稀有金属(英文版) 2018,37(04),316-325

Theoretical investigations of electrical transport properties in CoSb₃ skutterudites under hydrostatic loadings

Chongze Hu Peter Ni Li Zhan Huijuan Zhao Jian He Terry M.Tritt Jingsong Huang Bobby G.Sumpter

Department of Mechanical Engineering, Clemson University

Department of Mechanical Engineering, University of Minnesota-Twin Cities

Montgomery High School

Department of Physics and Astronomy,Clemson University

Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory

收稿日期：24 September 2017

基金：supported by the Office of Science of the US Department of Energy (Nos. DEAC05-00OR22750 and DE-AC02-05-CH11231);the support of National Science Foundation (No. DMR-1307740);

Theoretical investigations of electrical transport properties in CoSb₃ skutterudites under hydrostatic loadings

Chongze Hu Peter Ni Li Zhan Huijuan Zhao Jian He Terry M.Tritt Jingsong Huang Bobby G.Sumpter

Department of Mechanical Engineering, Clemson University

Department of Mechanical Engineering, University of Minnesota-Twin Cities

Montgomery High School

Department of Physics and Astronomy,Clemson University

Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory

Abstract：

CoSb₃-based skutterudites have been a benchmark mid-temperature thermoelectric material under intensive experimental and theoretical studies for decades.Doping and filling, to the first order, alter the crystal lattice constant of CoSb3 in the context of "chemical pressure." In this work, we employed ab initio density functional theory in conjunction with semiclassical Boltzmann transport theory to investigate the mechanical properties and especially how hydrostatic loadings, i.e., "physical pressure," impact the electronic band structure, Seebeck coefficient,and power factor of pristine CoSb₃. It is found that hydrostatic pressure enlarges the band gap, suppresses the density of states(DOS) near the valence band edge, and fosters the band convergence between the valley bands and the conduction band minimum(CBM). By contrast,hydrostatic tensile reduces the band gap, increases the DOS near the valence band edge, and diminishes the valley bands near the CBM. Therefore, applying hydrostatic pressure provides an alternative avenue for achieving band convergence to improve thermoelectric properties of N-type CoSb3, which is further supported by our carrier concentration studies. These results provide valuable insight into the further improvement of thermoelectric performance of CoSb3-based skutterudites via a synergy of physical and chemical pressures.

Keyword：

CoSb₃ skutterudite; Hydrostatic loadings; Mechanical properties; Electronic structure; Seebeck coefficient; Thermoelectrics;

Author： Jian He e-mail:Jianhe@clemson.edu; Jingsong Huang e-mail: huangj3@ornl.govo;

Received： 24 September 2017

1 Introduction

High-performance thermoelectric (TE) materials are at the heart of thermoelectrics,a vital green energy technology that directly converts waste heat to electricity with high reliability [ 1] .The TE performance of a material is measured by its dimensionless figure of merit, ,where S is the Seebeck coefficient (aka thermopower),σis the electrical conductivity,k_e is the carrier thermal conductivity,and k_l is the lattice thermal conductivity.In particular,the term S²σis called the power factor.Improving ZT of a given material is hinged upon optimizing the otherwise adversely inter-dependentσ,S,and k as a group.To this end,the“phonon-glass-electron crystal”(PGEC) is an effective approach [ 2, 3] ,and CoSb₃-based skutterudites are a prime example of the PGEC concept [ 2, 4] .While the covalent bonding in CoSb₃elicits a high charge carrier mobility,the same causes an undesired high k_l.Toward improving the TE performance of CoSb₃,its cagey crystal structure invites filling guest atoms into the cage [ 5, 6, 7] ,doping at the Co or Sb site [ 8, 9] ,and a combination of filling and doping [ 10, 11, 12, 13] .

