Abstract
Weyl semimetals (WSMs) have attracted the attention of the researchers due to their fascinating properties which are analogous to that of three-dimensional graphene. The density functional theory (under generalised gradient approximation (GGA) without spin-orbit coupling, GGA with spin-orbit coupling (GGA\(+\)SOC) and GGA with Hubbard correction (GGA\(+U\))) in combination with the stress–strain approach have been utilised to investigate the elastic and mechanical properties of ZrS and ZrTe. The thermodynamic properties have been evaluated using the quasi-harmonic approximations by incorporating GGA, GGA\(+\)SOC and GGA\(+U\) approaches. The polycrystalline elastic moduli have been calculated using the single-crystal elastic constants and the mechanical stabilities have also been established. Physical parameters, such as Young’s modulus, shear modulus, Poisson’s ratio, Debye temperature and sound velocities, are also calculated. In addition, the anisotropic elastic properties such as Young’s modulus, linear compressibility, shear modulus and Poisson’s ratio as well as the anisotropic factors have been visualised in three dimensions (3D) using GGA, GGA\(+\)SOC and GGA\(+U\) approaches. The theoretical computation of thermodynamic properties such as specific heat, entropy, vibration energy and internal energy as a function of temperature for both Weyl semimetals are investigated and discussed for the first time. The calculated values of Debye temperature for ZrS (ZrTe) are 470.103 K (287.744 K), 486.572 K (298.295 K) and 442.0 K (234.346 K) using GGA approximations without SOC, with SOC and by implementing GGA\(+U\) calculations, respectively. Further, it is shown that the value of Debye temperature for ZrS is more than that of ZrTe. Hence, the present study of thermodynamic properties suggests their potential thermoelectric applications at high temperatures.
Similar content being viewed by others
References
P Hosur and X Qi, C. R. Phys. 14, 857 (2013)
Z Wang, Y Zheng, Z Shen, Y Lu, H Fang, F Sheng, Y Zhou, X Yang, Y Li, C Feng and Z A Xu, Phys. Rev. B 93, 121112 (R)(2016)
N J Ghimire, Y Luo, M Neupane, D J Williams, E D Bauer and F Ronning, J.Phys.: Condens. Matter 27, 152201 (2015)
F Arnold, C Shekhar, S C Wu, Y Sun, R Donizeth dos Reis, N Kumar, M Naumann, M O Ajeesh, M Schmidt, A G Grushin, J H Bardarson, M Baenitz, D Sokolov, H Borrmann, M Nicklas, C Felser, E Hassinger and B Yan, Nat. Commun. 7, 11615 (2016)
C Zhang, C Guo, H Lu, X Zhang, Z Yuan, Z Lin, J Wang and S Jia, Phys. Rev. B 92, 041203 (2015)
X Huang, L Zhao, Y Long, P Wang, D Chen, Z Yang, H Liang, M Xue, H Weng, Z Fang, X Dai and G Chen, Phys. Rev. B 5, 031023 (2015)
C Shekhar, A K Nayak, Y Sun, M Schmidt, M Nicklas, I Leermakers, U Zeitler, Y Skourski, J Wosnitza, Z Liu, Y Chen, W Schnelle, H Borrmann, Y Grin, C Felser and B Yan, Nat. Phys. 11, 645 (2015)
H Weng, C Fang, Z Fang and X Dai, Phys. Rev. B 94, 165201 (2016)
Y Gupta, M M Sinha and S S Verma, Phys. Status Solidi B 264, 1900117 (2019)
Z M Zhu, G W Winkler, Q Wu, J Li and A A Soluyanov, Phys. Rev. X 6, 031003 (2016)
G W Winkler, Q S Wu, M Troyer, P Krogstrup and A A Soluyanov, Phys. Rev. Lett. 117, 076403 (2016)
W L Zhu, J B He, S Zhang, D Chen, L Shan, Z A Ren and G F Chen, Phys. Rev. B 101, 245127 (2020)
J Li, Q Xie, S Ullah, R Li, H Ma, D Li, Y Li and X Q Chen, Phys. Rev. B 97, 054305 (2018)
Y Gupta, M M Sinha and S S Verma, Physica C 577, 1353714 (2020)
T Ouyang, H P Xiao, C Tang, M Hu and J X Zhong, Phys. Chem. Chem. Phys. 18, 16709 (2016)
B Peng, H Zhang, H Z Shao, H L Lu, D W Zhang and H Y Zhua, Nano Energy 30, 225 (2016)
J Buckeridge, D Jevdokimovs, C R A Catlow and A A Sokol, Phys. Rev. B 93, 125205 (2016)
S D Guo, J. Phys.: Condens. Matter 29, 435704 (2017)
Y Gupta, M M Sinha and S S Verma, Physica B 590, 412222 (2020)
W Y Ching, Y N Xu, B N Harmon, J Ye and T C Leung, Phys. Rev. B 42, 4460 (1990)
Y Kong and F Li, Phys. Rev. B 56, 3153 (1997)
Y Wang, Z K Liu and L Q Chen, Acta. Mater. 52, 2665 (2004)
S L Shang, Y Wang, D Kim and Z K Liu, Comput. Mater. Sci. 47, 1040 (2010)
P Hohenberg and W Kohn, Phys. Rev. 136 , B864 (1964)
W Kohn and L J Sham, Phys. Rev. 140, A1133 (1965)
P Giannozzi et al, J. Phys.: Condens. Matter 21 (39), 395502 (2009)
J P Perdew, K Burke and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
N Marzari, D Vanderbilt, A D Vita and M C Payne, Surf. Phys. Rev. Lett. 82, 3296 (1999)
H J Monkhorst and J D Pack, Phys. Rev. B 13, 5188(1976)
C Lee and X Gonze, Phys. Rev. B 51, 8610 (1995)
I Timrov, N Marzari and M Cococcioni, Phys. Rev. B 98, 085127 (2018)
Y Lu, B T Wang, R W Li, H L Shi and P Zhang, J. Nucl. Mater. 410, 46 (2011)
W Voigt, Lehrbuch der Kristallphysik: mitAusschlu\(\beta \) der Kristalloptik (Leipzig-viewg+TeubnerVerlag, 1966).
A Reuss, Z. Angew. Math. Mech. 9, 49 (1929)
R Hill, Proc. Phys. Soc. Sect. A 65, 349 (1952)
Y Gupta, M M Sinha and S S Verma, J. Solid State Chem. 304, 122601 (2021)
Y Gupta, M M Sinha and S S Verma, Mater. Chem. Phys. 265, 124518 (2021)
Y Gupta, M M Sinha and S S Verma, Mater. Today Commun. 27, 102195 (2021)
J Haines, J M Leger and G Bocquillion, Annu. Rev. Mater. Res. 31, 1 (2001)
R Gaillac, P Pullumbi and F X Coudert, J. Phys.: Condens. Matter. 28, 275201 (2016)
R Li, Y Duan, Philo. Mag., https://doi.org/10.1080/14786435.2016.1234081 (2016)
V Mankad, N Rathod, S D Gupta, S K Gupta and P K Jha, Mater. Phys. Chem. 129, 816 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, Y., Sinha, M.M. & Verma, S.S. Probing the elastic, mechanical and thermodynamic properties of Weyl semimetals ZrX (X=S and Te). Pramana - J Phys 96, 75 (2022). https://doi.org/10.1007/s12043-022-02315-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-022-02315-0