Mechanical and Optical Properties of Topological Semimetal Compound YPtBi

We have reported the mechanical properties of topological semimetals half-Heusler compound YPtBi with LDA and GGA approximation which is implemented in density functional theory. We have calculated elastic parameters which ensure good machinability, covalent bonding, brittleness, low value of Kleinman parameter and high Vickers hardness. Our results reveal the hardness or large resistance of these topological semimetals. Moreover, Born mechanical stability conditions are well fulfilled by the topological semimetal YPtBi. Present study reveals that the low value of bulk modulus and shear modulus wheras high value of Youngs modulus of this topological semimetals which deforms easily with applied external force. We have also calculated optical properties of topological semi-metal YPtBi with both LDA and GGA. Optical properties are calculated in terms of dielectric function and we have calculated dielectric constant, optical reflectivity, absorption co-efficient, optical conductivity, refractive index and electron energy loss in the energy range 0 – 14 eV. We have found higher dielectric constants with GGA in comparison to LDA that imply YPtBi is excellent materials in solar cell applications. Also, YPtBi possess high refractive index in the visible range and it is optically isotropic.


Introduction
Topological state is the combination of two quantum anomalous hall effects with spin up and spin down spin channels carrying opposite Chern number.[1].These topologically non trivial gapless material is known as topological semimetals (TSM) that exhibits topological band crossing around the Fermi level.Topological half-Heusler semimetals RPdBi (R=lanthanide atom) are very well studied for its magnetic properties.[2].The topological state mainly includes Weyl points, Dirac and nodal line semimetal.There have been many studies on topological semimetals (TSM) compounds viz RENiBi (RE = Gd, Nd and Y) due to magnetoresistance at low temperature and spintronic applications.First-principle study of topological superconductor LuPtBi including elastic and optical properties is done by Hossain et al. [3].Also, mechanical, thermoelectric and vibration properties of XPtBi (X=Sc and Y) are studied by Goyal et al. [4].A detailed study of various mechanical parameters of topological semimetal CaSn3 is done including elastic anisotropy, bonding and Vicker's hardness [5].
Tight binding method based on maximally localized Wannier functions (MLWFs) include localized properties of Wannier function is done by Huang et al. [6].Also, ab initio calculations of mechanical and optical properties of topological weyl semimetals MoTe2 has been done recently [7,8].The strained induced electronic structure of YPtBi and YPdBi are studied to understand the multiple band inversion by Chatterjee et al. [ 9].They reported that increasing tensile strain shifts the triple point crossing to higher momenta making the material as a source of highly mobile electrons and thus tuned the bulk as well as the surface transport to these TSM compounds.
The available literature reveals that there is yet no thorough understanding of mechanical and optical properties of YPtBi.In this present work, we have reported the elastic and optical properties of YPtBi with LDA and GGA.Since elastic parameters show the stiffer nature for engineering applications while optical parameters indicate reflectivity and refractivity in the broad range of frequency for optoelectronic applications

2.Computational Details
Topological semi metal (TSM) compound YPtBi crystallizes in cubic NaCl structure (F-43m, 216) where the atoms are located at Y (0.5, 0.5, 0.5), Pt ( 0.25, 0.25, 0.25) and Bi (0, 0, 0) [9] and experimental lattice parameter is 6.64Å [10] .We have employed Full potential linear augmented plane wave (FP-LAPW) method as stated in density functional theory (DFT) which is implemented in WIEN2k code [11].We have applied local density approximation (LDA) and generalized gradient approximation (GGA) (Perdew Burke and Ernzerhof (PBE) [11] for the treatment the 4f electron.Now, we use Birch-Murnaghan equation of state [12,13] and data are used to find the structural stability of YPtBi in terms of energy vs volume graph.A dense mesh of 1728 k points are taken with a grid size of 12x12x12 points and tetrahedral method has been used for the Brillouin zones integration.We have converged charge and total energy by 10 -4 Ry.Further, we have expanded the basis function up to RMT* KMAX.=7.5, where RMT is the smallest atomic radius in unit cell and KMAX.refers the magnitude of the largest k vector in the plane wave expansion.Meanwhile, the maximum value of angular momentum of partial waves lmax inside the atomic sphere is 10, the charge density is Fourier expanded up to Gmax=12 (a.u) -1 and the core energy cutoff is taken as -6.0 Ry.We have used the IRElast code to determine the elastic constants.The expressions used for elastic and optical parameters are defined in our earlier work [14].Moreover, we have also reported the correlations between hardness and elasticity of material in terms of Vickers hardness parameter defined as HV=2[k 2 G] 0.585 -3 which is described in work [5]

