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SCIENTIA SINICA Technologica, Volume 49 , Issue 10 : 1133-1147(2019) https://doi.org/10.1360/SST-2019-0055

Strain effects on novel quantum materials

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  • ReceivedFeb 14, 2019
  • AcceptedMay 21, 2019
  • PublishedOct 8, 2019

Abstract

Novel quantum materials have been one of the most important topics in condensed matter physics due to their unique physical properties and potential applications. Many effective methods, especially for strain, have been developed to tune the properties of solid state materials. This paper systematically reviews several novel quantum materials discovered in recent years with a focus on their strain effects. Firstly, we introduce strain-induced topological phase transitions in topological materials. Secondly, we discuss the effects on electron transport in monolayer MoS2 and superconductivity in phosphorene. Finally, we analyze the tunable magnetic moment or spontaneous electrical polarization in two-dimensional ferromagnetic or ferroelectric materials.


Funded by

国家自然科学基金(11734003,11574029)

国家重点研发计划(2016YFA0300600,2017YFB0701600)

中国科学院战略先导科技专项(B类)


References

[1] Kane C L, Mele E J. Quantum spin Hall effect in graphene. Phys Rev Lett, 2005, 95: 226801 CrossRef PubMed ADS Google Scholar

[2] Bernevig B A, Hughes T L, Zhang S C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 2006, 314: 1757-1761 CrossRef PubMed ADS Google Scholar

[3] König M, Wiedmann S, Brune C, et al. Quantum spin Hall insulator state in HgTe quantum wells. Science, 2007, 318: 766-770 CrossRef PubMed ADS arXiv Google Scholar

[4] Knez I, Du R R, Sullivan G. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys Rev Lett, 2011, 107: 136603 CrossRef PubMed ADS arXiv Google Scholar

[5] Hasan M Z, Kane C L. Colloquium: Topological insulators. Rev Mod Phys, 2010, 82: 3045-3067 CrossRef ADS arXiv Google Scholar

[6] Qi X L, Zhang S C. Topological insulators and superconductors. Rev Mod Phys, 2011, 83: 1057-1110 CrossRef ADS arXiv Google Scholar

[7] Wan X G, Turner A M, Vishwanath A, et al. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys Rev B, 2011, 83: 205101 CrossRef ADS arXiv Google Scholar

[8] Wang Z J, Sun Y, Chen X Q, et al. Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb). Phys Rev B, 2012, 85: 195320 CrossRef ADS Google Scholar

[9] Wang Z J, Weng H M, Wu Q S, et al. Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys Rev B, 2013, 88: 125427 CrossRef ADS arXiv Google Scholar

[10] Liu Z K, Zhou B, Zhang Y, et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science, 2014, 343: 864-867 CrossRef PubMed ADS arXiv Google Scholar

[11] Liu Z K, Jiang J, Zhou B, et al. A stable three-dimensional topological Dirac semimetal Cd3As2. Nat Mater, 2014, 13: 677-681 CrossRef PubMed ADS Google Scholar

[12] Weng H, Fang C, Fang Z, et al. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys Rev X, 2015, 5: 011029 CrossRef ADS arXiv Google Scholar

[13] Lv B Q, Weng H M, Fu B B, et al. Experimental discovery of Weyl semimetal TaAs. Phys Rev X, 2015, 5: 031013 CrossRef ADS arXiv Google Scholar

[14] Huang S M, Xu S Y, Belopolski I, et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat Commun, 2015, 6: 7373 CrossRef PubMed ADS Google Scholar

[15] Yang S A. Dirac and Weyl materials: Fundamental aspects and some spintronics applications. SPIN, 2016, 06: 1640003 CrossRef ADS arXiv Google Scholar

[16] Feng B J, Fu B T, Kasamatsu S, et al. Experimental realization of two-dimensional Dirac nodal line fermions in monolayer Cu2Si. Nat Commun, 2017, 8: 1007 CrossRef PubMed ADS arXiv Google Scholar

[17] Li S, Yu Z M, Liu Y, et al. Type-II nodal loops: Theory and material realization. Phys Rev B, 2017, 96: 081106 CrossRef ADS arXiv Google Scholar

[18] Weng H M, Liang Y Y, Xu Q N, et al. Topological node-line semimetal in three-dimensional graphene networks. Phys Rev B, 2015, 92: 045108 CrossRef ADS arXiv Google Scholar

