Инд. авторы: Shikin A.M., Estyunin D.A., Zaitsev N.L., Glazkova D., Klimovskikh I.I., Filnov S.O., Rybkin A.G., Schwier E.F., Kumar S., Kimura A., Mamedov N., Aliev Z., Babanly M.B., Kokh K.A., Tereshchenko O.E., Otrokov M.M., Chulkov E.V., Zvezdin K.A., Zvezdin A.K.
Заглавие: Sample-dependent dirac-point gap in and its response to applied surface charge: a combined photoemission and ab initio study
Библ. ссылка: Shikin A.M., Estyunin D.A., Zaitsev N.L., Glazkova D., Klimovskikh I.I., Filnov S.O., Rybkin A.G., Schwier E.F., Kumar S., Kimura A., Mamedov N., Aliev Z., Babanly M.B., Kokh K.A., Tereshchenko O.E., Otrokov M.M., Chulkov E.V., Zvezdin K.A., Zvezdin A.K. Sample-dependent dirac-point gap in and its response to applied surface charge: a combined photoemission and ab initio study // Physical Review B. - 2021. - Vol.104. - Iss. 11. - Art.115168. - ISSN 2469-9950. - EISSN 2469-9969.
Идентиф-ры: DOI: 10.1103/PhysRevB.104.115168; РИНЦ: 46768768;
Реферат: eng: Recently discovered intrinsic antiferromagnetic topological insulator presents an exciting platform for realization of the quantum anomalous Hall effect and a number of related phenomena at elevated temperatures. An important characteristic making this material attractive for applications is its predicted large magnetic gap at the Dirac point (DP). However, while the early experimental measurements reported on large DP gaps, a number of recent studies claimed to observe a gapless dispersion of the Dirac cone. Here, using micro()-laser angle-resolved photoemission spectroscopy, we study the electronic structure of 15 different samples, grown by two different chemists groups. Based on the careful energy distribution curves analysis, the DP gaps between 15 and 65 meV are observed, as measured below the Néel temperature at about 10-16 K. At that, roughly half of the studied samples show the DP gap of about 30 meV, while for a quarter of the samples the gaps are in the 50 to 60 meV range. Summarizing the results of both our and other groups, in the currently available samples the DP gap can acquire an arbitrary value between a few and several tens of meV. Furthermore, based on the density functional theory, we discuss a possible factor that might contribute to the reduction of the DP gap size, which is the excess surface charge that can appear due to various defects in surface region. We demonstrate that the DP gap is influenced by the applied surface charge and even can be closed, which can be taken advantage of to tune the DP gap size.
Ключевые слова: photoelectron spectroscopy; surface charge; Ab initio study; Anomalous Hall effects; Applied surface; Dirac cones; Dirac point; elevated temperature; gap size; magnetic gap; density functional theory; electronic structure; topological insulators; Microlaser;
Издано: 2021
Физ. хар-ка: 115168
Цитирование: 1. Qi, X.-L., Hughes, T.L., Zhang, S.-C. (2008) Topological field theory of time-reversal invariant insulators // Physical Review B - Condensed Matter and Materials Physics, 78 (19), art. no. 195424. http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevB.78.195424&metadataPrefix=oai_apsmeta_2
2. Qi, X.-L., Zhang, S.-C. (2011) Topological insulators and superconductors // Reviews of Modern Physics, 83 (4), art. no. 1057. http://oai.aps.org/filefetch?identifier=10.1103/RevModPhys.83.1057&component=fulltext&description=markup&format=xml
3. Chang, C.-Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., (..), Xue, Q.-K. (2013) Experimental observation of the quantum anomalous Hall effect in a magnetic topological Insulator // Science, 340 (6129), pp. 167-170. http://www.sciencemag.org/content/340/6129/167.full.pdf
4. Liu, C.-X., Zhang, S.-C., Qi, X.-L. (2016) The Quantum Anomalous Hall Effect: Theory and Experiment // Annual Review of Condensed Matter Physics, 7, pp. 301-321. http://www.annualreviews.org/journal/conmatphys
5. Tokura, Y., Yasuda, K., Tsukazaki, A. (2019) Magnetic topological insulators // Nature Reviews Physics, 1 (2), pp. 126-143. nature.com/natrevphys
6. Chang, C.-Z., Li, M. (2016) Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators // Journal of Physics Condensed Matter, 28 (12), art. no. 123002. http://iopscience.iop.org/article/10.1088/0953-8984/28/12/123002/pdf