Elastic Properties
Energy volume curves for both LDA and GGA are shown in Fig. 1 and Fig. 2 and optimised lattice parameters for both the cases are a = 6.7476Å and a'= 6.6016 Å respectively.For non-centrosymmetric cubic structure, the three independent elastic tensors are C11, C12 and C44.Since, YPtBi is noncentrosymmetric cubic non-trivial TSM, its elastic properties are calculated in terms of three independent elastic constants C11, C12 and C44 using both exchange correlation functional LDA and GGA and are shown in Table 1.In both cases we have observed that the Born stability criteria is well satisfied i.e. ,YPtBi is mechanically stable.Born-Huang criteria for mechanical stability is defined in work [15].C11 -C12> 0, C44.>0, C11+2 C12> 0 and C12< B <C11 Various mechanical properties -Bulk modulus (B), Shear modulus (G), Young's modulus (E ), Pugh's ratio (B/G), Poisson's ratio (ν), Zener Anisotropy (A) , Kleinman Parameter (ξ ) and Vicker's Hardness (Hv ) are calculated in terms of C11, C12 and C44 and are shown in Table 2.As observed from Table 1 that the values of different elastic properties obtained using exchange correlation functional GGA is close to the values observed in [4].Since, Bulk modulus measures the resistance to change in volume with application of pressure and greater the bulk modulus greater will be the resistance.The calculated values of Bulk modulus as mentioned in Table 1. is 83.56 GPa (with GGA) and 77.47 GPa (with LSDA).The result obtained with GGA is closer to the previous result [4].
Since, Shear modulus give the ability of solid to resist transverse deformation.For YPtBi , we have calculated shear modulus 55.205 GPa (with GGA) and 37.375GPa (with LDA) which are higher and thus shows higher resistance to tangential deformation.The Young's modulus measures the stiffness of the solid, higher value of Young's modulus 166.617GPa with GGA and 96.5921GPa with LDA signifies that YPtBi half-Heusler TSM compound is highly tensile.Also, calculated Pugh's ratio(B/G) is 1.51 which is very near to 1.75, this shows semi metallic nature with LDA and 2.07>1.75 with GGA shows high ductility as in metals, the above results are in agreement with the previous findings [4].Also, Zener Anisotropy is greater than 1 shows anisotropic nature of YPtBi.Higher value of Vicker's Hardness is reported with 12.1914 with GGA and 5.2414 with LDA, that indicates metallic nature of YPtBi.
Poisson's ratio (ν ) value equal to or greater than 0.26 reveals ductile nature of solid [16].We have observed ν = 0.23 with GGA less than 0.26 implying semi metallic behaviour and ν = 0.29 with LDA greater than 0.26 signifying metallic nature of YPtBi.Another important elastic constant, Kleinman Parameter (ζ ) is calculated with the help of elastic constants [17].The range of Kleinman Parameter (ζ) is 0 ≤ ζ ≤ 1 [18].Higher value of ζ indicates low resistance to bond angle distortion and large value represents low resistance to distortion due to bond stretching/contracting.Here, the calculated value of Kleinman parameter (ζ) is 0.5678 with GGA and 0.6006 with LDA that signifies mechanical strength is mainly due to bond bending contribution and bond stretching contribution to the mechanical strength is insignificant.The positive value of Cauchy Pressure [19] indicates ductile nature and ionic bonding nature of compound.The calculated value of Cauchy Pressure (C12 -C44) is 7.672 with GGA and 14.605 with LDA signifies ductile nature of YPtBi and dominance of ionic bonding.Local spin density approximation (LDA) is suitable for materials where charge density is considered constant but this approximation finds limitation for strongly correlated system.GGA is more consistent as it includes charge density and its gradient [20,21].Hence results with GGA is more appropriate and closer to the results reported earlier [4].

Optical Properties:
We have calculated optical properties of TSM compound YPtBi with both LDA and GGA.Optical properties are calculated in terms of dielectric function.Dielectric function is a complex function ε =  1 +  2 with real dielectric function  1 which is measure of phase velocity and imaginary dielectric function  2 which is a measure of extinction co-efficient.We have calculated dielectric function, optical reflectivity, absorption co-efficient, optical conductivity, refractive index and electron energy loss in the energy range 0 -14 eV.We have observed that the static dielectric constant of YPtBi is  1 (0) = 60 with GGA as shown in Fig. 3(a) which decreases with increases in energy and real dielectric constant becomes small positive at 2.5 eV in the visible region.Above 4 eV dielectric constant becomes negative that indicates group velocity will be greater than speed of light and thus material exhibits non-linear response.The negative dielectric constant indicates negative permittivity and permeability which signifies that material lost its dielectric property.But with LDA, we have observed in Fig. 3(b) static dielectric constant  1 (0)= 46.

Conclusions
From the first principles study of elastic and optical properties of TSM compound YPtBi, we have observed high value of Bulk modulus, Shear modulus and Young's modulus which signifies-high resistance to change in volume, shear deformation and high tensile strength as compared to previous work.High value of Pugh's ratio, Poisson's ratio and positive Cauchy pressure signifies high ductility and dominance of ionic bonding.Hence it is suitable for application where high ductility requires as in making high tensile ropes.Value of Kleinman parameter of YPtBi shows that mechanical strength is due bond bending contribution and not due to bond stretching contribution.We have explored frequency dependent optical properties viz Real Dielectric tensor, Optical reflectivity, Absorption co-efficient, Real Optical conductivity, Refractive index and Electron energy loss for the first time.High Dielectric constant restricts the electron-hole recombination at the PN junction of solar cell hence makes it suitable candidate for solar cell and other optoelectronic applications.We found that all observations show better results with GGA than with LDA exchange correlation functional.

Figure 2
Figure 2 Energy -Volume Optimisation curve with Local spin Density Approximation.Optimised lattice parameter a'= 6.6016 Å

Figure 3 .
Figure 3. Variation of Real Dielectric Tensor with Energy in eV (a) with GGA (b) with LDA

Figure 4 .
Figure 4. Variation of Optical Reflectivity with Energy in eV (a) with GGA (b) with LDA

Figure 5 .
Figure 5. Variation of Absorption co-efficient (10 4 /cm) with Energy in eV(a) with GGA (b) with LDA

Figure 8 .
Figure 8. Variation of Electron Energy Loss (arb units) with Energy in eV (a) with GGA (b) with LDA

Table 2 .
Elastic Figure 1.Energy Volume Optimisation curve with Generalised Gradient Approximation.Optimised lattice parameter a = 6.7476Å