To the first order,filling and doping alter the bond length/angle on the atomic level,thereby giving rise to a lattice constant change in the context of“chemical pressure.”The comparison between the effects of“chemical pressure”and its counterpart of“physical pressure”(i.e.,the externally applied forces) has been an appealing longstanding topic of research in the field of condensed matter physics and materials sciences [ 14, 15] .Inspired by the analogy between the chemical pressure and physical pressure,in this work we studied the effects of hydrostatic loadings (pressure and tensile) on the electronic band structure and Seebeck coefficient of pristine CoSb₃.We note that there exists a plethora of prior experimental and theoretical studies of hydrostatic loadings effects on the mechanical properties in CoSb₃.For example,Li and Rogl [ 16] investigated the stress-strain relation in multiple directions for the brittle mechanism in CoSb₃.Rogl et al. [ 17] studied a variety of mechanical properties of CoSb₃ as a function of temperature,doping/filling ratio,and packing density.Ruan et al. [ 18] reported the results of low-cycle fatigue properties.Schmidt et al. [ 19] calculated the coefficients of thermal expansion for several filling and doping compositions.Yang et al. [ 20] employed molecular dynamics (MD) to study the stress-strain curve in CoSb₃.Takizawa et al. [ 21] reported atomic insertion of group-14elements into CoSb₃ under a physical pressure up to 5 GPa.Kraimer et al. [ 22] proposed an isothermal equation of state for pristine CoSb₃ and LaFe₃CoSb₁₂ based on a pressuredependent structural study up to 20 GPa.On the other hand,studies of hydrostatic loadings effects on the electronic band structure and electrical transport properties of CoSb₃-based skutterudites are relatively scarce.Jacobsen et al. [ 23] correlated the pressure-induced transport anomalies in Ce_0.8Fe₃CoSb_12.1 to an electronic topological transition,and the results reported therein suggested that a higher physical pressure is thermoelectrically beneficial.

In this work,we employed first-principles density functional theory (DFT) combined with semiclassical Boltzmann transport theory to calculate the mechanical properties,electronic band structures,Seebeck coefficients,and power factors under hydrostatic pressure and tensile,i.e.,“physical pressure.”The results shed light on the further improvement of thermoelectric performance in CoSb₃ via doping and filling (“chemical pressure”) or a synergy of physical and chemical pressures.Figure 1shows a schematic diagram of hydrostatic loadings in a cubic cell of CoSb₃.

2 Methodology

The Vienna ab initio simulation package (VASP-5.3.5version) was used for all DFT calculations [ 24, 25] ,and Kohn-Sham equations were solved by a projected-augmented wave (PAW) method [ 26, 27] .The van der Waals(vdW) interactions were taken into account by using the optB86b-vdW [ 28] functional for the structural optimizations as previous works have revealed that the effect of vdW is critical for not only layer-structured materials [ 29, 30] but also three-dimensional (3D) bulk materials [ 31, 32] ,including CoSb₃ skutterudites [ 5] .The convergence criteria for structural optimizations were reached until the Hellmann-Feynman forces are under0.1 eV·nm^-1.The Brillouin-zone integrations were sampled on k-point grids of aΓ-centered 8×8×8 mesh.The kinetic energy cutoff for plane waves was set to 500 eV,the convergence criteria for electronic self-consistency was set at 1×10^-5 eV,and the“accurate”precision was utilized to avoid wrap errors.

After the structural optimizations,the cubic unit cell of CoSb₃ was used to calculate the mechanical (elastic)properties by performing six finite distortions of the lattice,and the elastic tensors were obtained from the strain-stress relation [ 33] .We investigated the effects of (i) pressure and(ii) tensile hydrostatic loadings by applying strains from-0.1 (pressure) to 0.1 (tensile) at an increment of 0.02 in CoSb₃.For simplicity,all the figures show a range of strains from-0.04 to 0.04 unless otherwise noted.

The static electronic band structure calculations were performed in a primitive cell of CoSb₃ by using the Perdew-Burke-Ernzerhof (PBE) [ 34] exchange-correlation functional.The band structures were subsequently plotted along the high-symmetry k-pointsΓ(0,0,0),H (0.5,-0.5,0.5),N (0,0,0.5),and P (0.25,0.25,0.25) in the primitive cell of CoSb₃.In addition to the PBE functional,we also performed high-precision electronic structure calculations using the Heyd-Scuseria-Ernzerhof (HSE06)hybrid functional [ 35] ,from which the bands were obtained using the Wannier90 program [ 36] .Since the previous studies indicated that the effects of spin-orbit coupling(SOC) and spin polarization are insignificant in pristine CoSb₃ [ 5, 37, 38] ,we did not consider these effects in the present work.

