2D materials for quantum information science

Abstract

The transformation of digital computers from bulky machines to portable systems has been enabled by new materials and advanced processing technologies that allow ultrahigh integration of solid-state electronic switching devices. As this conventional scaling pathway has approached atomic-scale dimensions, the constituent nanomaterials (such as SiO2 gate dielectrics, poly-Si floating gates and Co–Cr–Pt ferromagnetic alloys) increasingly possess properties that are dominated by quantum physics. In parallel, quantum information science has emerged as an alternative to conventional transistor technology, promising new paradigms in computation, communication and sensing. The convergence between quantum materials properties and prototype quantum devices is especially apparent in the field of 2D materials, which offer a broad range of materials properties, high flexibility in fabrication pathways and the ability to form artificial states of quantum matter. In this Review, we discuss the quantum properties and potential of 2D materials as solid-state platforms for quantum-dot qubits, single-photon emitters, superconducting qubits and topological quantum computing elements. By focusing on the interplay between quantum physics and materials science, we identify key opportunities and challenges for the use of 2D materials in the field of quantum information science.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Graphene single-quantum-dot devices.
Fig. 2: Graphene multi-quantum-dot devices.
Fig. 3: Single-photon emitters in 2D materials.
Fig. 4: 2D superconducting qubits.
Fig. 5: Topological quantum computing.
Fig. 6: Emerging opportunities.

References

  1. 1.

    Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  Google Scholar 

  2. 2.

    Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).

    Article  Google Scholar 

  3. 3.

    DiVincenzo, D. P. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000).

    Article  Google Scholar 

  4. 4.

    Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001).

    CAS  Article  Google Scholar 

  5. 5.

    Monz, T. et al. Realization of a scalable Shor algorithm. Science 351, 1068–1070 (2016).

    CAS  Article  Google Scholar 

  6. 6.

    Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197 (2005).

    CAS  Article  Google Scholar 

  7. 7.

    Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    CAS  Article  Google Scholar 

  8. 8.

    Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).

    CAS  Article  Google Scholar 

  9. 9.

    Liu, X. & Hersam, M. C. Interface characterization and control of 2D materials and heterostructures. Adv. Mater. 30, 1801586 (2018).

    Article  CAS  Google Scholar 

  10. 10.

    Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).

    CAS  Article  Google Scholar 

  11. 11.

    Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    CAS  Article  Google Scholar 

  12. 12.

    Nowack, K. C., Koppens, F. H. L., Nazarov, Y. V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007).

    CAS  Article  Google Scholar 

  13. 13.

    Rashba, E. I. & Efros, Al. L. Orbital mechanisms of electron-spin manipulation by an electric field. Phys. Rev. Lett. 91, 126405 (2003).

    CAS  Article  Google Scholar 

  14. 14.

    Pioro-Ladrière, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008).

    Article  CAS  Google Scholar 

  15. 15.

    Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

    CAS  Article  Google Scholar 

  16. 16.

    Kloeffel, C. & Loss, D. Prospects for spin-based quantum computing in quantum dots. Annu. Rev. Condens. Matter Phys. 4, 51–81 (2013).

    CAS  Article  Google Scholar 

  17. 17.

    Medford, J. et al. Quantum-dot-based resonant exchange qubit. Phys. Rev. Lett. 111, 050501 (2013).

    CAS  Article  Google Scholar 

  18. 18.

    Landig, A. J. et al. Coherent spin–photon coupling using a resonant exchange qubit. Nature 560, 179–184 (2018).

    CAS  Article  Google Scholar 

  19. 19.

    Gorman, J., Hasko, D. G. & Williams, D. A. Charge-qubit operation of an isolated double quantum dot. Phys. Rev. Lett. 95, 090502 (2005).

    CAS  Article  Google Scholar 

  20. 20.

    Hayashi, T., Fujisawa, T., Cheong, H. D., Jeong, Y. H. & Hirayama, Y. Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003).

