta plays a crucial role in understanding the electrical transport properties of TaAs. It has beenpredicted

33、that non-interacting Weyl semimetallike bad metalswith a vanishingly small DOS at the Fervel 49,50.Although the charge transport in Weyl semimetals exhibits a rich variety of behavior, the semiclassical Boltzmann transport theory has been proved to be an eective tool for investigating their electric

34、al transport properties 49,51. To determine the transport properties, we use the rigid band approximation, in which the electronic structure isassumed to be unchanged with doand only the Fervel isthe three-phonon scattering rate, which is the inverse ofThe .anharmonic IFCs are calculated using a sup

35、ercell-based, nite-dier- ence method 47, and the same 3 × 3 × 3 supercell with 3 × 3 × 3 k- mesh is used. An interaction range of 4.9 is considered herein, which includes eighth-nearest-neighbor atoms. The convergence of thermal conductivity with respect to k points is tested in

36、our calculation. A discretization of the Brillouin zone (BZ) into a -centered regular grid of 25 × 25 × 25 k points is introduced. In order to enforce the conservation of energy in the three-phonon processes, a Gaussian function is used 46 with scale parameter for broadening chosen as 0.1.

37、shifted. Within the Boltzmann transport theory, the transport coe-cients at temperature T and Fervel can be calculated using theFermi-Dirac distribution function f 38,f (T , ) 1 d,T , = ()(2)f (T , ) d, 1 ST , = () eT (T , )(3)226B. Peng et al.Nano Energy 30 (2016) 225234Fig. 2. Electronic band stru

38、cture of TaAs along high-symmetry path (a) without and (b) with SOC.where kB is the Boltzmann constant. Eq. (6) implies that enhanced energy dependence of the carrier concentration n () can come from a local increase in N () may lead to larger Seebeck coecient.Fig. 5 shows the dependence of the calc

39、ulated electrical conductiv-Total Ta-s Ta-p Ta-d As-s As-pity / on the Fervel . The / is highly anisotropic(xx/ = yy/ zz/). The carrier relaxation time is determined byseveral scattering mechanisms including electron-phonon scattering (both acoustic and optical phonons), piezoelectric scattering and

40、 impurity scattering (both ionised and neutral). The relaxation time can be obtained from the experimental electron relaxation time el. TaAs exhibits a high carrier mobility at 2 K, and the corresponding relaxation time is 4.51 × 1011 s , which can be used as input in the ab initio approach 26.

41、 For thermoelectric materials in power generation application, acoustic phonons are usually assumed as predominant electron scattering resources 3, i.e. T 1. Thus we obtain the electron relaxation time at dierent temperatures, as listed in Table 1.The electronic thermal conductivityrelates to the el

42、ectrical conductivity via the Wiedemann-Franz law-0.8-0.40.0Energy (eV)0.40.8elFig. 3. Total and partial DOS N () of TaAs in the energy range from 0.8 to 0.8 eV.el = LT ,(7)el 2 f (T , ) 1 where L is the Lorenz number. The Lorenz number can be derived from the calculated Seebeck coecients 53,54, and

43、 the results along xx and zz directions are presented in Fig. 6. We also list the Lorenz numbers L of pristine TaAs at dierent temperatures in Table 1. For both pristine and doped TaAs, the true Lorenz number is in fact lower than L0 (2.45 × 108 W/K2). Using the carrier relaxation time and Lore

44、nz number, the electronic thermal conductivity of TaAs can be calculated, as shown in Fig. 7. Similar to the electrical conductivity, the el of TaAsT , = ()( ) d,e T 2(4)where and are Cartesian indices, is the volume of the unit cell, and e is the charge of an electron. The transport distribution fu

45、nction () is given by 2 ( )ei,q () =v i, q v i, q,i,q elelel = ). As listed in Table 1, ofelNdis highly anisotropic as well (xxyyzz0(5)pristine TaAs increases with increasing temperature. It should benoticed that the electronic thermal conductivity along zz direction is more than 2 times lower than

46、that along xx direction, which may result in higher thermoelectric eciency along zz direction.where N0 is the number of q points sampling, i is the band index, respectively, v is the electron group velocity and is the electron relaxation time.The calculated Seebeck coecients are weakly anisotropic (

47、Sxx = Syy Szz). The xx and zz tensor components of the Seebeck3.2. Lattice thermal conductivitycoecient as a function of the Fervel are shown in Fig. 4(a) and(b), respectively. A negative means p-type do, while a positive The inclusion of lattice contributions to the thermal conductivity is essentia

48、l for an accurate prediction of thermoelectric properties of TaAs. The lattice thermal conductivity l can be calculated using the self-consistent iterative approach 4447 as a sum of contribution of all the phonon modes 55,56, which comprises both a phonon branch index p and a wave vector q,means n-t

49、ype do. It has been reported that when the Fervel isat the Weyl nodes, the Seebeck coecient vanishes 51, which is the case in our results. The calculated S along xx and zz directions forpristine TaAs are 42.19 V/K and 48.78 V/K, respectively, which give reasonable estimates compared with the experim

50、ental value of38.94 V/K using pieces of polycrystalline pellets of TaAs 52. The peaks in S along both xx and zz directions can be attributed to a sharp energy dependence of the DOS, i.e. large N ()/, as present in Fig. 3, which can be rationalized by the Mott relation 3= 1 C v2 l, (8)where C is the

51、heat capacity per mode, and are the group velocity and relaxation time of mode along direction, respectively. The lattice dynamical properties C and in Eq. (8) can be obtained by the phonon dispersion relation with harmonic interatomic force constants2 k T 1 dn ()21 d (),BS =+3e n d d=(6)227DOS (sta

52、tes/eV)B. Peng et al.Nano Energy 30 (2016) 225234Fig. 4. Seebeck coecient S as a function of the Fervel along (a) xx and (b) zz directions.(a)(b)Fig. 5. Electrical conductivity / as a function of the Fervel along (a) xx and (b) zz directions.Fig. 8 shows the calculated phonon dispersion of TaAs, whi

53、ch is in agreement with previous works 36,57. There are four atoms in one unit cell, corresponding to three acoustic and nine optical phonon branches. The dispersion is divided into two regions containing six branches with a gap about 30.3 cm1. We predict the vibrational mode of TaAs based on group-

54、theory analysis. Since TaAs belongs to the C4v point group, the optical lattice-vibration modes at point can be thus decomposed as 57Table 1Electron relaxation time el, Lorenz number L and electronic thermal conductivity el of pristine TaAs at 300 K, 500 K, 700 K and 900 K.T (K)el (×1013 s)Lxx (108 W/ K )el (W/L (108 W/el (W/xxzzK2)zz2mK)mK)3005007009003.011.801.291