新型拓扑相及自旋动量锁定效应的对称性设计

对称性的研究一直是物理学中的重要方向。在本文中，我们通过对凝聚态物理中重要问题进行对称性分析，从而给出对称性逆向设计方案，以寻找承载这些物理效应的材料载体。结合第一性原理计算验证材料的物理性质，我们能够根据对称性设计筛选出合适的材料载体。

首先，我们介绍了对称性在物理学中的广泛应用，以及逆向设计的研究思想。另外，还讨论了当前凝聚态物理中的重要方向——电子能带拓扑和自旋电子学领域的研究背景和重要的概念。逆向设计不同于常规从材料出发研究物理性质的方法，而是通过物理性质给出设计原则，从而发掘承载材料的新型研究思路。因此，逆向设计的思想在对称性的研究当中非常适用，因为对称性本身对材料的物性具有强大的先验性能力。接下来，我们详细介绍了电子能带拓扑和自旋电子学的背景，特别关注对称性在这些领域的研究中所起到的作用。

基于对电子能带拓扑和自旋电子学领域的研究背景分析，我们发现在这些领域存在一些值得研究的问题，并在后文中详细介绍了我们对这些问题的具体研究成果。包括反铁磁陈绝缘体、阻塞原子绝缘体表面重构以及自旋动量锁定的通用对称性理论三个方面。在反铁磁陈绝缘体的研究中，我们首先从理论上分析了其对称性需求以说明其可实现性。然后通过推导出的完整对称性设计方案并结合第一性原理计算，提供了具体的材料示例。最后，我们研究了反铁磁陈绝缘体与传统铁磁陈绝缘体之间的差异，包括面外磁矩倾斜对陈数的调控和贝里曲率在倒空间中的分布等。

在阻塞原子绝缘体的研究中，我们首先介绍了提出该概念的背景。之后，针对实验中能够生长的阻塞原子绝缘体SrIn2P2，我们通过第一性原理计算的方法展示了其作为阻塞原子绝缘体的特殊性质，包括实空间中远离真实原子位置的局域电荷分布和在分割局域电荷的截断面上出现的阻塞表面态等。接着，我们讨论了阻塞原子绝缘体中难以避免的表面重构现象。表面重构会导致阻塞表面态的劈裂，进而引其阻塞原子绝缘体体边对应和表面重构对称性破缺之间的竞争。我们的第一性原理计算结果和相应的实验结果也能很好的契合。

最后，我们将这种对称性理论框架延伸到自旋电子学领域，通过对自旋电子学中重要基础——自旋动量锁定的研究建立起了其和完整对称性要素（原子轨道，原子位点，𝑘 点小群）之间的联系。在这个自旋动量锁定的通用对称性理论框架下，我们通过对称性约束的𝑘 ⋅ 𝑝 哈密顿量中引起自旋劈裂的𝑘 多项式阶数对所有磁点群进行了分类。进一步，我们找到了许多新颖的自旋纹理类型，包括二次型自旋纹理、反铁磁中Zeeman 型自旋劈裂、磁序引起的高阶自旋纹理、轨道依赖的自旋纹理、自旋动量位点锁定效应等。

[1] NOETHER E. Invariante variationsprobleme[J]. Nachrichten von der Gesellschaft der Wissenschaftenzu Göttingen, mathematisch-physikalische Klasse, 1918, 1918: 235-257.
[2] ANDERSON P W. More Is Different: Broken symmetry and the nature of the hierarchical structure of science.[J]. Science, 1972, 177(4047): 393-396.
[3] GEIM A K. Graphene: status and prospects[J]. Science, 2009, 324(5934): 1530-1534.
[4] TIWARI S K, SAHOO S, WANG N, et al. Graphene research and their outputs: Status and prospect[J]. Journal of Science: Advanced Materials and Devices, 2020, 5(1): 10-29.
[5] YU W, SISI L, HAIYAN Y, et al. Progress in the functional modification of graphene/graphene oxide: A review[J]. RSC Advances, 2020, 10(26): 15328-15345.
[6] OLABI A G, ABDELKAREEM M A, WILBERFORCE T, et al. Application of graphene in energy storage device–A review[J]. Renewable and Sustainable Energy Reviews, 2021, 135: 110026.
[7] DENG Y, YU Y, SHI M Z, et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4[J]. Science, 2020, 367(6480): 895-900.