    CAS  Article  Google Scholar 

  21. 21.

    Nadj-Perge, S., Frolov, S. M., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

    CAS  Article  Google Scholar 

  22. 22.

    Stockklauser, A. et al. Strong coupling cavity QED with gate-defined double quantum dots enabled by a high impedance resonator. Phys. Rev. X 7, 011030 (2017).

    Google Scholar 

  23. 23.

    Mi, X., Cady, J. V., Zajac, D. M., Deelman, P. W. & Petta, J. R. Strong coupling of a single electron in silicon to a microwave photon. Science 355, 156–158 (2017).

    CAS  Article  Google Scholar 

  24. 24.

    Samkharadze, N. et al. Strong spin-photon coupling in silicon. Science 359, 1123–1127 (2018).

    CAS  Article  Google Scholar 

  25. 25.

    De Sousa, R. & Sarma, S. D. Electron spin coherence in semiconductors: Considerations for a spin-based solid-state quantum computer architecture. Phys. Rev. B 67, 033301 (2003).

    Article  CAS  Google Scholar 

  26. 26.

    Fuchs, M., Rychkov, V. & Trauzettel, B. Spin decoherence in graphene quantum dots due to hyperfine interaction. Phys. Rev. B 86, 085301 (2012).

    Article  CAS  Google Scholar 

  27. 27.

    Huertas-Hernando, D., Guinea, F. & Brataas, A. Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B 74, 155426 (2006).

    Article  CAS  Google Scholar 

  28. 28.

    Güttinger, J., Frey, T., Stampfer, C., Ihn, T. & Ensslin, K. Spin states in graphene quantum dots. Phys. Rev. Lett. 105, 116801 (2010).

    Article  CAS  Google Scholar 

  29. 29.

    Hanson, R. et al. Zeeman energy and spin relaxation in a one-electron quantum dot. Phys. Rev. Lett. 91, 196802 (2003).

    CAS  Article  Google Scholar 

  30. 30.

    Eich, M. et al. Spin and valley states in gate-defined bilayer graphene quantum dots. Phys. Rev. X 8, 031023 (2018).

    CAS  Google Scholar 

  31. 31.

    Cho, C.-H., Kim, B.-H. & Park, S.-J. Room-temperature Coulomb blockade effect in silicon quantum dots in silicon nitride films. Appl. Phys. Lett. 89, 013116 (2006).

    Article  CAS  Google Scholar 

  32. 32.

    Shin, S. J. et al. Room-temperature charge stability modulated by quantum effects in a nanoscale silicon island. Nano Lett. 11, 1591–1597 (2011).

    CAS  Article  Google Scholar 

  33. 33.

    Ponomarenko, L. A. et al. Chaotic Dirac billiard in graphene quantum dots. Science 320, 356–358 (2008).

    CAS  Article  Google Scholar 

  34. 34.

    Wurm, J. et al. Symmetry classes in graphene quantum dots: universal spectral statistics, weak localization, and conductance fluctuations. Phys. Rev. Lett. 102, 056806 (2009).

    Article  CAS  Google Scholar 

  35. 35.

    Stampfer, C. et al. Energy gaps in etched graphene nanoribbons. Phys. Rev. Lett. 102, 056403 (2009).

    CAS  Article  Google Scholar 

  36. 36.

    Stampfer, C. et al. Tunable graphene single electron transistor. Nano Lett. 8, 2378–2383 (2008).

    CAS  Article  Google Scholar 

  37. 37.

    Güttinger, J. et al. Electron-hole crossover in graphene quantum dots. Phys. Rev. Lett. 103, 046810 (2009).

    Article  CAS  Google Scholar 

  38. 38.

    Volk, C. et al. Probing relaxation times in graphene quantum dots. Nat. Commun. 4, 1753 (2013).

    Article  CAS  Google Scholar 

  39. 39.

    Schnez, S. et al. Observation of excited states in a graphene quantum dot. Appl. Phys. Lett. 94, 012107 (2009).