The BoltzWann code [ 39] combined with Wannier90program [ 36] was used to calculate the Seebeck coefficients (S) and the power factor (S²σ) as a function of both chemical potential (μ) and temperature (T).The relaxation time was set to 10 fs [ 5, 39] .A dense 200×200×200mesh was adopted for band interpolation with a bin width of 1×10^-3 eV.To obtain the Seebeck coefficients as a function of T,we integrated the total number of electrons

Fig.1 Schematic diagram of applying a hydrostatic pressure and b hydrostatic tensile onto a cubic cell of CoSb₃ (red arrows denote direction of strain)

at each given temperature (T),wheref(E) is the Fermi-Dirac distribution function and g(E) is the density of state (DOS).The integrated n_e was used to pinpoint the chemical potential,μ(T),and then,the Seebeck coefficients were interpolated from the grid ofμand T to obtain S (T).For simplicity,only majority carriers were considered.

3 Results and discussion

3.1 Mechanical properties of CoSb3 skutterudite

Previous studies [ 5] have shown that the vdW-DFT optB86b functional has a non-negligible effect on the lattice constant of CoSb₃.We thus take the vdW corrections into consideration to obtain the energy-strain relation(Fig.2a) and the stress-strain relation (Fig.2b).Themechanical elastic constants were subsequently obtained from the stress (σ) and strain (s) linear relationσ_i=C_ijε_j.It should be noted that the linear relation may not hold at high strain (Fig.2b).By employing symmetry operations,the6×6 elastic constant C_ij matrix is reduced to three independent constants C₁₁,C₁₂,and C₄₄ for cubic-structured CoSb₃.These elastic constants allow us to further calculate the bulk modulus (B),shear modulus (G),Young's modulus (E),and Poisson's ratio (v) in the scheme of VoigtReuss-Hill approximation [ 40] .The results are presented in Table 1.The details for calculating the upper (Voigt) [ 41] and lower (Reuss) [ 42] limits of these moduli are described in Sect.1 in the Supporting Information (SI).

As listed in Table 1,our calculations with the optB86b functional overestimate C₁₁ of CoSb₃ while yielding C₁₂and C₄₄ in good agreement with previous theoretical and/or experimental results.Early calculations by others with the PBE functional obtained a reasonably good C₁₁,but they overestimated C₁₂ and underestimated C₄₄ slightly.Though known as a good choice for calculating mechanical properties of solids,the PBEsol functional overestimated both C₁₁ and C₁₂ [ 45] .In comparison,the RPBE functional produced a C₁₁ that matched with the experimental result,but it underestimated C₄₄ [ 45] ;more importantly,the RPBE functional yielded a lattice constant of 0.9174 nm that is too large compared to the commonly accepted value of 0.9034 nm-0.9081 nm [ 5] .Also according to Rasander and Moram [ 45] ,the PBE0 calculated C₄₄ and lattice constant of 0.9033 nm matched with experiments,but it overestimated C₁₁.Based on these comparisons,and because the computation cost of optB86b is significantly lower than that of PBE0,we choose the optB86b functional for all further calculations in this study,if not otherwise noted.

Fig.2 a Total energy per unit cell and b stress calculated by optB86b functional as a function of strain from-0.1 (compression) to 0.1(expansion) at an increment of 0.02

  下载原图

Table 1 Calculated elastic constants C₁₁,C₁₂,and C₄₄,bulk modulus (B),shear modulus (G),Young's modulus (E),and Poisson's ratio (v),compared with available elastic constants C₁₁ and C₄₄ derived from extrapolating experimental data to 0 K

3.2 Strain effect on electronic band structure

Figure 3 shows the electronic band structure for the1×1×1 primitive cell of CoSb₃ under hydrostatic loadings (pressure and tensile) in a range of strains from 0to±0.04 at an increment of±0.02.For the non-strained CoSb₃ (Fig.3a),the band structure has a direct band gap(E_gap～0.23 eV) at theΓpoint.The valley band located at 0.13 eV above the conduction band minimum (CBM) in theΓ-N zone represents one of twelve degenerate Fermi electron pockets (FEPs) in the entire Brillouin zone with twelve congruent rhombic faces [ 5, 49] .Notably,these FEPs account for CoSb₃'s high power factor at high electron carrier concentration or high N-doping ratios [ 50] .In comparison,there is a notable feature of a hill band at-0.34 eV below the valence band maximum (VBM) in the zone H-N.Similar to the valley band,the hill band is also highly degenerate due to the twelve congruent faces of the rhombic-dodecahedron-shaped Brillouin zone.The top of the hill band represents the starting point to form degenerate Fermi hole pockets (FHPs) instead of electron pockets due to P-type doping.Likewise,the FHPs are beneficial for high P-type performance in CoSb₃.