[8] OTROKOV M M, KLIMOVSKIKH I I, BENTMANN H, et al. Prediction and observation of an antiferromagnetic topological insulator[J]. Nature, 2019, 576(7787): 416-422.
[9] LI J, LI Y, DU S, et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials[J]. Science Advances, 2019, 5(6): eaaw5685.
[10] WU X, LI J, MA X M, et al. Distinct topological surface states on the two terminations of MnBi4Te7[J]. Physical Review X, 2020, 10: 031013.
[11] WANG N, KAPLAN D, ZHANG Z, et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet[J]. Nature, 2023, 621(7979): 487-492.
[12] LIU C, WANG Y, LI H, et al. Robust axion insulator and Chern insulator phases in a twodimensional antiferromagnetic topological insulator[J]. Nature Materials, 2020, 19(5): 522-527.
[13] HU C, GORDON K N, LIU P, et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling[J]. Nature Communications, 2020, 11(1): 97.
[14] ZUNGER A. Inverse design in search of materials with target functionalities[J]. Nature Reviews Chemistry, 2018, 2(4): 0121.
[15] KLITZING K V, DORDA G, PEPPER M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance[J]. Physical Review Letters, 1980, 45(6): 494.
[16] HALDANE F D M. Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the” parity anomaly”[J]. Physical Review Letters, 1988, 61(18): 2015.
[17] KANE C L, MELE E J. Quantum spin Hall effect in graphene[J]. Physical Review Letters, 2005, 95(22): 226801.
[18] KANE C L, MELE E J. Z2 topological order and the quantum spin Hall effect[J]. Physical Review Letters, 2005, 95(14): 146802.
[19] CHANG C Z, ZHANG J, FENG X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator[J]. Science, 2013, 340(6129): 167-170.
[20] CHANG C Z, LIU C X, MACDONALD A H. Colloquium: Quantum anomalous hall effect[J]. Reviews of Modern Physics, 2023, 95(1): 011002.
[21] LIU C X, QI X L, DAI X, et al. Quantum anomalous Hall effect in Hg1−𝑦Mn𝑦Te quantum wells [J]. Physical Review Letters, 2008, 101(14): 146802.
[22] LI T, JIANG S, SHEN B, et al. Quantum anomalous Hall effect from intertwined moiré bands [J]. Nature, 2021, 600(7890): 641-646.
[23] FU L, KANE C L. Topological insulators with inversion symmetry[J]. Physical Review B, 2007, 76(4): 045302.
[24] PO H C, VISHWANATH A, WATANABE H. Symmetry-based indicators of band topology in the 230 space groups[J]. Nature Communications, 2017, 8(1): 50.
[25] BRADLYN B, ELCORO L, CANO J, et al. Topological quantum chemistry[J]. Nature, 2017, 547(7663): 298-305.
[26] SONG Z, ZHANG T, FANG Z, et al. Quantitative mappings between symmetry and topology in solids[J]. Nature Communications, 2018, 9(1): 3530.
[27] WATANABE H, PO H C, VISHWANATH A. Structure and topology of band structures in the 1651 magnetic space groups[J]. Science Advances, 2018, 4(8): eaat8685.
[28] ELCORO L, WIEDER B J, SONG Z, et al. Magnetic topological quantum chemistry[J]. Nature Communications, 2021, 12(1): 5965.
[29] ZHANG T, JIANG Y, SONG Z, et al. Catalogue of topological electronic materials[J]. Nature, 2019, 566(7745): 475-479.
[30] TANG F, PO H C, VISHWANATH A, et al. Comprehensive search for topological materials using symmetry indicators[J]. Nature, 2019, 566(7745): 486-489.
[31] XU Y, ELCORO L, SONG Z D, et al. High-throughput calculations of magnetic topological materials[J]. Nature, 2020, 586(7831): 702-707.
[32] OHNO H, CHIBA D, MATSUKURA F, et al. Electric-field control of ferromagnetism[J]. Nature, 2000, 408(6815): 944-946.
[33] CHAPPERT C, FERT A, VAN DAU F N. The emergence of spin electronics in data storage[J]. Nature Materials, 2007, 6(11): 813-823.
[34] WUNDERLICH J, PARK B G, IRVINE A C, et al. Spin Hall effect transistor[J]. Science, 2010, 330(6012): 1801-1804.