    Article  CAS  Google Scholar 

  40. 40.

    Liu, X. L., Hug, D. & Vandersypen, L. M. K. Gate-defined graphene double quantum dot and excited state spectroscopy. Nano Lett. 10, 1623–1627 (2010).

    CAS  Article  Google Scholar 

  41. 41.

    Fujisawa, T., Tokura, Y. & Hirayama, Y. Energy relaxation process in a quantum dot studied by DC current and pulse-excited current measurements. Phys. B Condens. Matter 298, 573–579 (2001).

    CAS  Article  Google Scholar 

  42. 42.

    Engels, S. et al. Etched graphene quantum dots on hexagonal boron nitride. Appl. Phys. Lett. 103, 073113 (2013).

    Article  CAS  Google Scholar 

  43. 43.

    Xue, J. et al. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 10, 282–285 (2011).

    CAS  Article  Google Scholar 

  44. 44.

    Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2, 620–625 (2006).

    CAS  Article  Google Scholar 

  45. 45.

    Matulis, A. & Peeters, F. M. Quasibound states of quantum dots in single and bilayer graphene. Phys. Rev. B 77, 115423 (2008).

    Article  CAS  Google Scholar 

  46. 46.

    Bardarson, J. H., Titov, M. & Brouwer, P. W. Electrostatic confinement of electrons in an integrable graphene quantum dot. Phys. Rev. Lett. 102, 226803 (2009).

    CAS  Article  Google Scholar 

  47. 47.

    Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Controlling the electronic structure of bilayer graphene. Science 313, 951–954 (2006).

    CAS  Article  Google Scholar 

  48. 48.

    Oostinga, J. B., Heersche, H. B., Liu, X., Morpurgo, A. F. & Vandersypen, L. M. K. Gate-induced insulating state in bilayer graphene devices. Nat. Mater. 7, 151–157 (2008).

    CAS  Article  Google Scholar 

  49. 49.

    Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).

    CAS  Article  Google Scholar 

  50. 50.

    Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl. Acad. Sci. USA 110, 11256–11260 (2013).

    CAS  Article  Google Scholar 

  51. 51.

    Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    CAS  Article  Google Scholar 

  52. 52.

    Eich, M. et al. Coupled quantum dots in bilayer graphene. Nano Lett. 18, 5042–5048 (2018).

    CAS  Article  Google Scholar 

  53. 53.

    Goossens, A. et al. Gate-defined confinement in bilayer graphene-hexagonal boron nitride hybrid devices. Nano Lett. 12, 4656–4660 (2012).

    CAS  Article  Google Scholar 

  54. 54.

    Kurzmann, A. et al. Excited states in bilayer graphene quantum dots. arXiv:1904.07185 [cond-mat.mes-hall] (2019).

  55. 55.

    Klimov, N. N. et al. Electromechanical properties of graphene drumheads. Science 336, 1557–1561 (2012).

    CAS  Article  Google Scholar 

  56. 56.

    Freitag, N. M. et al. Large tunable valley splitting in edge-free graphene quantum dots on boron nitride. Nat. Nanotechnol. 13, 392–397 (2018).

    CAS  Article  Google Scholar 

  57. 57.

    Eng, K. et al. Isotopically enhanced triple-quantum-dot qubit. Sci. Adv. 1, e1500214 (2015).

    Article  Google Scholar 

  58. 58.

    Connolly, M. R. et al. Gigahertz quantized charge pumping in graphene quantum dots. Nat. Nanotechnol. 8, 417–420 (2013).

    CAS  Article  Google Scholar 

  59. 59.

    Volk, C. et al. Electronic excited states in bilayer graphene double quantum dots. Nano Lett. 11, 3581–3586 (2011).

    CAS  Article  Google Scholar 

  60. 60.

    Chiu, K. L. et al. Magnetic-field-induced charge redistribution in disordered graphene double quantum dots. Phys. Rev. B 92, 155408 (2015).