Band engineering to converge conduction (or valence)bands is known as a general strategy to obtain highly degenerate band valleys (or hills) toward higher N-type (or P-type) thermoelectric performance [ 49, 50] .However,band convergence is mainly achieved by doping and/or filling under the scheme of“chemical pressure” [ 49, 50] .As shown in Fig.3b,the direct band gap (E_gap) at theΓpoint increases to 0.42 eV upon a hydrostatic pressure strain of-0.02.Meanwhile,the bottom of valley band decreases down to a value that is comparable with the CBM and thus forms an indirect pseudogap～0.45 eV with the VBM.The near degeneracy between the valley band and the CBM indicates that“physical pressure”such as hydrostatic loadings can also be used to foster band convergence.

As the strain is further increased to-0.04 (Fig.3c),the bottom of valley band continues to be pushed down and locates at 0.12 eV below the original CBM and finally forms an indirect E_gap of～0.51 eV with the VBM(Fig.3c).On the other hand,by applying the hydrostatic tensile strain,the direct E_gap in pristine CoSb₃ decreases to0.07 eV at a strain of 0.02 (Fig.3d) and closes to a zero gap at a strain of 0.04 (Fig.3e).As shown,the valley bands are very sensitive to the tensile strain.The diminishing valley with strain increasing degrades the power factor,consistent with the previous study by Tang et al. [ 49] .In contrast,hill bands are less sensitive to the tensile strain:As shown in Fig.3d,e,the tensile strain shifts up the hill band from-0.37 eV to-0.25 eV below the E_F as the strain increases from 0 to 0.04.

Since it is well known that the PBE functional tends to underestimate the band gap,we tried the HSE06 hybrid functional.The band structures calculated by the HSE06 functional are shown in Fig.S1 in the SupportingInformation.As shown,with HSE06 calculations,the bottom of valley band is lowered and becomes the CBM and forms an indirect gap of～0.78 eV with the VBM in pristine CoSb₃ (Fig.S1 a).This indirect E_gap is too large compared to the experimental value in the range of0.31 eV-0.35 eV [ 51, 52] .Hence,we conclude that such a hybrid functional does not capture an accurate band gap(band structure) of CoSb₃.Although the HSE06 functional produces larger band gaps,the variation of these gaps as a function of strains shows a similar trend compared with the values obtained with the PBE functional (Fig.4).Notably,the E_gap calculated by both functionals monotonically decreases by applying the strain from hydrostatic pressure(-0.04) to tensile strain (0.04).With the PBE functional,theE_gap decreases from 0.51 eV to 0 eV in a range of strains from-0.04 to 0.04,where a zero E_gap occurs at a strain of 0.04,leading to a metal-to-insulator transition(MIT).Although this feature is not observed in the HSE06calculations due to an enlarged E_gap,it is plausible to conjecture that the applied tensile strain will eventually close the band gap.Accordingly,we adopt the PBE functional in the following calculations.

Fig.3 Band structures of 1 x 1×1 primitive cell of CoSb₃ calculated by PBE functional under a non-strain,hydrostatic pressure with strain of b-0.02 and c-0.04,hydrostatic tensile with strain of d 0.02 and e 0.04 (Fermi energy,E_F,being set to 0 eV as indicated by horizontal dashed lines)

Fig.4 Band gap Egap calculated by PBE and HSE functionals as a function of strain from-0.04 (hydrostatic pressure) to 0.04 (hydrostatic tensile) at an increment of 0.02 (empty markers denoting indirect band gaps,while solid markers denoting direct band gaps)

