| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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A Programmable k$\cdot$p Hamiltonian Method and Application to Magnetic Topological Insulator MnBi$_2$Te$_4$ |
| Guohui Zhan1†, Minji Shi1†, Zhilong Yang1, and Haijun Zhang1,2* |
1National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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| Cite this article: |
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Guohui Zhan, Minji Shi, Zhilong Yang et al 2021 Chin. Phys. Lett. 38 077105 |
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Abstract In the band theory, first-principles calculations, the tight-binding method and the effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model are usually employed to investigate electronic structures of condensed matters. The effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model has a compact form with a clear physical picture, and first-principles calculations can give more accurate results. Nowadays, it has been widely recognized to combine the $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model and first-principles calculations to explore topological materials. However, the traditional method to derive the $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian is complicated and time-consuming by hand. We independently developed a programmable algorithm to construct effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians for condensed matters. Symmetries and orbitals are used as the input information to produce the one-/two-/three-dimensional $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian in our method, and the open-source code can be directly downloaded online. At last, we also demonstrated the application to MnBi$_2$Te$_4$-family magnetic topological materials.
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Received: 08 May 2021
Published: 18 June 2021
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| PACS: |
71.15.-m
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(Methods of electronic structure calculations)
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71.15.Ap
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(Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.))
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73.20.At
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(Surface states, band structure, electron density of states)
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| Fund: Supported by the Fundamental Research Funds for the Central Universities (Grant No. 020414380185), the Natural Science Foundation of Jiangsu Province (Grant No. BK20200007), the National Natural Science Foundation of China (Grant Nos. 12074181 and 11834006), and the Fok Ying-Tong Education Foundation of China (Grant No. 161006). |
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| [1] | Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 |
| [2] | Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 |
| [3] | Armitage N P, Mele E J, and Vishwanath A 2018 Rev. Mod. Phys. 90 015001 |
| [4] | Fu L and Kane C L 2007 Phys. Rev. B 76 045302 |
| [5] | Bernevig B A, Hughes T L, and Zhang S C 2006 Science 314 1757 |
| [6] | Zhang H and Zhang S C 2013 Phys. Status Solidi RRL 7 72 |
| [7] | Zhang H, Liu C X, Qi X L, Dai X, Fang Z, and Zhang S C 2009 Nat. Phys. 5 438 |
| [8] | Luttinger J M and Kohn W 1955 Phys. Rev. 97 869 |
| [9] | Kane E O 1966 The ${\boldsymbol k}\cdot{\boldsymbol p}$ Method (Amsterdam: Elsevier) chap 3 p 75 |
| [10] | Voon L C L Y and Willatzen M 2009 The ${\boldsymbol k}$$\cdot$${\boldsymbol p}$ Method: Electronic Properties of Semiconductors (Berlin: Springer Science & Business Media) |
| [11] | Liu C X, Qi X L, Zhang H, Dai X, Fang Z, and Zhang S C 2010 Phys. Rev. B 82 045122 |
| [12] | Fu L 2009 Phys. Rev. Lett. 103 266801 |
| [13] | Xu G, Weng H, Wang Z, Dai X, and Fang Z 2011 Phys. Rev. Lett. 107 186806 |
| [14] | Gresch D 2018 Identifying Topological Semimetals (PhD Dissertation) (Troyer, Matthias, ETH Zürich) |
| [15] | Gresch D kdotp-Symmetry Code |
| [16] | Varjas D et al. 2018 New J. Phys. 20 093026 |
| [17] | Akhmerov A Qsymm Code |
| [18] | Zhang D, Shi M, Zhu T, Xing D, Zhang H, and Wang J 2019 Phys. Rev. Lett. 122 206401 |
| [19] | Zhang J, Wang D, Shi M, Zhu T, Zhang H, and Wang J 2020 Chin. Phys. Lett. 37 077304 |
| [20] | Wang H, Wang D, Yang Z, Shi M, Ruan J, Xing D, Wang J, and Zhang H 2020 Phys. Rev. B 101 081109 |
| [21] | Li J, Li Y, Du S, Wang Z, Gu B L, Zhang S C, He K, Duan W, and Xu Y 2019 Sci. Adv. 5 eaaw5685 |
| [22] | Gong Y, Guo J, Li J, Zhu K, Liao M, Liu X, Zhang Q, Gu L, Tang L, Feng X, Zhang D, Li W, Song C, Wang L, Yu P, Chen X, Wang Y, Yao H, Duan W, Xu Y, Zhang S C, Ma X, Xue Q K, and He K 2019 Chin. Phys. Lett. 36 076801 |
| [23] | Otrokov M M, Klimovskikh I I, Bentmann H, Estyunin D, and Chulkov E V 2019 Nature 576 416 |
| [24] | Otrokov M M, Rusinov I P, Blanco-Rey M, Hoffmann M, Vyazovskaya A Y, Eremeev S V, Ernst A, Echenique P M, Arnau A, and Chulkov E V 2019 Phys. Rev. Lett. 122 107202 |
| [25] | Deng Y, Yu Y, Shi M Z, Guo Z, Xu Z, Wang J, Chen X H, and Zhang Y 2020 Science 367 895 |
| [26] | Liu C, Wang Y, Li H, Wu Y, Li Y, Li J, He K, Xu Y, Zhang J, and Wang Y 2020 Nat. Mater. 19 522 |
| [27] | Chen B, Fei F, Zhang D, Zhang B, Liu W, Zhang S, Wang P, Wei B, Zhang Y, and Zuo Z 2019 Nat. Commun. 10 4469 |
| [28] | Klimovskikh I I, Otrokov M M, Estyunin D, Eremeev S V, and Chulkov E V 2020 npj Quantum Mater. 5 54 |
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