[35] WANG K L, KOU X F, UPADHYAYA P, et al. Electric-field control of spin-orbit interaction for low-power spintronics[J]. Proceedings of the Ieee, 2016, 104(10): 1974-2008
[36] DATTA S, DAS B. Electronic analog of the electro‐optic modulator[J]. Applied Physics Letters, 1990, 56(7): 665-667.
[37] KOO H C, KWON J H, EOM J, et al. Control of spin precession in a spin-injected field effect transistor[J]. Science, 2009, 325(5947): 1515-1518.
[38] GANICHEV S D. Spin-galvanic effect and spin orientation by current in non-magnetic semiconductors[J]. International Journal of Modern Physics B, 2008, 22(1-2): 1-26.
[39] SLONCZEWSKI J C. Current-driven excitation of magnetic multilayers[J]. Journal of Magnetism and Magnetic Materials, 1996, 159(1-2): L1-L7.
[40] ŠMEJKAL L, SINOVA J, JUNGWIRTH T. Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry[J]. Physical Review X, 2022, 12(3): 031042.
[41] GONZÁLEZ-HERNÁNDEZ R, ŠMEJKAL L, VỲBORNỲ K, et al. Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism[J]. Physical Review Letters, 2021, 126(12): 127701.
[42] BAI H, HAN L, FENG X, et al. Observation of spin splitting torque in a collinear antiferromagnet RuO2[J]. Physical Review Letters, 2022, 128(19): 197202.
[43] BAI H, ZHANG Y, ZHOU Y, et al. Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO2[J]. Physical Review Letters, 2023, 130(21): 216701.
[44] BOSE A, SCHREIBER N J, JAIN R, et al. Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide[J]. Nature Electronics, 2022, 5(5): 267-274.
[45] ŠMEJKAL L, HELLENES A B, GONZÁLEZ-HERNÁNDEZ R, et al. Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spinmomentum coupling[J]. Physical Review X, 2022, 12(1): 011028.
[46] TSAI H, HIGO T, KONDOU K, et al. Electrical manipulation of a topological antiferromagnetic state[J]. Nature, 2020, 580(7805): 608-613.
[47] HIGO T, KONDOU K, NOMOTO T, et al. Perpendicular full switching of chiral antiferromagnetic order by current[J]. Nature, 2022, 607(7919): 474-479.
[48] DRESSELHAUS G. Spin-Orbit Coupling Effects in Zinc Blende Structures[J]. Physical Review, 1955, 100(2): 580-586.
[49] RASHBA E I. Properties of semiconductors with an Extremum Loop .1. cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop[J]. Soviet Physics-Solid State, 1960, 2(6): 1109-1122.
[50] ISHIZAKA K, BAHRAMY M, MURAKAWA H, et al. Giant Rashba-type spin splitting in bulk BiTeI[J]. Nature Materials, 2011, 10(7): 521-526.
[51] EREMEEV S V, NECHAEV I A, KOROTEEV Y M, et al. Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides [J]. Physical Review Letters, 2012, 108(24): 246802.
[52] BAHRAMY M, ARITA R, NAGAOSA N. Origin of giant bulk Rashba splitting: Application to BiTeI[J]. Physical Review B, 2011, 84(4): 041202.
[53] LIEBMANN M, RINALDI C, DI SANTE D, et al. Giant Rashba-type spin splitting in ferroelectric GeTe (111)[J]. Advanced Materials, 2016, 28(3): 560-565.
[54] DI SANTE D, BARONE P, BERTACCO R, et al. Electric control of the giant Rashba effect in bulk GeTe[J]. Advanced Materials (Deerfield Beach, Fla.), 2012, 25(4): 509-513.
[55] ACOSTA C M, YUAN L D, DALPIAN G M, et al. Different shapes of spin textures as a journey through the Brillouin zone[J]. Physical Review B, 2021, 104(10): 104408.
[56] ZHANG X W, LIU Q H, LUO J W, et al. polarization in inversion-symmetric bulk crystals[J]. Nature Physics, 2014, 10(5): 387-393.
[57] LIU Q H, GUO Y Z, FREEMAN A J. Tunable Rashba effect in two-dimensional LaOBiS2 films: ultrathin candidates for spin field effect transistors[J]. Nano Letters, 2013, 13(11): 5264-5270.
[58] ŽELEZNỲ J, GAO H, VỲBORNỲ K, et al. Relativistic Néel-order fields induced by electrical current in antiferromagnets[J]. Physical Review Letters, 2014, 113(15): 157201.