7. Wang, J., Lian, B., Qi, X.-L., Zhang, S.-C. (2015) Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state // Physical Review B - Condensed Matter and Materials Physics, 92 (8), art. no. 081107. http://harvest.aps.org/bagit/articles/10.1103/PhysRevB.92.081107/apsxml
8. Essin, A.M., Moore, J.E., Vanderbilt, D. (2009) Magnetoelectric polarizability and axion electrodynamics in crystalline insulators // Physical Review Letters, 102 (14), art. no. 146805. http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevLett.102.146805&metadataPrefix=oai_apsmeta_2
9. Otrokov, M.M., Menshchikova, T.V., Vergniory, M.G., Rusinov, I.P., Vyazovskaya, A.Y., Koroteev, Y.M., Bihlmayer, G., (..), Chulkov, E.V. (2017) Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects // 2D Materials, 4 (2), art. no. 025082. http://iopscience.iop.org/article/10.1088/2053-1583/aa6bec/pdf
10. Otrokov, M.M., Menshchikova, T.V., Rusinov, I.P., Vergniory, M.G., Kuznetsov, V.M., Chulkov, E.V. (2017) Magnetic extension as an efficient method for realizing the quantum anomalous hall state in topological insulators // JETP Letters, 105 (5), pp. 297-302. http://www.springerlink.com/content/119842
11. Eremeev, S.V., Otrokov, M.M., Chulkov, E.V. (2017) Competing rhombohedral and monoclinic crystal structures in MnPn2Ch4 compounds: An ab-initio study // Journal of Alloys and Compounds, 709, pp. 172-178.
12. Otrokov, M.M., Rusinov, I.P., Blanco-Rey, M., Hoffmann, M., Vyazovskaya, A.Yu., Eremeev, S.V., Ernst, A., (..), Chulkov, E.V. (2019) Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi2Te4 Films // Physical Review Letters, 122 (10), art. no. 107202. http://harvest.aps.org/bagit/articles/10.1103/PhysRevLett.122.107202/apsxml
13. Otrokov, M.M., Klimovskikh, I.I., Bentmann, H., Estyunin, D., Zeugner, A., Aliev, Z.S., Gaß, S., (..), Chulkov, E.V. (2019) Prediction and observation of an antiferromagnetic topological insulator // Nature, 576 (7787), pp. 416-422. http://www.nature.com/nature/index.html
14. Li, J., Li, Y., Du, S., Wang, Z., Gu, B.-L., Zhang, S.-C., He, K., (..), Xu, Y. (2019) Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials // Science Advances, 5 (6), art. no. eaaw5685. https://advances.sciencemag.org/content/5/6/eaaw5685/tab-pdf
15. Zhang, D., Shi, M., Zhu, T., Xing, D., Zhang, H., Wang, J. (2019) Topological Axion States in the Magnetic Insulator MnBi2Te4 with the Quantized Magnetoelectric Effect // Physical Review Letters, 122 (20), art. no. 206401. http://harvest.aps.org/bagit/articles/10.1103/PhysRevLett.122.206401/apsxml
16. Aliev, Z.S., Amiraslanov, I.R., Nasonova, D.I., Shevelkov, A.V., Abdullayev, N.A., Jahangirli, Z.A., Orujlu, E.N., (..), Chulkov, E.V. (2019) Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: Synthesis and crystal structure // Journal of Alloys and Compounds, 789, pp. 443-450. https://www.journals.elsevier.com/journal-of-alloys-and-compounds
17. Yan, J.-Q., Zhang, Q., Heitmann, T., Huang, Z., Chen, K.Y., Cheng, J.-G., Wu, W., (..), McQueeney, R.J. (2019) Crystal growth and magnetic structure of MnBi2Te4 // Physical Review Materials, 3 (6), art. no. 064202. http://harvest.aps.org/bagit/articles/10.1103/PhysRevMaterials.3.064202/apsxml
18. Zeugner, A., Nietschke, F., Wolter, A.U.B., Gaß, S., Vidal, R.C., Peixoto, T.R.F., Pohl, D., (..), Isaeva, A. (2019) Chemical Aspects of the Candidate Antiferromagnetic Topological Insulator MnBi 2 Te 4 // Chemistry of Materials, 31 (8), pp. 2795-2806. http://pubs.acs.org/journal/cmatex
19. Li, B., Yan, J.-Q., Pajerowski, D.M., Gordon, E., Nedić, A.-M., Sizyuk, Y., Ke, L., (..), McQueeney, R.J. (2020) Competing Magnetic Interactions in the Antiferromagnetic Topological Insulator MnBi2Te4 // Physical Review Letters, 124 (16), art. no. 167204. http://harvest.aps.org/bagit/articles/10.1103/PhysRevLett.124.167204/apsxml
20. Deng, Y., Yu, Y., Shi, M.Z., Guo, Z., Xu, Z., Wang, J., Chen, X.H., (..), Zhang, Y. (2020) Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4 // Science, 367 (6480), pp. 895-900. https://science.sciencemag.org/content/367/6480/895/tab-pdf
21. Liu, C., Wang, Y., Li, H., Wu, Y., Li, Y., Li, J., He, K., (..), Wang, Y. (2020) Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator // Nature Materials, 19 (5), pp. 522-527. http://www.nature.com/nmat
22. Petrov, E. K., Men'shov, V. N., Rusinov, I. P., Hoffmann, M., Ernst, A., Otrokov, M. M., Dugaev, V. K., (..), Chulkov, E. V. (2021) Domain wall induced spin-polarized flat bands in antiferromagnetic topological insulators // Phys. Rev. B, 103.