The monotonic variation of E_gap with hydrostatic loading shown in Figs.3 and 4 can also be seen in the total DOS (Fig.5).Under hydrostatic pressure (Fig.5a),the states associated with the conduction bands shift up in energy.Notably,the rigid band approximation fails.For example,a strain of-0.02 nearly aligns the valley band and the triply degenerate band atΓpoint (Fig.3b),and thus,one would expect an enhanced DOS in the context of the rigid band approximation.Instead,we observed a slightly decreased DOS at strain of-0.02 compared to the case of no strain (Fig.5a),which indicates that the hydrostatic pressure not only converges the bands but also makes these bands more dispersive.More dispersive bands favor larger carrier mobility.By contrast,hydrostatic tensile shifts the states associated with the conduction bands to lower energy and therefore decreases E_gap (Fig.5b).Notably,near the valence band edge,the magnitude of DOS is significantly suppressed (enlarged) as the strain of hydrostatic pressure (tensile) increases.Once the Fermi level is deep into the valence band,say,the CoSb₃ can be considered as a degenerate semiconductor or metal.In this case,according to the Mott's relation, DOS(E)/ ,the Seebeck coefficient (S) is proportional to 1/DOS and the derivative of DOS at E_F.Since the derivative of DOS at E_F is not sensitive to strain,a suppressed (enlarged) TDOS under hydrostatic pressure (tensile) strain is favorable (detrimental) to the S.

Fig.5 Total DOS (TDOS) under a hydrostatic pressure and b hydrostatic tensile (Fermi energy,E_F,being set to 0 eV as indicated by vertical dashed lines;arrows indicate the trend of DOS under hydrostatic loadings;orbital decomposed partial DOS can be found in Ref. [5] :Co-d states and Sb-p states dominating DOS near CBM and that near VBM,respectively)

3.3 Effects of hydrostatic loading on electrical transport properties

To quantitatively understand the effect of hydrostatic loading on the Seebeck coefficient,we calculated S as a functional of the chemical potentialμat T=100 K,300 K,and 500 K.The results are shown in Fig.6.Without hydrostatic loadings (Fig.6a),the S of pristine CoSb₃exhibits two peaks (one positive and one negative) sandwiched between VBM and CBM.In the light doping region,the magnitude of S (i.e.,|S|) is found to decrease with T increasing,as expected for a semiconductor.Upon heavy doping,the|S|is proportional to T,which behaves like a degenerate semiconductor or a metal.With hydrostatic pressure strain applied (Fig.6b,c),this general trend still holds.Furthermore,the|S|increases significantly with strain increasing,especially for the magnitude of two S peaks sandwiched in the gap region (Fig.6a-c).By contrast,hydrostatic tensile strain significantly decreases the|S|(Fig.6a,d,e).At a tensile strain of 0.02 (Fig.6d),the position of the positive S peak is shifted below the VBM,while the negative S peak is located at the VBM.When the tensile strain is further increased to 0.04,both S peaks are shifted below the E_F (Fig.6e).We found that the|S|of hydrostatic pres sure-strained and the|S|of nonstrained CoSb₃ follow an order (100 K>300 K>500 K),while hydrostatic tensile-strained CoSb₃ follows the opposite,i.e.,(500 K>300 K>100 K).

As shown in Fig.6,the peak value of|S|(S_peak) is positively correlated with E_gap.To quantify the correlation between the S_peak and the E_gap,we plotted the S_peak as a function of E_gap at T=100 K,300 K,and 500 K in Fig.7a.Apparently,there is a clear linear correlation between the S_peak and E_gap at each temperature.By taking the derivative of dS_peak/dE_gap and plotting edS_peak/dE_gap as a function of 1/T,we also found a perfect linear relation for both positive and negative S peaks with a slope of 0.50 and-0.52,respectively (Fig.7b).A simple relation dS_peak/dE_gap=1/(2eT) is thus obtained,which is reminiscent of the well-known Goldsmid-Sharp rule [ 53] :S_max=E_gap/(2eT_max),where e is the elementary charge,and T_max is the absolute temperature at which the S peaks.