[59] WADLEY P, HOWELLS B, ŽELEZNý J, et al. Electrical switching of an antiferromagnet[J]. Science, 2016, 351(6273): 587-590.
[60] ZHANG K, ZHAO S X, HAO Z Y, et al. Observation of spin-momentum-layer locking in a centrosymmetric crystal[J]. Physical Review Letters, 2021, 127(12): 126402.
[61] CHEN W Z, GU M Q, LI J Y, et al. Role of Hidden Spin Polarization in Nonreciprocal Transport of Antiferromagnets[J]. Physical Review Letters, 2022, 129(27): 276601.
[62] LI Y L, LUDWIG J, LOW T, et al. Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2[J]. Physical Review Letters, 2014, 113(26): 266804.
[63] MERA ACOSTA C, FAZZIO A, DALPIAN G M. Zeeman-type spin splitting in nonmagnetic three-dimensional compounds[J]. npj Quantum Materials, 2019, 4(1): 41.
[64] ZHAO H J, NAKAMURA H, ARRAS R, et al. Purely cubic spin splittings with persistent spin textures[J]. Physical Review Letters, 2020, 125(21): 216405.
[65] BRADLEY C, CRACKNELL A. The mathematical theory of symmetry in solids: representation theory for point groups and space groups[M]. Oxford University Press, 2010.
[66] EVARESTOV R A, SMIRNOV V P. Site symmetry in crystals: theory and applications: Vol. 108[M]. Springer Science & Business Media, 2012.
[67] CRACKNELL A P. Corepresentations of magnetic point groups[J]. Progress of Theoretical Physics, 1966, 35(2): 196-213.
[68] XIAO Z, ZHAO J, LI Y, et al. Spin space groups: full classification and applications[A]. 2023, arXiv:2307.10364.
[69] REN J, CHEN X, ZHU Y, et al. Enumeration and representation of spin space groups[A]. 2023, arXiv:2307.10369.
[70] JIANG Y, SONG Z, ZHU T, et al. Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders[A]. 2023, arXiv:2307.10371.
[71] DRESSELHAUS M S, DRESSELHAUS G, JORIO A. Group theory: application to the physics of condensed matter[M]. Springer Science & Business Media, 2007.
[72] BORN M, OPPENHEIMER R. Zur Quantentheorie der Molekeln Annalen der Physik, v. 84 [Z]. 1927.
[73] HOHENBERG P, KOHN W. Inhomogeneous electron gas[J]. Physical Review, 1964, 136(3B): B864.
[74] KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects[J]. Physical Review, 1965, 140(4A): A1133.
[75] THOMAS L H. The calculation of atomic fields[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1927, 23(5): 542–548.
[76] FERMI E. Un metodo statistico per la determinazione di alcune priorieta dell’atome[J]. Rend. Accad. Naz. Lincei, 1927, 6(602-607): 32.
[77] CEPERLEY D M, ALDER B J. Ground state of the electron gas by a stochastic method[J]. Physical Review Letters, 1980, 45(7): 566.
[78] PERDEW J P, ZUNGER A. Self-interaction correction to density-functional approximations for many-electron systems[J]. Physical Review B, 1981, 23(10): 5048.
[79] HEDIN L, LUNDQVIST B I. Explicit local exchange-correlation potentials[J]. Journal of Physics C: Solid State Physics, 1971, 4(14): 2064.
[80] PERDEW J P, WANG Y. Accurate and simple analytic representation of the electron-gas correlation energy[J]. Physical Review B, 1992, 45(23): 13244.
[81] PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996, 77(18): 3865.
[82] PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)][J]. Physical Review Letters, 1997, 78: 1396-1396.
[83] NAGAOSA N, SINOVA J, ONODA S, et al. Anomalous hall effect[J]. Reviews of Modern Physics, 2010, 82(2): 1539.
[84] LIU C X, ZHANG S C, QI X L. The quantum anomalous Hall effect: theory and experiment [J]. Annual Review of Condensed Matter Physics, 2016, 7: 301-321.
[85] SERLIN M, TSCHIRHART C, POLSHYN H, et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure[J]. Science, 2020, 367(6480): 900-903.
[86] JUNGWIRTH T, MARTI X, WADLEY P, et al. Antiferromagnetic spintronics[J]. Nature Nanotechnology, 2016, 11(3): 231-241.