[19] Chen Y P, Xie Y, Yang S A, et al. Nanostructured carbon allotropes with Weyl-like loops and points. Nano Lett, 2015, 15: 6974-6978 CrossRef PubMed ADS Google Scholar

[20] Xie L S, Schoop L M, Seibel E M, et al. A new form of Ca3P2 with a ring of Dirac nodes. APL Mater, 2015, 3: 083602 CrossRef ADS Google Scholar

[21] Du Y P, Tang F, Wang D, et al. CaTe: A new topological node-line and Dirac semimetal. npj Quant Mater, 2017, 2: 3 CrossRef ADS arXiv Google Scholar

[22] Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666-669 CrossRef PubMed ADS Google Scholar

[23] Novoselov K S, Jiang D, Schedin F, et al. Two-dimensional atomic crystals. Proc Natl Acad Sci USA, 2005, 102: 10451-10453 CrossRef PubMed ADS Google Scholar

[24] Wang Q H, Kalantar-Zadeh K, Kis A, et al. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotech, 2012, 7: 699-712 CrossRef PubMed ADS Google Scholar

[25] Butler S Z, Hollen S M, Cao L, et al. Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano, 2013, 7: 2898-2926 CrossRef PubMed Google Scholar

[26] Xu M S, Liang T, Shi M M, et al. Graphene-like two-dimensional materials. Chem Rev, 2013, 113: 3766-3798 CrossRef PubMed Google Scholar

[27] Watanabe K, Taniguchi T, Kanda H. Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal. Nat Mater, 2004, 3: 404-409 CrossRef PubMed ADS Google Scholar

[28] Mak K F, Lee C, Hone J, et al. Atomically thin MoS2: A new direct-gap semiconductor. Phys Rev Lett, 2010, 105: 136805 CrossRef PubMed ADS arXiv Google Scholar

[29] Koenig S P, Doganov R A, Schmidt H, et al. Electric field effect in ultrathin black phosphorus. Appl Phys Lett, 2014, 104: 103106 CrossRef ADS arXiv Google Scholar

[30] Shi Y, Hamsen C, Jia X, et al. Synthesis of few-layer hexagonal boron nitride thin film by chemical vapor deposition. Nano Lett, 2010, 10: 4134-4139 CrossRef PubMed ADS Google Scholar

[31] Lee Y H, Zhang X Q, Zhang W, et al. Synthesis of large-area MoS2 atomic layers with chemical vapor deposition. Adv Mater, 2012, 24: 2320-2325 CrossRef PubMed Google Scholar

[32] Castellanos-Gomez A, Barkelid M, Goossens A M, et al. Laser-thinning of MoS2: On demand generation of a single-layer semiconductor. Nano Lett, 2012, 12: 3187-3192 CrossRef PubMed ADS arXiv Google Scholar

[33] Chang K, Liu J, Lin H, et al. Discovery of robust in-plane ferroelectricity in atomic-thick SnTe. Science, 2016, 353: 274-278 CrossRef PubMed ADS Google Scholar

[34] Huang B, Clark G, Navarro-Moratalla E, et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 2017, 546: 270-273 CrossRef PubMed ADS arXiv Google Scholar

[35] Jiang L, Chawla N. Mechanical properties of Cu6Sn5 intermetallic by micropillar compression testing. Scripta Mater, 2010, 63: 480-483 CrossRef Google Scholar

[36] Hÿtch M, Houdellier F, Hüe F, et al. Nanoscale holographic interferometry for strain measurements in electronic devices. Nature, 2008, 453: 1086-1089 CrossRef PubMed ADS Google Scholar

[37] Cortijo A, Ferreirós Y, Landsteiner K, et al. Elastic gauge fields in Weyl semimetals. Phys Rev Lett, 2015, 115: 177202 CrossRef PubMed ADS arXiv Google Scholar

[38] Kim K S, Zhao Y, Jang H, et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature, 2009, 457: 706-710 CrossRef PubMed ADS Google Scholar

[39] Bertolazzi S, Brivio J, Kis A. Stretching and breaking of ultrathin MoS2. ACS Nano, 2011, 5: 9703-9709 CrossRef PubMed Google Scholar

[40] Castellanos-Gomez A, Poot M, Steele G A, et al. Mechanical properties of freely suspended semiconducting graphene-like layers based on MoS2. Nanoscale Res Lett, 2012, 7: 233 CrossRef PubMed ADS Google Scholar

