量子異常霍爾效應具有在材料邊界流動且不易受到雜質散射的電流。此特殊的電子傳輸特性使其成為學界公認具有潛力成為次世代低耗能的自旋電子元件，甚至是量子電腦中量子位元的材料。受惠於拓樸材料的發現，科學家們於2020年初首次於本質磁性拓樸材料MnBi2Te4中實現量子異常霍爾效應。然而由於物理定律的限制，該材料厚度需達到至少8 nm以上，這存在許多應用層面上的限制。為了盡可能縮小元件尺寸，我們必須尋找MnBi2Te4之外的材料。
在此研究工作中，我們將單層石墨烯放置於單層MnBi2Te4上，透過在石墨烯中引入強自旋-軌道耦合、凱庫勒畸變、與鐵磁之交換能，我們成功預測單層石墨烯中的量子異常霍爾效應。此外我們提出此系統之拓撲相圖，發現藉由調控鐵磁的交換能強度，可以調控此系統的霍爾電導。由於石墨烯厚度僅有單層原子且具有良好的導電性以及可調控性，2018更發現了雙層魔角石墨烯中的超導特性，我們的研究提供在石墨烯上研究磁性拓撲以及超導之間交互作用的一條全新方向。

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a significant challenge in future applications. Despite numerous theoretical works proposed for the QAH effect with C=2 in graphene, neglecting magnetism sources such as proper substrate effects remain experimental evidence absent. In this work, we propose the QAH effect in graphene/MnBi2Te4 (MBT) heterostructure based on density-functional theory (DFT). The monolayer MBT introduces spin-orbital coupling, Zeeman exchange field, and Kekulé distortion as a substrate effect into graphene, resulting in QAH with C=1 in the heterostructure. Our effective Hamiltonian further presents a rich phase diagram that has not been studied previously. Our work provides a new and practical way to explore the QAH effect in monolayer graphene and the magnetic topological phases by the flexibility of MBT family materials.

[1] Bansil, A., Lin, H. & Das, T. Colloquium: Topological band theory. Rev. Mod. Phys. 88, 021004 (2016).
[2] Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
[3] Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: Quantum anomalous hall effect. Rev. Mod. Phys. 95, 011002 (2023).
[4] Zhang, J. et al. Topology-driven magnetic quantum phase transition in topological insulators. Science 339, 1582–1586 (2013).
[5] Chang, C.-Z. et al. Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).
[6] Chang, C.-Z. et al. High-precision realization of robust quantum anomalous hall state in a hard ferromagnetic topological insulator. Nature Materials 14, 473–477 (2015).
[7] Deng, Y. et al. Quantum anomalous hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).
[8] Hu, C. et al. Realization of an intrinsic ferromagnetic topological state in MnBi8Te13. Science Advances 6, eaba4275 (2020).
[9] Serlin, M. et al. Intrinsic quantized anomalous hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
[10] Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
[11] Kane, C. L. & Mele, E. J. Quantum spin hall effect in graphene. Physical Review Letters 95, 226801 (2005).
[12] Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin hall effect. Physical Review Letters 95, 146802 (2005).
[13] Tse, W.-K., Qiao, Z., Yao, Y., MacDonald, A. H. & Niu, Q. Quantum anomalous hall effect in single-layer and bilayer graphene. Physical Review B 83, 155447 (2011).
[14] Ezawa, M. Valley-polarized metals and quantum anomalous hall effect in silicene. Physical Review Letters 109, 055502 (2012).
[15] Qiao, Z. et al. Quantum anomalous hall effect in graphene from Rashba and exchange effects. Physical Review B 82, 161414 (2010).
[16] Qiao, Z., Jiang, H., Li, X., Yao, Y. & Niu, Q. Microscopic theory of quantum anomalous hall effect in graphene. Physical Review B 85, 115439 (2012).
[17] Zhang, J., Zhao, B., Yao, Y. & Yang, Z. Quantum anomalous hall effect in graphene-based heterostructure. Scientific Reports 5, 10629 (2015).
[18] Qiao, Z. et al. Quantum anomalous hall effect in graphene proximity coupled to an antiferromagnetic insulator. Physical Review Letters 112, 116404 (2014).
[19] Zhang, J., Zhao, B., Yao, Y. & Yang, Z. Robust quantum anomalous hall effect in graphene-based van der Waals heterostructures. Physical Review B 92, 165418 (2015).
[20] Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Science Advances 5, eaaw5685 (2019).
[21] Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Physics 5, 438–442 (2009).
[22] Khokhriakov, D. et al. Tailoring emergent spin phenomena in Dirac material heterostructures. Science Advances 4, eaat9349 (2018).
[23] Song, K. et al. Spin proximity effects in graphene/topological insulator heterostructures. Nano Letters 18, 2033–2039 (2018).
[24] Lin, Z. et al. Competing gap opening mechanisms of monolayer graphene and graphene nanoribbons on strong topological insulators. Nano Letters 17, 4013–4018 (2017).
[25] Gutiérrez, C. et al. Imaging chiral symmetry breaking from kekulé bond order in graphene. Nature Physics 12, 950–958 (2016).
[26] Blöchl, P. E. Projector augmented-wave method. Physical Review B 50, 17953–17979 (1994).
[27] Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B 59, 1758–1775 (1999).
[28] Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6, 15–50 (1996).
[29] Becke, A. D. & Johnson, E. R. A simple effective potential for exchange. The Journal of Chemical Physics 124, 221101 (2006).
[30] Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 27, 1787–1799 (2006).
[31] Haldane, F. D. M. Model for a quantum hall effect without landau levels: Condensed-matter realization of the "parity anomaly". Physical Review Letters 61, 2015–2018 (1988).
[32] Yao, Y.-T. et al. Feature-energy duality of topological boundary states in multi-layer quantum spin hall insulator. URL https://doi.org/10.48550/arXiv.2312.11794.
[33] Sheng, D. N., Weng, Z. Y., Sheng, L. & Haldane, F. D. M. Quantum spin-hall effect and topologically invariant chern numbers. Physical Review Letters 97, 036808 (2006).
[34] Prodan, E. Robustness of the spin-chern number. Physical Review B 80, 125327 (2009).
[35] Yang, Y. et al. Time-reversal-symmetry-broken quantum spin hall effect. Physical Review Letters 107, 066602 (2011).
[36] Chen, P. et al. Tailoring the magnetic exchange interaction in MnBi2Te4 superlattices via the intercalation of ferromagnetic layers. Nature Electronics 6, 18–27 (2023).
[37] Gao, Y., Liu, K. & Lu, Z.-Y. Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials MnX2B2T6. Physical Review Research 4, 023030 (2022).
[38] Qian, T. et al. Magnetic dilution effect and topological phase transitions in
Mn1−xPbxBi2Te4. Physical Review B 106, 045121 (2022).