[87] ŽELEZNỲ J, WADLEY P, OLEJNÍK K, et al. Spin transport and spin torque in antiferromagnetic devices[J]. Nature Physics, 2018, 14(3): 220-228.
[88] HAYAMI S, YANAGI Y, KUSUNOSE H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering[J]. Journal of the Physical Society of Japan, 2019, 88(12): 123702.
[89] YUAN L D, WANG Z, LUO J W, et al. Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets[J]. Physical Review B, 2020, 102(1): 014422.
[90] CHEN H, NIU Q, MACDONALD A H. Anomalous Hall effect arising from noncollinear antiferromagnetism[J]. Physical Review Letters, 2014, 112(1): 017205.
[91] ŠMEJKAL L, GONZÁLEZ-HERNÁNDEZ R, JUNGWIRTH T, et al. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets[J]. Science Advances, 2020, 6(23): eaaz8809.
[92] NÉEL L. Propriétés magnétiques des ferrites ; ferrimagnétisme et antiferromagnétisme[J]. Annales De Physique, 1948, 12(3): 137-198.
[93] COEY J M. Magnetism and magnetic materials[M]. Cambridge university press, 2010.
[94] MAZIN I, et al. Altermagnetism—a new punch line of fundamental magnetism[J]. Physical Review X, 2022, 12(4): 040002.
[95] FINLEY J, LIU L. Spintronics with compensated ferrimagnets[J]. Applied Physics Letters, 2020, 116(11).
[96] KIM S K, BEACH G S, LEE K J, et al. Ferrimagnetic spintronics[J]. Nature Materials, 2022, 21(1): 24-34.
[97] ZHOU P, SUN C, SUN L. Two dimensional antiferromagnetic Chern insulator: NiRuCl6[J]. Nano Letters, 2016, 16(10): 6325-6330.
[98] WANG J. Antiferromagnetic Dirac semimetals in two dimensions[J]. Physical Review B, 2017, 95(11): 115138.
[99] JIANG K, ZHOU S, DAI X, et al. Antiferromagnetic Chern insulators in noncentrosymmetric systems[J]. Physical Review Letters, 2018, 120(15): 157205.
[100] JAIN A, ONG S P, HAUTIER G, et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation[J]. Apl Materials, 2013, 1(1): 011002.
[101] LIU P F, LI J Y, HAN J Z, et al. Spin-group symmetry in magnetic materials with negligible spin-orbit coupling[J]. Physical Review X, 2022, 12(2): 021016.
[102] REN Y, ZENG J, DENG X, et al. Quantum anomalous Hall effect in atomic crystal layers from in-plane magnetization[J]. Physical Review B, 2016, 94(8): 085411.
[103] LIU Z, ZHAO G, LIU B, et al. Intrinsic quantum anomalous Hall effect with in-plane magnetization: searching rule and material prediction[J]. Physical Review Letters, 2018, 121(24): 246401.
[104] GEORGIOU T, JALIL R, BELLE B D, et al. Vertical field-effect transistor based on graphene–WS2 heterostructures for flexible and transparent electronics[J]. Nature Nanotechnology, 2013, 8(2): 100-103.
[105] LEE G H, YU Y J, CUI X, et al. Flexible and transparent MoS2 field-effect transistors on hexagonal boron nitride-graphene heterostructures[J]. ACS Nano, 2013, 7(9): 7931-7936.
[106] KOSKINEN P, FAMPIOU I, RAMASUBRAMANIAM A. Density-functional tight-binding simulations of curvature-controlled layer decoupling and band-gap tuning in bilayer MoS2[J]. Physical Review Letters, 2014, 112(18): 186802.
[107] KRESSE G, FURTHMÜLLER J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Physical review B, 1996, 54(16): 11169.
[108] KRESSE G, JOUBERT D. From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Physical Review B, 1999, 59(3): 1758.
[109] MOSTOFI A A, YATES J R, LEE Y S, et al. Wannier90: A tool for obtaining maximallylocalised Wannier functions[J]. Computer Physics Communications, 2008, 178(9): 685-699.
[110] MARZARI N, MOSTOFI A A, YATES J R, et al. Maximally localized Wannier functions: Theory and applications[J]. Reviews of Modern Physics, 2012, 84(4): 1419.
[111] WU Q, ZHANG S, SONG H F, et al. WannierTools: An open-source software package for novel topological materials[J]. Computer Physics Communications, 2018, 224: 405-416.
