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Chin. Phys. B, 2021, Vol. 30(5): 056202    DOI: 10.1088/1674-1056/abd6f6

High-pressure elastic anisotropy and superconductivity of hafnium: A first-principles calculation

Cheng-Bin Zhang(张成斌)1,2,3, Wei-Dong Li(李卫东)1, Ping Zhang(张平)4, and Bao-Tian Wang(王保田)2,3,4,†
1 Institute of Theoretical Physics and Department of Physics, and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China;
2 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China;
3 Spallation Neutron Source Science Center, Dongguan 523803, China;
4 LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract  The elastic anisotropy and superconductivity upon hydrostatic compression of α, ω, and β Hf are investigated using first-principle methods. The results of elastic anisotropies show that they increase with increasing pressure for α and ω phases, while decrease upon compression for β phase. The calculated superconducting transition temperatures are in excellent agreement with experiments. Electron-phonon coupling constants (λ) are increasing with pressure for α and ω phases, while decreasing for β phase. For β phase, the large values of λ are mainly due to the obvious TA1 soft mode. Under further compression, the TA1 soft vibrational mode will disappear gradually.
Keywords:  first-principles      elastic anisotropy      superconductivity      hafnium  
Received:  27 July 2020      Revised:  18 December 2020      Accepted manuscript online:  28 December 2020
PACS:  62.20.-x (Mechanical properties of solids) (Elastic moduli)  
  63.20.-e (Phonons in crystal lattices)  
  74.70.-b (Superconducting materials other than cuprates)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874247 and U1530258), the National Key R&D Program of China (Grant No. 2017YFA0304500), the 111 Plan of China (Grant No. D18001), the Hundred Talent Program of the Shanxi Province (2018), and the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices of China (Grant Nos. KF201703 and KF201904).
Corresponding Authors:  Bao-Tian Wang     E-mail:

Cite this article: 

Cheng-Bin Zhang(张成斌), Wei-Dong Li(李卫东), Ping Zhang(张平), and Bao-Tian Wang(王保田) High-pressure elastic anisotropy and superconductivity of hafnium: A first-principles calculation 2021 Chin. Phys. B 30 056202

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