#
Evolution of Mn_{1−x}Ge_{x}Bi_{2}Te_{4} Electronic Structure under Variation of Ge Content

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Experimental Results

#### 3.2. Theoretical Calculations

#### 3.2.1. Bulk Mn/Ge Substitution

#### 3.2.2. Surface Mn/Ge Substitution

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Hasan, M.Z.; Kane, C.L. Colloquium: Topological insulators. Rev. Mod. Phys.
**2010**, 82, 3045. [Google Scholar] [CrossRef] [Green Version] - Qi, X.L.; Hughes, T.L.; Zhang, S.C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B
**2008**, 78, 195424. [Google Scholar] [CrossRef] [Green Version] - Qi, X.L.; Zhang, S.C. Topological insulators and superconductors. Rev. Mod. Phys.
**2011**, 83, 1057. [Google Scholar] [CrossRef] [Green Version] - Chen, Y.P. Topological insulator-based energy efficient devices. In Proceedings of the Micro-and Nanotechnology Sensors, Systems, and Applications IV, Baltimore, MD, USA, 23–27 April 2012; Volume 8373, pp. 94–98. [Google Scholar]
- Wang, J.; DaSilva, A.M.; Chang, C.Z.; He, K.; Jain, J.; Samarth, N.; Ma, X.C.; Xue, Q.K.; Chan, M.H. Evidence for electron-electron interaction in topological insulator thin films. Phys. Rev. B
**2011**, 83, 245438. [Google Scholar] [CrossRef] [Green Version] - Tokura, Y.; Yasuda, K.; Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys.
**2019**, 1, 126–143. [Google Scholar] [CrossRef] - Chang, C.Z.; Zhang, J.; Feng, X.; Shen, J.; Zhang, Z.; Guo, M.; Li, K.; Ou, Y.; Wei, P.; Wang, L.L.; et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science
**2013**, 340, 167–170. [Google Scholar] [CrossRef] [Green Version] - He, Q.L.; Pan, L.; Stern, A.L.; Burks, E.C.; Che, X.; Yin, G.; Wang, J.; Lian, B.; Zhou, Q.; Choi, E.S.; et al. Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure. Science
**2017**, 357, 294–299. [Google Scholar] [CrossRef] [Green Version] - Otrokov, M.M.; Klimovskikh, I.I.; Bentmann, H.; Estyunin, D.; Zeugner, A.; Aliev, Z.S.; Gaß, S.; Wolter, A.; Koroleva, A.; Shikin, A.M.; et al. Prediction and observation of an antiferromagnetic topological insulator. Nature
**2019**, 576, 416–422. [Google Scholar] [CrossRef] [Green Version] - Li, J.; Li, Y.; Du, S.; Wang, Z.; Gu, B.L.; Zhang, S.C.; He, K.; Duan, W.; Xu, Y. Intrinsic magnetic topological insulators in van der Waals layered MnBi
_{2}Te_{4}-family materials. Sci. Adv.**2019**, 5, eaaw5685. [Google Scholar] [CrossRef] [Green Version] - Shikin, A.; Makarova, T.; Eryzhenkov, A.; Usachov, D.Y.; Estyunin, D.; Glazkova, D.; Klimovskikh, I.; Rybkin, A.; Tarasov, A. Routes for the topological surface state energy gap modulation in antiferromagnetic MnBi
_{2}Te_{4}. Phys. B Condens. Matter**2023**, 649, 414443. [Google Scholar] [CrossRef] - Shikin, A.; Zaitsev, N.; Tarasov, A.; Makarova, T.; Glazkova, D.; Estyunin, D.; Klimovskikh, I. Electronic and Spin Structure of Topological Surface States in MnBi
_{4}Te_{7}and MnBi_{6}Te_{10}and Their Modification by an Applied Electric Field. JETP Lett.**2022**, 116, 556–566. [Google Scholar] [CrossRef] - Shikin, A.M.; Estyunin, D.; Zaitsev, N.L.; Glazkova, D.; Klimovskikh, I.I.; Filnov, S.; Rybkin, A.G.; Schwier, E.; Kumar, S.; Kimura, A.; et al. Sample-dependent Dirac-point gap in MnBi
