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Topological Phase Transitions Driven by Sn Doping in (Mn_{1−x}Sn_{x})Bi_{2}Te_{4}

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Infinite Crystal Calculations

#### 3.2. Experimental Results

#### 3.3. Surface Calculations

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The KKR–calculated bulk band structure of (Mn${}_{1-x}$Sn${}_{x}$)Bi${}_{2}$Te${}_{4}$ along $K\Gamma M$ path in the first Brillouin zone for $x=0$ (

**a**), $x=0.2$ (

**b**), $x=0.3$ (

**c**), $x=0.4$ (

**d**), $x=0.5$ (

**e**), $x=0.6$ (

**f**). The general dependence of bulk gap as a function of Sn content is plotted on (

**g**).

**Figure 2.**DFT–calculated bulk band structure of $2\times 2$ (Mn${}_{1-x}$Sn${}_{x}$)Bi${}_{2}$Te${}_{4}$ supercell along $K\Gamma Z$ path in the first Brillouin zone, corresponding concentrations are $x=0$ (

**a**,

**f**), $x=0.25$ (

**b**,

**g**), $x=0.5$ (

**c**,

**h**), $x=0.75$ (

**d**,

**i**), $x=1$ (

**e**,

**j**). General plot of the bulk band gap value as a function of Sn content x is on the panel (

**k**). The total spectral weight unfolded to $1\times 1$ primitive cell is shown in black. Red and blue colours indicate regions of Bi-p and Te-p orbital weight dominance, respectively.

**Figure 3.**Band structure of valence and conduction states in ARPES spectra taken from (Mn${}_{1-x}$Sn${}_{x}$)Bi${}_{2}$Te${}_{4}$ crystal for x = 0 (

**a**), 0.19 (

**b**), 0.36 (

**c**), 0.52 (

**d**) and 0.86 (

**e**). White dotted horizontal lines indicate the approximate positions of the edges of bulk band gap. Sn–derived states in panels (

**e**) are marked by red dotted parabolas.

**Figure 4.**Calculated electronic structure of the TSSs and the nearest valence and conduction band states for different Sn concentrations: 0% (

**a**), 25% (

**b**), 50% (

**c**), 75% (

**d**). The positions of the edges of the bulk band gap are marked with horizontal dotted lines, and the energy gap in the TSS (where they are present) is marked with green solid lines indicating its magnitude. Sn–derived states in panels (

**c**,

**d**) are marked by red dotted lines.

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/sym15020469

**AMA Style**

Tarasov AV, Makarova TP, Estyunin DA, Eryzhenkov AV, Klimovskikh II, Golyashov VA, Kokh KA, Tereshchenko OE, Shikin AM.
Topological Phase Transitions Driven by Sn Doping in (Mn_{1−x}Sn_{x})Bi_{2}Te_{4}. *Symmetry*. 2023; 15(2):469.
https://doi.org/10.3390/sym15020469

**Chicago/Turabian Style**

Tarasov, Artem V., Tatiana P. Makarova, Dmitry A. Estyunin, Alexander V. Eryzhenkov, Ilya I. Klimovskikh, Vladimir A. Golyashov, Konstantin A. Kokh, Oleg E. Tereshchenko, and Alexander M. Shikin.
2023. "Topological Phase Transitions Driven by Sn Doping in (Mn_{1−x}Sn_{x})Bi_{2}Te_{4}" *Symmetry* 15, no. 2: 469.
https://doi.org/10.3390/sym15020469