23. Ge, J., Liu, Y., Li, J., Li, H., Luo, T., Wu, Y., Xu, Y., (..), Wang, J. (2020) High-Chern-number and high-temperature quantum Hall effect without Landau levels // National Science Review, 7 (8), pp. 1280-1287. http://nsr.oxfordjournals.org
24. Xu, B., Zhang, Y., Alizade, E.H., Jahangirli, Z.A., Lyzwa, F., Sheveleva, E., Marsik, P., (..), Bernhard, C. (2021) Infrared study of the multiband low-energy excitations of the topological antiferromagnet MnBi2Te4 // Physical Review B, 103 (12), art. no. L121103. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.L121103
25. Perez-Piskunow, P.M., Roche, S. (2021) Hinge Spin Polarization in Magnetic Topological Insulators Revealed by Resistance Switch // Physical Review Letters, 126 (16), art. no. 167701. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.167701
26. Wang, P., Ge, J., Li, J., Liu, Y., Xu, Y., Wang, J. (2021) Intrinsic magnetic topological insulators // Innovation (China), 2 (2), art. no. 100098. www.cell.com/the-innovation
27. Wu, J., Liu, F., Sasase, M., Ienaga, K., Obata, Y., Yukawa, R., Horiba, K., (..), Hosono, H. (2019) Natural van der Waals heterostructural single crystals with both magnetic and topological properties // Science Advances, 5 (11), art. no. eaax9989. https://advances.sciencemag.org/content/5/11/eaax9989/tab-pdf
28. Hu, C., Gordon, K.N., Liu, P., Liu, J., Zhou, X., Hao, P., Narayan, D., (..), Ni, N. (2020) A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling // Nature Communications, 11 (1), art. no. 97. http://www.nature.com/ncomms/index.html
29. Klimovskikh, I.I., Otrokov, M.M., Estyunin, D., Eremeev, S.V., Filnov, S.O., Koroleva, A., Shevchenko, E., (..), Chulkov, E.V. (2020) Tunable 3D/2D magnetism in the (MnBi2Te4)(Bi2Te3)m topological insulators family // npj Quantum Materials, 5 (1), art. no. 54. www.nature.com/npjquantmats
30. Jahangirli, Z.A., Alizade, E.H., Aliev, Z.S., Otrokov, M.M., Ismayilova, N.A., Mammadov, S.N., Amiraslanov, I.R., (..), Chulkov, E.V. (2019) Electronic structure and dielectric function of Mn-Bi-Te layered compounds // Journal of Vacuum Science and Technology B: Nanotechnology and Microelectronics, 37 (6), art. no. 062910. http://avspublications.org/jvstb
31. Vidal, R.C., Zeugner, A., Facio, J.I., Ray, R., Haghighi, M.H., Wolter, A.U.B., Corredor Bohorquez, L.T., (..), Isaeva, A. (2019) Topological Electronic Structure and Intrinsic Magnetization in MnBi4Te7: A Bi2Te3 Derivative with a Periodic Mn Sublattice // Physical Review X, 91 (4), art. no. 041065. http://harvest.aps.org/bagit/articles/10.1103/PhysRevX.9.041065/apsxml
32. Chen, B., Fei, F., Zhang, D., Zhang, B., Liu, W., Zhang, S., Wang, P., (..), Wang, B. (2019) Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes // Nature Communications, 10 (1), art. no. 4469. http://www.nature.com/ncomms/index.html
33. Yan, J.-Q., Okamoto, S., McGuire, M.A., May, A.F., McQueeney, R.J., Sales, B.C. (2019) Evolution of structural, magnetic, and transport properties in MnBi2-xSbxTe4 // Physical Review B, 100 (10), art. no. 104409. http://harvest.aps.org/bagit/articles/10.1103/PhysRevB.100.104409/apsxml
34. Ko, W., Kolmer, M., Yan, J., Pham, A.D., Fu, M., Lüpke, F., Okamoto, S., (..), Li, A.-P. (2020) Realizing gapped surface states in the magnetic topological insulator MnBi2-xSbxTe4 // Physical Review B, 102 (11), art. no. 115402. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.115402
35. Abdullayev, N. A., Aliguliyeva, V., Zverev, V. N., Aliev, Z. S., Amiraslanov, I. R., Babanly, M. B., Jahangirli, Z. A., (..), Chulkov, E. V. (2021) Phys. Solid State, 63.