[41] Wei Q, Peng X. Superior mechanical flexibility of phosphorene and few-layer black phosphorus. Appl Phys Lett, 2014, 104: 251915 CrossRef ADS arXiv Google Scholar

[42] Peng H L, Lai K, Kong D, et al. Aharonov-Bohm interference in topological insulator nanoribbons. Nat Mater, 2010, 9: 225-229 CrossRef PubMed ADS arXiv Google Scholar

[43] Yao Y G, Ye F, Qi X L, et al. Spin-orbit gap of graphene: First-principles calculations. Phys Rev B, 2007, 75: 041401 CrossRef ADS Google Scholar

[44] Liu C C, Feng W X, Yao Y G. Quantum spin Hall effect in silicene and two-dimensional germanium. Phys Rev Lett, 2011, 107: 076802 CrossRef PubMed ADS arXiv Google Scholar

[45] Liu C C, Jiang H, Yao Y G. Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys Rev B, 2011, 84: 195430 CrossRef ADS arXiv Google Scholar

[46] Xu Y, Yan B H, Zhang H J, et al. Large-gap quantum spin Hall insulators in tin films. Phys Rev Lett, 2013, 111: 136804 CrossRef PubMed ADS arXiv Google Scholar

[47] Qian X F, Liu J W, Fu L, et al. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science, 2014, 346: 1344-1347 CrossRef PubMed ADS Google Scholar

[48] Weng H, Dai X, Fang Z. Transition-metal pentatelluride ZrTe5 and HfTe5: A paradigm for large-gap quantum spin hall insulators. Phys Rev X, 2014, 4: 011002 CrossRef ADS arXiv Google Scholar

[49] Zhou J J, Feng W X, Liu C C, et al. Large-gap quantum spin Hall insulator in single layer bismuth monobromide Bi4Br4. Nano Lett, 2014, 14: 4767-4771 CrossRef PubMed ADS arXiv Google Scholar

[50] Song Z, Liu C C, Yang J, et al. Quantum spin Hall insulators and quantum valley Hall insulators of BiX/SbX (X=H, F, Cl and Br) monolayers with a record bulk band gap. NPG Asia Mater, 2014, 6: e147 CrossRef Google Scholar

[51] Liu C C, Guan S, Song Z, et al. Low-energy effective Hamiltonian for giant-gap quantum spin Hall insulators in honeycomb X-hydride/halide (X=N--Bi) monolayers. Phys Rev B, 2014, 90: 085431 CrossRef ADS arXiv Google Scholar

[52] Li X R, Zhang Z Y, Yao Y G, et al. High throughput screening for two-dimensional topological insulators. 2D Mater, 2018, 5: 045023 CrossRef ADS Google Scholar

[53] Volovik G E. The Universe in a Helium Droplet. Oxford: Oxford University Press, 2003. Google Scholar

[54] Horava P. Stability of Fermi surfaces and K theory. Phys Rev Lett, 2005, 95: 016405 CrossRef PubMed ADS Google Scholar

[55] Nielsen H B, Ninomiya M. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys Lett B, 1983, 130: 389-396 CrossRef ADS Google Scholar

[56] Son D T, Yamamoto N. Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids. Phys Rev Lett, 2012, 109: 181602 CrossRef PubMed ADS arXiv Google Scholar

[57] Liu C C, Zhou J J, Yao Y, et al. Weak topological insulators and composite Weyl semimetals: β-Bi4X4 (X=Br, I).. Phys Rev Lett, 2016, 116: 066801 CrossRef PubMed ADS arXiv Google Scholar

[58] Autès G, Isaeva A, Moreschini L, et al. A novel quasi-one-dimensional topological insulator in bismuth iodide β-Bi4I4. Nat Mater, 2016, 15: 154-158 CrossRef PubMed ADS arXiv Google Scholar

[59] Qi Y, Shi W, Werner P, et al. Pressure-induced superconductivity and topological quantum phase transitions in a quasi-one-dimensional topological insulator: Bi4I4. npj Quant Mater, 2018, 3: 4 CrossRef ADS arXiv Google Scholar

[60] Noguchi R, Takahashi T, Kuroda K, et al. A weak topological insulator state in quasi-one-dimensional bismuth iodide. Nature, 2019, 566: 518-522 CrossRef PubMed Google Scholar