    Article  CAS  Google Scholar 

  61. 61.

    Rohling, N. & Burkard, G. Universal quantum computing with spin and valley states. New J. Phys. 14, 083008 (2012).

    Article  Google Scholar 

  62. 62.

    Recher, P., Nilsson, J., Burkard, G. & Trauzettel, B. Bound states and magnetic field induced valley splitting in gate-tunable graphene quantum dots. Phys. Rev. B 79, 085407 (2009).

    Article  CAS  Google Scholar 

  63. 63.

    Pereira, J. M., Peeters, F. M., Vasilopoulos, P., Costa Filho, R. N. & Farias, G. A. Landau levels in graphene bilayer quantum dots. Phys. Rev. B 79, 195403 (2009).

    Article  CAS  Google Scholar 

  64. 64.

    Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphene quantum dots. Nat. Phys. 3, 192–196 (2007).

    CAS  Article  Google Scholar 

  65. 65.

    Fal’ko, V. Quantum information on chicken wire. Nat. Phys. 3, 151–152 (2007).

    Article  Google Scholar 

  66. 66.

    Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

    CAS  Article  Google Scholar 

  67. 67.

    Weinmann, D., Häusler, W. & Kramer, B. Spin blockades in linear and nonlinear transport through quantum dots. Phys. Rev. Lett. 74, 984–987 (1995).

    CAS  Article  Google Scholar 

  68. 68.

    Sols, F., Guinea, F. & Neto, A. H. C. Coulomb blockade in graphene nanoribbons. Phys. Rev. Lett. 99, 166803 (2007).

    CAS  Article  Google Scholar 

  69. 69.

    Deng, G.-W. et al. Charge number dependence of the dephasing rates of a graphene double quantum dot in a circuit QED architecture. Phys. Rev. Lett. 115, 126804 (2015).

    Article  CAS  Google Scholar 

  70. 70.

    Deng, G.-W. et al. Coupling two distant double quantum dots with a microwave resonator. Nano Lett. 15, 6620–6625 (2015).

    CAS  Article  Google Scholar 

  71. 71.

    Hamer, M. et al. Gate-defined quantum confinement in InSe-based van der Waals heterostructures. Nano Lett. 18, 3950–3955 (2018).

    CAS  Article  Google Scholar 

  72. 72.

    Liu, X. et al. Rotationally commensurate growth of MoS2 on epitaxial graphene. ACS Nano 10, 1067–1075 (2016).

    CAS  Article  Google Scholar 

  73. 73.

    Manzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A. 2D transition metal dichalcogenides. Nat. Rev. Mater. 2, 17033 (2017).

    CAS  Article  Google Scholar 

  74. 74.

    Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).

    CAS  Article  Google Scholar 

  75. 75.

    Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).

    CAS  Article  Google Scholar 

  76. 76.

    Toda, Y., Moriwaki, O., Nishioka, M. & Arakawa, Y. Efficient carrier relaxation mechanism in InGaAs/GaAs self-assembled quantum dots based on the existence of continuum states. Phys. Rev. Lett. 82, 4114–4117 (1999).

    CAS  Article  Google Scholar 

  77. 77.

    Elzerman, J. M. et al. Few-electron quantum dot circuit with integrated charge read out. Phys. Rev. B 67, 161308 (2003).

    Article  CAS  Google Scholar 

  78. 78.

    Björk, M. T. et al. Few-electron quantum dots in nanowires. Nano Lett. 4, 1621–1625 (2004).

    Article  CAS  Google Scholar 

  79. 79.

    Kormányos, A., Zólyomi, V., Drummond, N. D. & Burkard, G. Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides. Phys. Rev. X 4, 011034 (2014).

    Google Scholar 

  80. 80.

    Pawłowski, J., Z˙ebrowski, D. & Bednarek, S. Valley qubit in a gated MoS2 monolayer quantum dot. Phys. Rev. B 97, 155412 (2018).