36. Wimmer, S., Sánchez-Barriga, J., Küppers, P., Ney, A., Schierle, E., Freyse, F., Caha, O., (..), Rader, O. (2021) Mn-Rich MnSb2Te4: A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45-50 K // Advanced Materials, 33 (42), art. no. 2102935. http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4095
37. Eremeev, S.V., Rusinov, I.P., Koroteev, Y.M., Vyazovskaya, A.Y., Hoffmann, M., Echenique, P.M., Ernst, A., (..), Chulkov, E.V. (2021) Topological magnetic materials of the (MnSb2Te4)•(Sb2Te3)nvan der waals compounds family // Journal of Physical Chemistry Letters, 12 (17), pp. 4268-4277. http://pubs.acs.org/journal/jpclcd
38. Huan, S., Zhang, S., Jiang, Z., Su, H., Wang, H., Zhang, X., Yang, Y., (..), Guo, Y. (2021) Multiple Magnetic Topological Phases in Bulk van der Waals Crystal MnSb4Te7 // Physical Review Letters, 126 (24), art. no. 246601. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.246601
39. Huan, S., Wang, D., Su, H., Wang, H., Wang, X., Yu, N., Zou, Z., (..), Guo, Y. (2021) Magnetism-induced ideal Weyl state in bulk van der Waals crystal MnSb2Te4 // Applied Physics Letters, 118 (19), art. no. 192105. http://scitation.aip.org/content/aip/journal/apl
40. Deng, H., Chen, Z., Wołoś, A., Konczykowski, M., Sobczak, K., Sitnicka, J., Fedorchenko, I.V., (..), Krusin-Elbaum, L. (2021) High-temperature quantum anomalous Hall regime in a MnBi2Te4/Bi2Te3 superlattice // Nature Physics, 17 (1), pp. 36-42. http://www.nature.com/nphys/index.html
41. Lee, S.H., Zhu, Y., Wang, Y., Miao, L., Pillsbury, T., Yi, H., Kempinger, S., (..), Mao, Z. (2019) Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi2Te4 // Physical Review Research, 1 (1), art. no. 012011. https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.1.012011
42. Vidal, R.C., Bentmann, H., Peixoto, T.R.F., Zeugner, A., Moser, S., Min, C.-H., Schatz, S., (..), Reinert, F. (2019) Surface states and Rashba-type spin polarization in antiferromagnetic MnBi2Te4 (0001) // Physical Review B, 100 (12), art. no. 121104. http://harvest.aps.org/bagit/articles/10.1103/PhysRevB.100.121104/apsxml
43. Hao, Y.-J., Liu, P., Feng, Y., Ma, X.-M., Schwier, E.F., Arita, M., Kumar, S., (..), Liu, C. (2019) Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi2Te4 // Physical Review X, 91 (4), art. no. 041038. http://harvest.aps.org/bagit/articles/10.1103/PhysRevX.9.041038/apsxml
44. Li, H., Gao, S.-Y., Duan, S.-F., Xu, Y.-F., Zhu, K.-J., Tian, S.-J., Gao, J.-C., (..), Ding, H. (2019) Dirac Surface States in Intrinsic Magnetic Topological Insulators EuSn2As2 and MnBi2nTe3n+1 // Physical Review X, 91 (4), art. no. 041039. http://harvest.aps.org/bagit/articles/10.1103/PhysRevX.9.041039/apsxml
45. Chen, Y.J., Xu, L.X., Li, J.H., Li, Y.W., Wang, H.Y., Zhang, C.F., Li, H., (..), Chen, Y.L. (2019) Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi2Te4 // Physical Review X, 91 (4), art. no. 041040. http://harvest.aps.org/bagit/articles/10.1103/PhysRevX.9.041040/apsxml
46. Swatek, P., Wu, Y., Wang, L.-L., Lee, K., Schrunk, B., Yan, J., Kaminski, A. (2020) Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi2Te4 // Physical Review B, 101 (16), art. no. 161109. http://harvest.aps.org/bagit/articles/10.1103/PhysRevB.101.161109/apsxml