[61] Guan S, Yu Z M, Liu Y, et al. Artificial gravity field, astrophysical analogues, and topological phase transitions in strained topological semimetals. npj Quant Mater, 2017, 2: 23 CrossRef ADS arXiv Google Scholar

[62] Cheng T P. Relativity, Gravitation and Cosmology. New York: Oxford University Press, 2010. Google Scholar

[63] He L P, Jia Y T, Zhang S J, et al. Pressure-induced superconductivity in the three-dimensional topological Dirac semimetal Cd3As2. npj Quant Mater, 2016, 1: 16014 CrossRef Google Scholar

[64] Chang T R, Pletikosic I, Kong T, et al. Realization of a type-II nodal-line semimetal in Mg3Bi2. Adv Sci, 2019, 6: 1800897 CrossRef PubMed Google Scholar

[65] Radisavljevic B, Radenovic A, Brivio J, et al. Single-layer MoS2 transistors. Nat Nanotech, 2011, 6: 147-150 CrossRef PubMed ADS Google Scholar

[66] Wang H, Yu L L, Lee Y H, et al. Integrated circuits based on bilayer MoS2 transistors. Nano Lett, 2012, 12: 4674-4680 CrossRef PubMed ADS arXiv Google Scholar

[67] Bao W Z, Cai X H, Kim D, et al. High mobility ambipolar MoS2 field-effect transistors: Substrate and dielectric effects. Appl Phys Lett, 2013, 102: 042104 CrossRef ADS arXiv Google Scholar

[68] Das S, Chen H Y, Penumatcha A V, et al. High performance multilayer MoS2 transistors with scandium contacts. Nano Lett, 2013, 13: 100-105 CrossRef PubMed ADS Google Scholar

[69] Ye J T, Zhang Y J, Akashi R, et al. Superconducting dome in a gate-tuned band insulator. Science, 2012, 338: 1193-1196 CrossRef PubMed ADS Google Scholar

[70] Matetskiy A V, Ichinokura S, Bondarenko L V, et al. Two-dimensional superconductor with a giant rashba effect: One-atom-layer Tl-Pb compound on Si(111). Phys Rev Lett, 2015, 115: 147003 CrossRef PubMed ADS Google Scholar

[71] Zhang H M, Sun Y, Li W, et al. Detection of a superconducting phase in a two-atom layer of hexagonal Ga film grown on semiconducting GaN(0001). Phys Rev Lett, 2015, 114: 107003 CrossRef PubMed ADS arXiv Google Scholar

[72] Kawamura H, Shirotani I, Tachikawa K. Anomalous superconductivity and pressure induced phase transitions in black phosphorus. Solid State Commun, 1985, 54: 775-778 CrossRef ADS Google Scholar

[73] Wittig J, Matthias B T. Superconducting phosphorus. Science, 1968, 160: 994-995 CrossRef PubMed ADS Google Scholar

[74] Shao D F, Lu W J, Lv H Y, et al. Electron-doped phosphorene: A potential monolayer superconductor. Europhys Lett, 2014, 108: 67004 CrossRef ADS arXiv Google Scholar

[75] Ge Y, Wan W, Feng W, et al. Effect of doping and strain modulations on electron transport in monolayer MoS2. Phys Rev B, 2014, 90: 035414 CrossRef ADS arXiv Google Scholar

[76] Li X D, Mullen J T, Jin Z H, et al. Intrinsic electrical transport properties of monolayer silicene and MoS2 from first principles. Phys Rev B, 2013, 87: 115418 CrossRef ADS arXiv Google Scholar

[77] Song Y, Dery H. Transport theory of monolayer transition-metal dichalcogenides through symmetry. Phys Rev Lett, 2013, 111: 026601 CrossRef PubMed ADS arXiv Google Scholar

[78] Chang C H, Fan X, Lin S H, et al. Orbital analysis of electronic structure and phonon dispersion in MoS2, MoSe2, WS2, and WSe2 monolayers under strain. Phys Rev B, 2013, 88: 195420 CrossRef ADS Google Scholar

[79] Ge Y, Wan W, Yang F, et al. The strain effect on superconductivity in phosphorene: A first-principles prediction. New J Phys, 2015, 17: 035008 CrossRef ADS Google Scholar