_{2}Te_{4}and its response to applied surface charge: A combined photoemission and ab-initio study. Phys. Rev. B**2021**, 104, 115168. [Google Scholar] [CrossRef] - Eremeev, S.; Vergniory, M.; Menshchikova, T.V.; Shaposhnikov, A.; Chulkov, E.V. The effect of van der Waal’s gap expansions on the surface electronic structure of layered topological insulators. New J. Phys.
**2012**, 14, 113030. [Google Scholar] [CrossRef] - Shikin, A.M.; Estyunin, D.; Klimovskikh, I.I.; Filnov, S.; Schwier, E.; Kumar, S.; Miyamoto, K.; Okuda, T.; Kimura, A.; Kuroda, K.; et al. Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi
_{2}Te_{4}. Sci. Rep.**2020**, 10, 13226. [Google Scholar] [CrossRef] - Makarova, T.; Shikin, A.; Eryzhenkov, A.; Tarasov, A. Influence of Structural Parameters on the Electronic Structure of Topological Surface States in MnBi
_{2}Te_{4}. J. Exp. Theor. Phys.**2023**, 136, 630–637. [Google Scholar] [CrossRef] - Qi, X.L.; Zhang, S.C. The quantum spin Hall effect and topological insulators. arXiv
**2010**, arXiv:1001.1602. [Google Scholar] [CrossRef] - Li, Y.; Huang, C.; Wang, G.; Hu, J.; Duan, S.; Xu, C.; Lu, Q.; Jing, Q.; Zhang, W.; Qian, D. Topological Dirac surface states in ternary compounds GeBi
_{2}Te_{4}, SnBi_{2}Te_{4}and Sn_{0.571}Bi_{2.286}Se_{4}. Chin. Phys. B**2021**, 30, 127901. [Google Scholar] [CrossRef] - Tarasov, A.V.; Makarova, T.P.; Estyunin, D.A.; Eryzhenkov, A.V.; Klimovskikh, I.I.; Golyashov, V.A.; Kokh, K.A.; Tereshchenko, O.E.; Shikin, A.M. Topological Phase Transitions Driven by Sn Doping in (Mn
_{1−x}Sn_{x}) Bi_{2}Te_{4}. Symmetry**2023**, 15, 469. [Google Scholar] [CrossRef] - Kuroda, K.; Miyahara, H.; Ye, M.; Eremeev, S.; Koroteev, Y.M.; Krasovskii, E.; Chulkov, E.; Hiramoto, S.; Moriyoshi, C.; Kuroiwa, Y.; et al. Experimental verification of PbBi
_{2}Te_{4}as a 3D topological insulator. Phys. Rev. Lett.**2012**, 108, 206803. [Google Scholar] [CrossRef] [Green Version] - Arita, M.; Sato, H.; Shimada, K.; Namatame, H.; Taniguchi, M.; Sasaki, M.; Kitaura, M.; Ohnishi, A.; Kim, H.J. Angle resolved photoemission study of GeBi
_{2}Te_{4}. In Proceedings of the 12th Asia Pacific Physics Conference (APPC12), Makuhari Messe, Japan, 14–19 July 2013; p. 012017. [Google Scholar] - Okamoto, K.; Kuroda, K.; Miyahara, H.; Miyamoto, K.; Okuda, T.; Aliev, Z.; Babanly, M.; Amiraslanov, I.; Shimada, K.; Namatame, H.; et al. Observation of a highly spin-polarized topological surface state in GeBi
_{2}Te_{4}. Phys. Rev. B**2012**, 86, 195304. [Google Scholar] [CrossRef] [Green Version] - Qian, T.; Yao, Y.T.; Hu, C.; Feng, E.; Cao, H.; Mazin, I.I.; Chang, T.R.; Ni, N. Magnetic dilution effect and topological phase transitions in (Mn
_{1−x}Pb_{x})Bi_{2}Te_{4}. Phys. Rev. B**2022**, 106, 045121. [Google Scholar] [CrossRef] - Zhu, J.; Naveed, M.; Chen, B.; Du, Y.; Guo, J.; Xie, H.; Fei, F. Magnetic and electrical transport study of the antiferromagnetic topological insulator Sn-doped MnBi