47. Estyunin, D.A., Klimovskikh, I.I., Shikin, A.M., Schwier, E.F., Otrokov, M.M., Kimura, A., Kumar, S., (..), Chulkov, E. V. (2020) Signatures of temperature driven antiferromagnetic transition in the electronic structure of topological insulator MnBi2Te4 // APL Materials, 8 (2), art. no. 021105. http://scitation.aip.org/content/aip/journal/aplmater
48. Shikin, A.M., Estyunin, D.A., Klimovskikh, I.I., Filnov, S.O., Schwier, E.F., Kumar, S., Miyamoto, K., (..), Chulkov, E.V. (2020) Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi 2Te 4 // Scientific Reports, 10 (1), art. no. 13226. www.nature.com/srep/index.html
49. Nevola, D., Li, H.X., Yan, J.-Q., Moore, R.G., Lee, H.-N., Miao, H., Johnson, P.D. (2020) Coexistence of Surface Ferromagnetism and a Gapless Topological State in MnBi2Te4 // Physical Review Letters, 125 (11), art. no. 117205. https://link.aps.org/doi/10.1103/PhysRevLett.125.117205
50. Yan, C., Fernandez-Mulligan, S., Mei, R., Lee, S.H., Protic, N., Fukumori, R., Yan, B., (..), Yang, S. (2021) Origins of electronic bands in the antiferromagnetic topological insulator MnBi2Te4 // Physical Review B, 104 (4), art. no. L041102. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.L041102
51. Bahramy, M.S., King, P.D.C., De La Torre, A., Chang, J., Shi, M., Patthey, L., Balakrishnan, G., (..), Baumberger, F. (2012) Emergent quantum confinement at topological insulator surfaces // Nature Communications, 3, art. no. 1159.
52. Sass, P.M., Kim, J., Vanderbilt, D., Yan, J., Wu, W. (2020) Robust A-Type Order and Spin-Flop Transition on the Surface of the Antiferromagnetic Topological Insulator MnBi2Te4 // Physical Review Letters, 125 (3), art. no. 037201. http://harvest.aps.org/bagit/articles/10.1103/PhysRevLett.125.037201
53. Yuan, Y., Wang, X., Li, H., Li, J., Ji, Y., Hao, Z., Wu, Y., (..), Xue, Q.-K. (2020) Electronic states and magnetic response of mnbi2te4 by scanning tunneling microscopy and spectroscopy // Nano Letters, 20 (5), pp. 3271-3277. http://pubs.acs.org/journal/nalefd
54. Liang, Z., Luo, A., Shi, M., Zhang, Q., Nie, S., Ying, J.J., He, J.-F., (..), Chen, X.-H. (2020) Mapping Dirac fermions in the intrinsic antiferromagnetic topological insulators (MnBi2Te4)(Bi2Te3)n (n=0, 1) // Physical Review B, 102 (16), art. no. 161115. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.161115
55. Huang, Z., Du, M.-H., Yan, J., Wu, W. (2020) Native defects in antiferromagnetic topological insulator MnBi2Te4 // Physical Review Materials, 4 (12), art. no. 121202. https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.4.121202
56. Hou, F., Yao, Q., Zhou, C.-S., Ma, X.-M., Han, M., Hao, Y.-J., Wu, X., (..), Lin, J. (2020) Te-Vacancy-Induced Surface Collapse and Reconstruction in Antiferromagnetic Topological Insulator MnBi2Te4 // ACS Nano, 14 (9), pp. 11262-11272. http://pubs.acs.org/journal/ancac3
57. Du, M.-H., Yan, J., Cooper, V.R., Eisenbach, M. (2021) Tuning Fermi Levels in Intrinsic Antiferromagnetic Topological Insulators MnBi2Te4 and MnBi4Te7 by Defect Engineering and Chemical Doping // Advanced Functional Materials, 31 (3), art. no. 2006516. http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1616-3028
58. Frantzeskakis, E., Ramankutty, S.V., De Jong, N., Huang, Y.K., Pan, Y., Tytarenko, A., Radovic, M., (..), Golden, M.S. (2017) Trigger of the ubiquitous surface band bending in 3D topological insulators // Physical Review X, 7 (4), art. no. 041041. https://journals.aps.org/prx