[80] Lee G H, Yu Y J, Cui X, et al. Flexible and transparent MoS2 field-effect transistors on hexagonal boron nitride-graphene heterostructures. ACS Nano, 2013, 7: 7931-7936 CrossRef PubMed Google Scholar

[81] Geim A K, Grigorieva I V. Van der Waals heterostructures. Nature, 2013, 499: 419-425 CrossRef PubMed Google Scholar

[82] Eda G, Maier S A. Two-dimensional crystals: Managing light for optoelectronics. ACS Nano, 2013, 7: 5660-5665 CrossRef PubMed Google Scholar

[83] Gong C, Li L, Li Z, et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature, 2017, 546: 265-269 CrossRef PubMed ADS arXiv Google Scholar

[84] Fei Z, Huang B, Malinowski P, et al. Two-dimensional itinerant ferromagnetism in atomically thin Fe3GeTe2. Nat Mater, 2018, 17: 778-782 CrossRef PubMed ADS arXiv Google Scholar

[85] Bonilla M, Kolekar S, Ma Y, et al. Strong room-temperature ferromagnetism in VSe2 monolayers on van der Waals substrates. Nat Nanotech, 2018, 13: 289-293 CrossRef PubMed ADS Google Scholar

[86] Feng B J, Zhang R W, Feng Y, et al. Discovery of Weyl nodal lines in a single-layer ferromagnet. Phys Rev Lett, 2019, 123: 116401. arXiv Google Scholar

[87] Liu F, You L, Seyler K L, et al. Room-temperature ferroelectricity in CuInP2S6 ultrathin flakes. Nat Commun, 2016, 7: 12357 CrossRef PubMed ADS Google Scholar

[88] Ding W, Zhu J, Wang Z, et al. Prediction of intrinsic two-dimensional ferroelectrics in In2Se3 and other III2-VI3 van der Waals materials. Nat Commun, 2017, 8: 14956 CrossRef PubMed ADS Google Scholar

[89] Zhou Y, Wu D, Zhu Y, et al. Out-of-Plane piezoelectricity and ferroelectricity in layered α-In2Se3 nanoflakes. Nano Lett, 2017, 17: 5508-5513 CrossRef PubMed ADS arXiv Google Scholar

[90] Fei Z Y, Zhao W J, Palomaki T A, et al. Ferroelectric switching of a two-dimensional metal. Nature, 2018, 560: 336-339 CrossRef PubMed ADS Google Scholar

[91] Cao T, Li Z, Louie S G. Tunable magnetism and half-metallicity in hole-doped monolayer GaSe. Phys Rev Lett, 2015, 114: 236602 CrossRef PubMed ADS arXiv Google Scholar

[92] Li Z, Xu W, Yu Y, et al. Monolayer hexagonal arsenene with tunable electronic structures and magnetic properties via impurity doping. J Mater Chem C, 2016, 4: 362-370 CrossRef Google Scholar

[93] Seixas L, Rodin A S, Carvalho A, et al. Multiferroic two-dimensional materials. Phys Rev Lett, 2016, 116: 206803 CrossRef PubMed ADS arXiv Google Scholar

[94] Gong S, Wan W H, Guan S, et al. Tunable half-metallic magnetism in an atom-thin holey two-dimensional C2N monolayer. J Mater Chem C, 2017, 5: 8424-8430 CrossRef Google Scholar

[95] Fu B T, Feng W X, Zhou X D, et al. Effects of hole doping and strain on magnetism in buckled phosphorene and arsenene. 2D Mater, 2017, 4: 025107 CrossRef ADS Google Scholar

[96] Zhou X D, Feng W X, Li F, et al. Large magneto-optical effects in hole-doped blue phosphorene and gray arsenene. Nanoscale, 2017, 9: 17405-17414 CrossRef PubMed Google Scholar

[97] Li F, Zhou X D, Feng W X, et al. Thickness-dependent magneto-optical effects in hole-doped GaS and GaSe multilayers: A first-principles study. New J Phys, 2018, 20: 043048 CrossRef ADS Google Scholar

[98] Feng W X, Guo G Y, Yao Y G. Tunable magneto-optical effects in hole-doped group-IIIA metal-monochalcogenide monolayers. 2D Mater, 2017, 4: 015017 CrossRef ADS Google Scholar