_{2}Te_{4}. Phys. Rev. B**2021**, 103, 144407. [Google Scholar] [CrossRef] - Changdar, S.; Ghosh, S.; Vijay, K.; Kar, I.; Routh, S.; Maheshwari, P.; Ghorai, S.; Banik, S.; Thirupathaiah, S. Nonmagnetic Sn doping effect on the electronic and magnetic properties of antiferromagnetic topological insulator MnBi
_{2}Te_{4}. Phys. B Condens. Matter**2023**, 657, 414799. [Google Scholar] [CrossRef] - Yan, J. The elusive quantum anomalous Hall effect in MnBi
_{2}Te_{4}: A materials perspective. arXiv**2021**, arXiv:2112.09070. [Google Scholar] [CrossRef] - Frolov, A.; Usachov, D.; Tarasov, A.; Fedorov, A.; Bokai, K.; Klimovskikh, I.; Stolyarov, V.; Sergeev, A.; Lavrov, A.; Golyashov, V.; et al. Magnetic Dirac semimetal state of (Mn,Ge)Bi
_{2}Te_{4}. arXiv**2023**, arXiv:2306.13024. [Google Scholar] - Neupane, M.; Xu, S.Y.; Wray, L.A.; Petersen, A.; Shankar, R.; Alidoust, N.; Liu, C.; Fedorov, A.; Ji, H.; Allred, J.M.; et al. Topological surface states and Dirac point tuning in ternary topological insulators. Phys. Rev. B
**2012**, 85, 235406. [Google Scholar] [CrossRef] [Green Version] - Iwasawa, H.; Schwier, E.F.; Arita, M.; Ino, A.; Namatame, H.; Taniguchi, M.; Aiura, Y.; Shimada, K. Development of laser-based scanning μ-ARPES system with ultimate energy and momentum resolutions. Ultramicroscopy
**2017**, 182, 85–91. [Google Scholar] [CrossRef] - Iwasawa, H.; Takita, H.; Goto, K.; Mansuer, W.; Miyashita, T.; Schwier, E.F.; Ino, A.; Shimada, K.; Aiura, Y. Accurate and efficient data acquisition methods for high-resolution angle-resolved photoemission microscopy. Sci. Rep.
**2018**, 8, 17431. [Google Scholar] [CrossRef] [Green Version] - Ozaki, T. Variationally optimized atomic orbitals for large-scale electronic structures. Phys. Rev. B
**2003**, 67, 155108. [Google Scholar] [CrossRef] - Ozaki, T.; Kino, H. Numerical atomic basis orbitals from H to Kr. Phys. Rev. B
**2004**, 69, 195113. [Google Scholar] [CrossRef] - Ozaki, T.; Kino, H. Efficient projector expansion for the ab-initio LCAO method. Phys. Rev. B
**2005**, 72, 045121. [Google Scholar] [CrossRef] - Troullier, N.; Martins, J.L. Efficient pseudopotentials for plane-wave calculations. II. Operators for fast iterative diagonalization. Phys. Rev. B
**1991**, 43, 8861. [Google Scholar] [CrossRef] [PubMed] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865. [Google Scholar] [CrossRef] [Green Version] - Vidal, R.; Bentmann, H.; Peixoto, T.; Zeugner, A.; Moser, S.; Min, C.H.; Schatz, S.; Kißner, K.; Ünzelmann, M.; Fornari, C.; et al. Surface states and Rashba-type spin polarization in antiferromagnetic MnBi
_{2}Te_{4}(0001). Phys. Rev. B**2019**, 100, 121104. [Google Scholar] [CrossRef] [Green Version] - Chen, Y.; Xu, L.; Li, J.; Li, Y.; Wang, H.; Zhang, C.; Li, H.; Wu, Y.; Liang, A.; Chen, C.; et al. Topological electronic structure and its temperature evolution in antiferromagnetic topological insulator MnBi
_{2}Te_{4}. Phys. Rev. X**2019**, 9, 041040. [Google Scholar] [CrossRef] [Green Version] - Ma, X.M.; Zhao, Y.; Zhang, K.; Kumar, S.; Lu, R.; Li, J.; Yao, Q.; Shao, J.; Hou, F.; Wu, X.; et al. Realization of a tunable surface Dirac gap in Sb-doped MnBi