59. Yazyev, O.V., Moore, J.E., Louie, S.G. (2010) Spin polarization and transport of surface states in the topological insulators Bi2Se3 and Bi2Te3 from first principles // Physical Review Letters, 105 (26), art. no. 266806. http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevLett.105.266806&metadataPrefix=oai_apsmeta_2
60. Menshchikova, T.V., Otrokov, M.M., Tsirkin, S.S., Samorokov, D.A., Bebneva, V.V., Ernst, A., Kuznetsov, V.M., (..), Chulkov, E.V. (2013) Band structure engineering in topological insulator based heterostructures // Nano Letters, 13 (12), pp. 6064-6069.
61. Supplemental Material at for the additional ARPES spectra obtained from other samples.
62. Rybkin, A.G., Rybkina, A.A., Otrokov, M.M., Vilkov, O.Y., Klimovskikh, I.I., Petukhov, A.E., Filianina, M.V., (..), Shikin, A.M. (2018) Magneto-Spin-Orbit Graphene: Interplay between Exchange and Spin-Orbit Couplings // Nano Letters, 18 (3), pp. 1564-1574. http://pubs.acs.org/journal/nalefd
63. Ozaki, T. (2003) Variationally optimized atomic orbitals for large-scale electronic structures // Physical Review B - Condensed Matter and Materials Physics, 67 (15).
64. Ozaki, T., Kino, H. (2004) Numerical atomic basis orbitals from H to Kr // Physical Review B - Condensed Matter and Materials Physics, 69 (19), art. no. 195113, pp. 195113-1-195113-19.
65. Ozaki, T., Kino, H. (2005) Efficient projector expansion for the ab initio LCAO method // Physical Review B - Condensed Matter and Materials Physics, 72 (4), art. no. 045121. http://oai.aps.org/oai/?verb=ListRecords&metadataPrefix=oai_apsmeta_2&set=journal:PRB:72
66. Troullier, N., Martins, J.L. (1991) Efficient pseudopotentials for plane-wave calculations // Physical Review B, 43 (3), pp. 1993-2006.
67. Perdew, J.P., Burke, K., Ernzerhof, M. (1996) Generalized gradient approximation made simple // Physical Review Letters, 77 (18), pp. 3865-3868.
68. Han, M.J., Ozaki, T., Yu, J. (2006) O (N) LDA+U electronic structure calculation method based on the nonorthogonal pseudoatomic orbital basis // Physical Review B - Condensed Matter and Materials Physics, 73 (4), art. no. 045110. http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevB.73.045110&metadataPrefix=oai_apsmeta_2
69. Dudarev, S., Botton, G. (1998) Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study // Physical Review B - Condensed Matter and Materials Physics, 57 (3), pp. 1505-1509.
70. Hirahara, T., Otrokov, M.M., Sasaki, T.T., Sumida, K., Tomohiro, Y., Kusaka, S., Okuyama, Y., (..), Chulkov, E.V. (2020) Fabrication of a novel magnetic topological heterostructure and temperature evolution of its massive Dirac cone // Nature Communications, 11 (1), art. no. 4821. http://www.nature.com/ncomms/index.html
71. Eremeev, S.V., Otrokov, M.M., Chulkov, E.V. (2018) New Universal Type of Interface in the Magnetic Insulator/Topological Insulator Heterostructures // Nano Letters, 18 (10), pp. 6521-6529. http://pubs.acs.org/journal/nalefd
72. Otani, M., Sugino, O. (2006) First-principles calculations of charged surfaces and interfaces: A plane-wave nonrepeated slab approach // Physical Review B - Condensed Matter and Materials Physics, 73 (11), art. no. 115407. http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org:PhysRevB.73.115407&metadataPrefix=oai_apsmeta_2