Finally,we discuss the effects of hydrostatic loadings on the S as a function of carrier concentration (p/n,where p for P-type doping and n for N-type doping) in CoSb₃.Figure 8shows the S(p/n) at light dopings (0.5×10¹⁷ cm^-3-5.0×10¹⁷ cm^-3 for P-type and 0.5×10¹⁸ cm^-3-5×10¹⁸ cm^-3 for N-type) and heavy dopings(1×10¹⁸ cm^-3-1×10¹⁹ cm^-3 for P-type and1×10¹⁹ cm^-3-1×10²⁰ cm^-3 for N-type) under hydrostatic pressure strains.The counterpart results under hydrostatic tensile strains are deposited in the Supporting Information.For light dopings but with no strain at T=100 K,the|S|monotonically decrease with the p and n increasing (Fig.8a).By contrast,this is not the case for the P-type non-strained CoSb₃ at T=300 K (Fig.8b),where the|S|first increases and then decreases when p exceeds 2.5×10¹⁷ cm^-3.Furthermore,the non-strained|S|at 500 K is proportional to p and n for both P-and N-type CoSb₃ (Fig.8c).As shown in Fig.8a-c,the|S|of lightly doped and pressure-strained CoSb₃ is generally inversely proportional with the p and n at 100 K and300 K,but becomes positively correlated with the p and n at 500 K.As shown in Fig.8d-f,the|S|of heavily doped and pres sure-strained CoSb₃ is generally inversely proportional with both p and n at each temperature.By comparing the|S|at the same carrier concentration under different hydrostatic pressures,we found that the|S|is generally enhanced for both lightly and heavily doped P-and N-type CoSb₃ as indicated by the arrows shown in Fig.8.The enhancement of|S|under hydrostatic pressure can be ascribed to the interplay of three factors:(i) the band convergence between the valley bands and the CBM for N-type doping (Fig.3a),(ii) the suppression of TDOS near valence band edge for P-type CoSb₃ in light of the Mott's relation (Fig.5a),and (iii) the larger E_gap induced by hydrostatic pressure for both P-and N-type dopings(Fig.7a).The results of power factor under hydrostatic pressure are presented in Fig.S2 in the Supporting Information.On the contrary,due to the complexity of band structure induced by hydrostatic tensile (Fig.3d,e),e.g.,with the occurrence of MIT at a strain of 0.04,we do not observe a monotonic variation of S(p/n) but an unusual behavior,as shown in Fig.S3 in the Supporting Information.

Fig.6 Calculated Seebeck coefficient (S) as a function of chemical potentialμunder a non-strain,hydrostatic pressure with strain of b-0.02and c-0.04,and hydrostatic tensile with strain of d 0.02 and e strain 0.04 (black vertical and dashed lines denoting VBM,CBM,and E_F)

Fig.7 a Two peaks of S(μ) as a function of E_gap at T=100 K,300 K,and 500 K and b calculated e·dS_peak/dE_gap as a function of 1/T(S⁺and S^-denoting P-type and N-type dopings,respectively)

Fig.8 Seebeck coefficient (S) as a function of carrier concentration (p/n,where p for P-type doping and n for N-type doping) under hydrostatic pressure:light doping ratios shown in a 100 K,b 300 K,and c 500 K,while heavy doping ratios shown in d 100 K,e 300 K,and f 500 K(arrows indicating trend of|S|under strain)

4 Conclusion

Inspired by the analogy between the effects of chemical pressure and physical pressure on the mechanical,electronic,and electrical transport properties,we have performed first-principles calculations combined with the Boltzmann transport equation to study pristine CoSb₃under hydrostatic loadings (pressure and tensile).We have found that hydrostatic pressure enlarges the band gap,suppresses the DOS near the valence band edge,and fosters the band convergence between the valley bands and the CBM,which is favorable for N-type thermoelectric performance.On the other hand,the hydrostatic tensile reduces band gap and induces a metal-to-insulator transition(MIT).Owing to the significant effect of an MIT on the electronic band structure and the Seebeck coefficient,it would be interesting to explore how it impacts thermoelectric properties in future.Furthermore,tensile increases the DOS near the valence band edge but diminishes the FEPs near the CBM,and therefore,it is unfavorable for N-type thermoelectric performance.Overall,the understanding of the strain effects of hydrostatic loadings reported here may provide new insight into the performance improvement of thermoelectricity in CoSb₃-based skutterudites via a synergy of chemical and physical pressure.One limitation of the present study is that we only focused on the effects of hydrostatic loadings (pressure and tensile);a complete understanding must take into account the uniaxial,biaxial,and shear strain,which can be a subject for future studies.

Acknowledgements This research was conducted at the Center for Nanophase Materials Sciences,which is a US Department of Energy Office of Science User Facility,and used resources of the National Energy Research Scientific Computing Center,which are supported by the Office of Science of the US Department of Energy (Nos.DE-AC05-00OR22750 and DE-AC02-05-CH11231).Chongze Hu and Jian He would like to acknowledge the support of National Science Foundation (No.DMR-1307740).

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