    Article  Google Scholar 

  81. 81.

    Széchenyi, G., Chirolli, L. & Pályi, A. Impurity-assisted electric control of spin-valley qubits in monolayer MoS2. 2D Mater. 5, 035004 (2018).

    Article  CAS  Google Scholar 

  82. 82.

    Lee, K., Kulkarni, G. & Zhong, Z. Coulomb blockade in monolayer MoS2 single electron transistor. Nanoscale 8, 7755–7760 (2016).

    CAS  Article  Google Scholar 

  83. 83.

    Song, X.-X. et al. Temperature dependence of Coulomb oscillations in a few-layer two-dimensional WS2 quantum dot. Sci. Rep. 5, 16113 (2015).

    Article  CAS  Google Scholar 

  84. 84.

    Song, X.-X. et al. A gate defined quantum dot on the two-dimensional transition metal dichalcogenide semiconductor WSe2. Nanoscale 7, 16867–16873 (2015).

    CAS  Article  Google Scholar 

  85. 85.

    Pisoni, R. et al. Gate-tunable quantum dot in a high quality single layer MoS2 van der Waals heterostructure. Appl. Phys. Lett. 112, 123101 (2018).

    Article  CAS  Google Scholar 

  86. 86.

    Wang, K. et al. Electrical control of charged carriers and excitons in atomically thin materials. Nat. Nanotechnol. 13, 128–132 (2018).

    CAS  Article  Google Scholar 

  87. 87.

    Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    CAS  Article  Google Scholar 

  88. 88.

    Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012).

    CAS  Article  Google Scholar 

  89. 89.

    Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015).

    Article  CAS  Google Scholar 

  90. 90.

    Abadillo-Uriel, J. C., Koiller, B. & Calderón, M. J. Two-dimensional semiconductors pave the way towards dopant-based quantum computing. Beilstein J. Nanotechnol. 9, 2668–2673 (2018).

    CAS  Article  Google Scholar 

  91. 91.

    Exarhos, A. L., Hopper, D. A., Patel, R. N., Doherty, M. W. & Bassett, L. C. Magnetic-field-dependent quantum emission in hexagonal boron nitride at room temperature. Nat. Commun. 10, 222 (2019).

    Article  CAS  Google Scholar 

  92. 92.

    Grosso, G. et al. Tunable and high-purity room temperature single-photon emission from atomic defects in hexagonal boron nitride. Nat. Commun. 8, 705 (2017).

    Article  CAS  Google Scholar 

  93. 93.

    Tran, T. T., Bray, K., Ford, M. J., Toth, M. & Aharonovich, I. Quantum emission from hexagonal boron nitride monolayers. Nat. Nanotechnol. 11, 37–41 (2016).

    CAS  Article  Google Scholar 

  94. 94.

    Moody, G. et al. Microsecond valley lifetime of defect-bound excitons in monolayer WSe2. Phys. Rev. Lett. 121, 057403 (2018).

    CAS  Article  Google Scholar 

  95. 95.

    Chakraborty, C., Kinnischtzke, L., Goodfellow, K. M., Beams, R. & Vamivakas, A. N. Voltage-controlled quantum light from an atomically thin semiconductor. Nat. Nanotechnol. 10, 507–511 (2015).

    CAS  Article  Google Scholar 

  96. 96.

    Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    CAS  Article  Google Scholar 

  97. 97.

    Dobrovitski, V. V., Fuchs, G. D., Falk, A. L., Santori, C. & Awschalom, D. D. Quantum control over single spins in diamond. Annu. Rev. Condens. Matter Phys. 4, 23–50 (2013).

    CAS  Article  Google Scholar 

  98. 98.

    Maurer, P. C. et al. Room-temperature quantum bit memory exceeding one second. Science 336, 1283–1286 (2012).

    CAS  Article  Google Scholar 

  99. 99.

    Neumann, P. et al. High-precision nanoscale temperature sensing using single defects in diamond. Nano Lett. 13, 2738–2742 (2013).

