摘要
The k·p method is significant in condensed matter physics for the compact and analytical Hamiltonian.In the presence of magnetic field,it is described by the effective Zeeman's coupling Hamiltonian with Landég-factors.Here,we develop an open-source package VASP2KP(including two parts:vasp2mat and mat2kp)to compute k·p parameters and Landég-factors directly from the wavefunctions provided by the density functional theory(DFT)as implemented in Vienna ab initio Simulation Package(VASP).First,we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operatorπ=p+1/2mc^(2)[s×■V(r)],spin operator s,time reversal operatorT,and crystalline symmetry operatorsR on the DFT wavefunctions.Second,we develop a python code mat2kp to obtain the unitary transformation U that rotates the degenerate DFT basis towards the standard basis,and then automatically compute the k·p parameters and g-factors.The theory and the methodology behind VASP2KP are described in detail.The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method.We apply this package to some materials,e.g.,Bi2Se3,Na3Bi,Te,InAs and 1H-TMD monolayers.The obtained effective model's dispersions are in good agreement with the DFT data around the specific wave vector,and the g-factors are consistent with experimental data.The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.
作者
章盛
盛昊昊
宋志达
梁晨昊
蒋毅
孙松
吴泉生
翁红明
方忠
戴希
王志俊
Sheng Zhang;Haohao Sheng;Zhi-Da Song;Chenhao Liang;Yi Jiang;Song Sun;Quansheng Wu;Hongming Weng;Zhong Fang;Xi Dai;and Zhijun Wang(Beijing National Laboratory for Condensed Matter Physics,and Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China;International Center for Quantum Materials,School of Physics,Peking University,Beijing 100871,China;Hefei National Laboratory,Hefei 230088,China;Collaborative Innovation Center of Quantum Matter,Beijing 100871,China;Department of Physics,Hong Kong University of Science and Technology,Hong Kong 999077,China)
基金
supported by the National Key R&D Program of Chain(Grant No.2022YFA1403800)
the National Natural Science Foundation of China(Grant Nos.11974395,12188101,11925408,12274436,and 11921004)
the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB33000000)
the Center for Materials Genome
supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302403)
the National Natural Science Foundation of China(Grant No.12274005)
the National Key Research and Development Program of China(Grant No.2021YFA1401900)
supported by the Informatization Plan of the Chinese Academy of Sciences(Grant No.CASWX2021SF0102)。