[112] THOULESS D J, KOHMOTO M, NIGHTINGALE M P, et al. Quantized Hall conductance in a two-dimensional periodic potential[J]. Physical Review Letters, 1982, 49(6): 405.
[113] XIAO D, CHANG M C, NIU Q. Berry phase effects on electronic properties[J]. Reviews ofModern Physics, 2010, 82(3): 1959.
[114] BIANCO R, RESTA R. Mapping topological order in coordinate space[J]. Physical Review B,2011, 84(24): 241106.
[115] CAIO M D, MÖLLER G, COOPER N R, et al. Topological marker currents in Chern insulators[J]. Nature Physics, 2019, 15(3): 257-261.
[116] ZAK J. Band representations of space-groups[J]. Physical Review B, 1982, 26(6): 3010-3023.
[117] XU Y, ELCORO L, LI G, et al. Three-dimensional real space invariants, obstructed atomicinsulators and a new principle for active catalytic sites[A]. 2021, arXiv:2111.02433.
[118] XU Y, ELCORO L, SONG Z D, et al. Filling-enforced obstructed atomic insulators[A]. 2021,arXiv:2106.10276.
[119] SONG Z, FANG Z, FANG C. (d-2)-dimensional edge states of rotation symmetry protectedtopological states[J]. Physical Review Letters, 2017, 119(24): 246402.
[120] WU H, WANG Y, XU Y, et al. The field-free Josephson diode in a van der Waals heterostructure[J]. Nature, 2022, 604(7907): 653-656.
[121] LI G, XU Y, SONG Z, et al. Obstructed surface states as the descriptor for predicting catalyticactive sites in inorganic crystalline materials[J]. Advanced Materials, 2022, 34(26): 2201328.
[122] JUNG J H, PARK C H, IHM J. A rigorous method of calculating exfoliation energies from firstprinciples[J]. Nano Letters, 2018, 18(5): 2759-2765.
[123] YUAN L D, WANG Z, LUO J W, et al. Giant momentum-dependent spin splitting in centrosymmetriclow-Z antiferromagnets[J]. Physical Review B, 2020, 102(1): 014422.
[124] YUAN L D, WANG Z, LUO J W, et al. Prediction of low-Z collinear and noncollinear antiferromagneticcompounds having momentum-dependent spin splitting even without spin-orbitcoupling[J]. Physical Review Materials, 2021, 5(1): 014409.
[125] ZHU Y P, CHEN X, LIU X R, et al. Observation of plaid-like spin splitting in a noncoplanarantiferromagnet[J]. Nature, 2024, 626(7999): 523-528.
[126] ROLAND W. Spin-orbit coupling effects in two-dimensional electron and hole systems[J].Springer Tracts in Modern Physiscs: Springer, Berlin, Heidelberg, 2003, 191.
[127] EDELSTEIN V M. Spin polarization of conduction electrons induced by electric current intwo-dimensional asymmetric electron systems[J]. Solid State Communications, 1990, 73(3):233-235.99参考文献
[128] MURAKAMI S, NAGAOSA N, ZHANG S C. Dissipationless quantum spin current at roomtemperature[J]. Science, 2003, 301(5638): 1348-1351.
[129] WUNDERLICH J, KAESTNER B, SINOVA J, et al. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system[J]. Physical ReviewLetters, 2005, 94(4): 047204.
[130] BERNEVIG B A, VAFEK O. Piezo-magnetoelectric effects in p-doped semiconductors[J].Physical Review B, 2005, 72(3): 033203.
[131] MANCHON A, ZHANG S. Theory of nonequilibrium intrinsic spin torque in a single nanomagnet[J]. Physical Review B, 2008, 78(21): 212405.
[132] MIRON I M, GARELLO K, GAUDIN G, et al. Perpendicular switching of a single ferromagneticlayer induced by in-plane current injection[J]. Nature, 2011, 476(7359): 189-U88.
[133] ISHIZAKA K, BAHRAMY M S, MURAKAWA H, et al. Giant Rashba-type spin splitting inbulk BiTeI[J]. Nature Materials, 2011, 10(7): 521-526.
[134] BERNEVIG B A, ORENSTEIN J, ZHANG S C. Exact SU(2) symmetry and persistent spinhelix in a spin-orbit coupled system[J]. Physical Review Letters, 2006, 97(23): 236601.