_{2}Te_{4}. Phys. Rev. B**2021**, 103, L121112. [Google Scholar] [CrossRef] - Nevola, D.; Li, H.X.; Yan, J.Q.; Moore, R.; Lee, H.N.; Miao, H.; Johnson, P.D. Coexistence of surface ferromagnetism and a gapless topological state in MnBi
_{2}Te_{4}. Phys. Rev. Lett.**2020**, 125, 117205. [Google Scholar] [CrossRef] - Estyunin, D.; Klimovskikh, I.I.; Shikin, A.M.; Schwier, E.; Otrokov, M.; Kimura, A.; Kumar, S.; Filnov, S.; Aliev, Z.S.; Babanly, M.; et al. Signatures of temperature driven antiferromagnetic transition in the electronic structure of topological insulator MnBi
_{2}Te_{4}. APL Mater.**2020**, 8, 021105. [Google Scholar] [CrossRef] [Green Version] - Garnica, M.; Otrokov, M.M.; Aguilar, P.C.; Klimovskikh, I.I.; Estyunin, D.; Aliev, Z.S.; Amiraslanov, I.R.; Abdullayev, N.A.; Zverev, V.N.; Babanly, M.B.; et al. Native point defects and their implications for the Dirac point gap at MnBi
_{2}Te_{4}(0001). npj Quantum Mater.**2022**, 7, 7. [Google Scholar] [CrossRef] - Otrokov, M.; Rusinov, I.P.; Blanco-Rey, M.; Hoffmann, M.; Vyazovskaya, A.Y.; Eremeev, S.; Ernst, A.; Echenique, P.M.; Arnau, A.; Chulkov, E.V. Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi
_{2}Te_{4}films. Phys. Rev. Lett.**2019**, 122, 107202. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Jiang, Y.; Zhang, J.; Liu, Z.; Yang, Z.; Wang, J. Intrinsic topological phases in Mn
_{2}Bi_{2}Te_{5}tuned by the layer magnetization. Phys. Rev. B**2020**, 102, 121107. [Google Scholar] [CrossRef] - Zhu, T.; Wang, H.; Zhang, H.; Xing, D. Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi
_{2}Te_{4}films. npj Comput. Mater.**2021**, 7, 121. [Google Scholar] [CrossRef] - Liang, A.; Chen, C.; Zheng, H.; Xia, W.; Huang, K.; Wei, L.; Yang, H.; Chen, Y.; Zhang, X.; Xu, X.; et al. Approaching a Minimal Topological Electronic Structure in Antiferromagnetic Topological Insulator MnBi
_{2}Te_{4}via Surface Modification. Nano Lett.**2022**, 22, 4307–4314. [Google Scholar] [CrossRef] [PubMed] - Fukasawa, T.; Kusaka, S.; Sumida, K.; Hashizume, M.; Ichinokura, S.; Takeda, Y.; Ideta, S.; Tanaka, K.; Shimizu, R.; Hitosugi, T.; et al. Absence of ferromagnetism in MnBi
_{2}Te_{4}/Bi_{2}Te_{3}down to 6 K. Phys. Rev. B**2021**, 103, 205405. [Google Scholar] [CrossRef] - Kagerer, P.; Fornari, C.; Buchberger, S.; Tschirner, T.; Veyrat, L.; Kamp, M.; Tcakaev, A.; Zabolotnyy, V.; Morelhão, S.; Geldiyev, B.; et al. Two-dimensional ferromagnetic extension of a topological insulator. Phys. Rev. Res.
**2023**, 5, L022019. [Google Scholar] [CrossRef] - Hirahara, T.; Eremeev, S.V.; Shirasawa, T.; Okuyama, Y.; Kubo, T.; Nakanishi, R.; Akiyama, R.; Takayama, A.; Hajiri, T.; Ideta, S.-i.; et al. Large-gap magnetic topological heterostructure formed by subsurface incorporation of a ferromagnetic layer. Nano Lett.
**2017**, 17, 3493–3500. [Google Scholar] [CrossRef] [Green Version] - Hirahara, T.; Otrokov, M.M.; Sasaki, T.; Sumida, K.; Tomohiro, Y.; Kusaka, S.; Okuyama, Y.; Ichinokura, S.; Kobayashi, M.; Takeda, Y.; et al. Fabrication of a novel magnetic topological heterostructure and temperature evolution of its massive Dirac cone. Nat. Commun.
**2020**, 11, 4821. [Google Scholar] [CrossRef]