[99] Wan W H, Liu C, Xiao W D, et al. Promising ferroelectricity in 2D group IV tellurides: A first-principles study. Appl Phys Lett, 2017, 111: 132904 CrossRef ADS Google Scholar

[100] Liu C, Wan W H, Ma J, et al. Robust ferroelectricity in two-dimensional SbN and BiP. Nanoscale, 2018, 10: 7984-7990 CrossRef PubMed Google Scholar

[101] Guan S, Liu C, Lu Y H, et al. Tunable ferroelectricity and anisotropic electric transport in monolayer β-GeSe. Phys Rev B, 2018, 97: 144104 CrossRef ADS arXiv Google Scholar

[102] Li J, Shan Z W, Ma E. Elastic strain engineering for unprecedented materials properties. MRS Bull, 2018, 39: 108-114 CrossRef Google Scholar

[103] Bedell S W, Khakifirooz A, Sadana D K. Strain scaling for CMOS. MRS Bull, 2014, 39: 131-137 CrossRef Google Scholar

[104] Dai Z, Liu L, Zhang Z. Strain engineering of 2D materials: Issues and opportunities at the interface. Adv Mater, 2019, 3: 1805417 CrossRef PubMed Google Scholar

  • 图 1

    (网络版彩图)Bi4Br4的结构和带隙随应力变化图. (a) 三维Bi4Br4的晶体结构图; (b) 单层Bi4Br4结构图; (c) 沿着b轴拓展的一维分子链; (d) 单轴应力调控带隙变化图示. 图片摘自文献[49]

  • 图 2

    (网络版彩图)不同单轴应变下Na3Bi的能带图. (a) 在c方向单轴应变下的Na3Bi示意图; (b) Na3Bi的能带图; (c)~(e) Г点附近在c方向不同单轴应变下Na3Bi的能带图, 分别对应应变为0%, −3%, −7%的情况. 图片摘自文献[61]

  • 图 3

    (网络版彩图) (a) 模拟白洞视界(上半部分)和黑洞视界(下半部分)的示意图. 箭头代表准粒子在相应区域内的运动方向. (b) Na3Bi中有效折射率n随应变的变化关系. (c)和(d)是类比引力透镜效应的图示. 其中白色曲线指的是准粒子在平面内的轨迹. 颜色表示应变大小. 图片摘自文献[61]

  • 图 4

    (网络版彩图) K4P3晶体结构以及能带图. (a) K4P3的晶体结构; (b) K4P3的布里渊区; (c) K4P3的能带结构; (d) 第一性原理计算K4P3(110)面上费米面附近的两个能级之差, 颜色条代表差值的大小, 其中白色线条(差值为零)即为节线. 图片摘自文献[17]

  • 图 5

    (网络版彩图)剪切应变下节线(白色线条)的演化情况. (a) 55°夹角; (b) 65.5°夹角; (c) 67°夹角. 图片摘自文献[17]

  • 图 6

    (网络版彩图)应变调控单层MoS2中声子限制的电子输运图. 图片摘自文献[75]

  • 图 7

    (网络版彩图)应变调控单层黑磷的超导电性. 图片摘自文献[79]

  • 图 8

    (网络版彩图) (a) h2D-C2N能带和态密度图; (b) 磁矩和自旋极化能随掺杂密度变化图; (c) 电子掺杂为6×1013 cm−2时自旋分辨的态密度图. 图片摘自文献[94]

  • 图 9

    (网络版彩图) (a) 在zigzag方向施加8%应变下的C2N能带图; (b) 在不同掺杂浓度下磁矩随单轴应变变化关系图. 图片摘自文献[94]

  • 图 10

    (网络版彩图) (a) 蓝磷烯价带顶的二维能带图; (b) 态密度图; (c) 在不同掺杂浓度下磁矩随双轴应变变化关系图. 图片摘自文献[95]

  • 图 11

    (网络版彩图)单层GaS在空穴掺杂数hole=0.23下磁矩(a)和磁光克尔角(b)随双轴应变的变化关系图. 图片摘自文献[97]

  • 图 12

    (网络版彩图)应变下单层GeTe和SnTe的电极化强度PS和翻转势垒Eb的变化关系图. (a) GeTe的电极化强度PS; (b) GeTe的翻转势垒Eb; (c) SnTe的电极化强度PS; (d) SnTe的翻转势垒Eb. 图片摘自文献[99]