[135] KORALEK J D, WEBER C P, ORENSTEIN J, et al. Emergence of the persistent spin helix insemiconductor quantum wells[J]. Nature, 2009, 458(7238): 610-613.
[136] TAO L, TSYMBAL E Y. Persistent spin texture enforced by symmetry[J]. Nature Communications,2018, 9(1): 2763.
[137] XIAO D, LIU G B, FENG W X, et al. Coupled spin and valley physics in monolayers of MoS2and other group-VI dichalcogenides[J]. Physical Review Letters, 2012, 108(19): 196802.
[138] ZHANG H J, LIU C X, ZHANG S C. Spin-orbital texture in topological insulators[J]. PhysicalReview Letters, 2013, 111(6): 066801.
[139] ZHAO H J, LIU X R, WANG Y C, et al. Zeeman effect in centrosymmetric antiferromagneticsemiconductors controlled by an electric field[J]. Physical Review Letters, 2022, 129(18): 187602.
[140] LIN M, ROBREDO I, SCHRöETER N B M, et al. Spin-momentum locking from topologicalquantum chemistry: Applications to multifold fermions[J]. Physical Review B, 2022, 106(24):245101.
[141] CAO T, WANG G, HAN W, et al. Valley-selective circular dichroism of monolayer molybdenumdisulphide[J]. Nature Communications, 2012, 3(1): 887.
[142] MAK K F, HE K L, SHAN J, et al. Control of valley polarization in monolayer MoS2 by opticalhelicity[J]. Nature Nanotechnology, 2012, 7(8): 494-498.
[143] ZENG H L, DAI J F, YAO W, et al. Valley polarization in MoS2 monolayers by optical pumping[J]. Nature Nanotechnology, 2012, 7(8): 490-493.
[144] CAO Y, WAUGH J A, ZHANG X W, et al. Mapping the orbital wavefunction of the surfacestates in three-dimensional topological insulators[J]. Nature Physics, 2013, 9(8): 499-504.
[145] CANO J, BRADLYN B, WANG Z J, et al. Building blocks of topological quantum chemistry:Elementary band representations[J]. Physical Review B, 2018, 97(3): 035139.100参考文献
[146] LUTTINGER J M. Quantum theory of cyclotron resonance in semiconductors: General theory[J]. Physical Review, 1956, 102(4): 1030.
[147] PARK S R, HAN J, KIM C, et al. Chiral orbital-angular momentum in the surface states ofBi2Se3[J]. Physical Review Letters, 2012, 108(4): 046805.
[148] ZHU Z H, VEENSTRA C N, LEVY G, et al. Layer-by-layer entangled spin-orbital texture ofthe topological surface state in Bi2Se3[J]. Physical Review Letters, 2013, 110(21): 216401.
[149] BERRY M V. Quantal Phase Factors Accompanying Adiabatic Changes[J]. Proceedings ofthe Royal Society of London Series a-Mathematical and Physical Sciences, 1984, 392(1802):45-57.
[150] XIAO D, CHANG M C, NIU Q. Berry phase effects on electronic properties[J]. Reviews ofModern Physics, 2010, 82(3): 1959-2007.
[151] ŠMEJKAL L, SINOVA J, JUNGWIRTH T. Beyond conventional ferromagnetism and antiferromagnetism:a phase with nonrelativistic spin and crystal rotation symmetry[J]. PhysicalReview X, 2022, 12(3): 031042.
[152] LITVIN D B. Spin point groups[J]. Acta Crystallographica Section A: Crystal Physics, Diffraction,Theoretical and General Crystallography, 1977, 33(2): 279-287.
[153] GALLEGO S V, PEREZ-MATO J M, ELCORO L, et al. MAGNDATA: towards a database ofmagnetic structures. I. The commensurate case[J]. Journal of Applied Crystallography, 2016,49(5): 1750-1776.
[154] GALLEGO S V, PEREZ-MATO J M, ELCORO L, et al. MAGNDATA: towards a databaseof magnetic structures. II. The incommensurate case[J]. Journal of Applied Crystallography,2016, 49(6): 1941-1956.
[155] HAYAMI S, KUSUNOSE H. Spin-orbital-momentum locking under odd-parity magneticquadrupole ordering[J]. Physical Review B, 2021, 104(4): 045117.
[156] YAO W, WANG E, HUANG H, et al. Direct observation of spin-layer locking by local Rashbaeffect in monolayer semiconducting PtSe2 film[J]. Nature Communications, 2017, 8(1): 14216.101