**Figure 1.**ARPES spectra of Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$ crystal with x = 0 (

**a**), 0.13 (

**b**), 0.31 (

**c**), 0.65 (

**d**), 0.9 (

**e**) measured at $T=76$ K using $h\nu $ = 21.2 eV. The white dashed lines depict Ge-derived states.

**Figure 2.**ARPES spectra of Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$ crystal for x = 0.13 (

**a**,

**e**), 0.26 (

**b**,

**f**), 0.45 (

**c**,

**g**), 0.8 (

**d**,

**h**), presented as $N\left(E\right)$-top line and ${d}^{2}N\left(E\right)/d{E}^{2}$-bottom line. The blue dashed lines depict Ge-derived states. The yellow dashed lines indicate Rashba-like states. Energy distribution curves at the $\Gamma $-point are shown on the left side of the top panels. $h\nu $ = 6.3 eV.

**Figure 3.**Calculated band structure of the TSS and the nearest valence and conduction band (BVB and BCB) states. The black markers depict Ge contribution (upper panel); the difference between Te ${p}_{z}$ (red) and Bi ${p}_{z}$ (blue) contributions (lower panel) for Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$ system with x = 0% (

**a**,

**e**), 25% (

**b**,

**f**), 50% (

**c**,

**g**), 75% (

**d**,

**h**). Structure of the MnBi${}_{2}$Te${}_{4}$ SL with the arrangement of atoms (

**i**). The black arrows represent the direction of the magnetic moment.

**Figure 4.**The band structure of Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$ system for x = 0% (

**a**), 25% (

**b**), 50% (

**c**), 75% (

**d**). The color scale indicate the surface localisation. Distribution in the TSS localisation for the lower and upper parts of the cone (blue and red points, respectively) (

**e**–

**h**). In panel (

**a**), the dotted circle indicates the area for which localisation was calculated. For all x values the k range from −0.01 to 0.01 ${\AA}^{-1}$ was used.

**Figure 5.**Calculated band structure of the TSS and the nearest valence and conduction band (BVB and BCB) states. The black markers depict Ge contribution (upper panel); the difference between Te ${p}_{z}$ (red) and Bi ${p}_{z}$ (blue) contributions (lower panel) for Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$/MnBi${}_{2}$Te${}_{4}$ system with x = 0% (

**a**,

**e**), 25% (

**b**,

**f**), 50% (

**c**,

**g**), 75% (

**d**,

**h**). Structure of the MnBi${}_{2}$Te${}_{4}$ SL with the arrangement of atoms (

**i**). The black arrows represent the direction of the magnetic moment.

**Figure 6.**The band structure of Mn${}_{1-x}$Ge${}_{x}$Bi${}_{2}$Te${}_{4}$/MnBi${}_{2}$Te${}_{4}$ system for x = 25% (

**a**), 50% (

**b**), 75% (

**c**), 100% (

**d**). The color scale indicates the surface localisation. Distribution in the TSS localisation for the lower and upper parts of the Dirac cone (blue and red points, respectively) (

**e**–

**h**). In panel (

**a**), the dotted circle indicates the area for which localisation was calculated. For all x values the k range from −0.01 to 0.01 ${\AA}^{-1}$ was used.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Estyunina, T.P.; Shikin, A.M.; Estyunin, D.A.; Eryzhenkov, A.V.; Klimovskikh, I.I.; Bokai, K.A.; Golyashov, V.A.; Kokh, K.A.; Tereshchenko, O.E.; Kumar, S.;
et al. Evolution of Mn_{1−x}Ge_{x}Bi_{2}Te_{4} Electronic Structure under Variation of Ge Content. *Nanomaterials* **2023**, *13*, 2151.
https://doi.org/10.3390/nano13142151

**AMA Style**

Estyunina TP, Shikin AM, Estyunin DA, Eryzhenkov AV, Klimovskikh II, Bokai KA, Golyashov VA, Kokh KA, Tereshchenko OE, Kumar S,
et al. Evolution of Mn_{1−x}Ge_{x}Bi_{2}Te_{4} Electronic Structure under Variation of Ge Content. *Nanomaterials*. 2023; 13(14):2151.
https://doi.org/10.3390/nano13142151

**Chicago/Turabian Style**

Estyunina, Tatiana P., Alexander M. Shikin, Dmitry A. Estyunin, Alexander V. Eryzhenkov, Ilya I. Klimovskikh, Kirill A. Bokai, Vladimir A. Golyashov, Konstantin A. Kokh, Oleg E. Tereshchenko, Shiv Kumar,
and et al. 2023. "Evolution of Mn_{1−x}Ge_{x}Bi_{2}Te_{4} Electronic Structure under Variation of Ge Content" *Nanomaterials* 13, no. 14: 2151.
https://doi.org/10.3390/nano13142151