    CAS  Article  Google Scholar 

  100. 100.

    Gupta, S., Yang, J.-H. & Yakobson, B. I. Two-level quantum systems in two-dimensional materials for single photon emission. Nano Lett. 19, 408–414 (2019).

    CAS  Article  Google Scholar 

  101. 101.

    Toth, M. & Aharonovich, I. Single photon sources in atomically thin materials. Annu. Rev. Phys. Chem. 70, 123–142 (2019).

    CAS  Article  Google Scholar 

  102. 102.

    Cassabois, G., Valvin, P. & Gil, B. Hexagonal boron nitride is an indirect bandgap semiconductor. Nat. Photonics 10, 262–266 (2016).

    CAS  Article  Google Scholar 

  103. 103.

    Zhao, H.-Q., Fujiwara, M. & Takeuchi, S. Suppression of fluorescence phonon sideband from nitrogen vacancy centers in diamond nanocrystals by substrate effect. Opt. Express 20, 15628–15635 (2012).

    CAS  Article  Google Scholar 

  104. 104.

    Li, X. et al. Nonmagnetic quantum emitters in boron nitride with ultranarrow and sideband-free emission spectra. ACS Nano 11, 6652–6660 (2017).

    CAS  Article  Google Scholar 

  105. 105.

    Lounis, B. & Orrit, M. Single-photon sources. Rep. Prog. Phys. 68, 1129–1179 (2005).

    CAS  Article  Google Scholar 

  106. 106.

    Jungwirth, N. R. et al. Temperature dependence of wavelength selectable zero-phonon emission from single defects in hexagonal boron nitride. Nano Lett. 16, 6052–6057 (2016).

    CAS  Article  Google Scholar 

  107. 107.

    Huxter, V. M., Oliver, T. A. A., Budker, D. & Fleming, G. R. Vibrational and electronic dynamics of nitrogen–vacancy centres in diamond revealed by two-dimensional ultrafast spectroscopy. Nat. Phys. 9, 744–749 (2013).

    CAS  Article  Google Scholar 

  108. 108.

    Tawfik, S. A. et al. First-principles investigation of quantum emission from hBN defects. Nanoscale 9, 13575–13582 (2017).

    CAS  Article  Google Scholar 

  109. 109.

    Noh, G. et al. Stark tuning of single-photon emitters in hexagonal boron nitride. Nano Lett. 18, 4710–4715 (2018).

    CAS  Article  Google Scholar 

  110. 110.

    Tran, T. T. et al. Robust multicolor single photon emission from point defects in hexagonal boron nitride. ACS Nano 10, 7331–7338 (2016).

    CAS  Article  Google Scholar 

  111. 111.

    Ziegler, J. et al. Deterministic quantum emitter formation in hexagonal boron nitride via controlled edge creation. Nano Lett. 19, 2121–2127 (2019).

    CAS  Article  Google Scholar 

  112. 112.

    Mendelson, N. et al. Engineering and tuning of quantum emitters in few-layer hexagonal boron nitride. ACS Nano 13, 3132–3140 (2019).

    CAS  Article  Google Scholar 

  113. 113.

    Dai, Z., Liu, L. & Zhang, Z. Strain engineering of 2D materials: issues and opportunities at the interface. Adv. Mater. 0, 1805417 (2019).

    Article  CAS  Google Scholar 

  114. 114.

    Ziegler, J. et al. Single-photon emitters in boron nitride nanococoons. Nano Lett. 18, 2683–2688 (2018).

    CAS  Article  Google Scholar 

  115. 115.

    Srivastava, A. et al. Optically active quantum dots in monolayer WSe2. Nat. Nanotechnol. 10, 491–496 (2015).

    CAS  Article  Google Scholar 

  116. 116.

    Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

    CAS  Article  Google Scholar 

  117. 117.

    He, Y.-M. et al. Single quantum emitters in monolayer semiconductors. Nat. Nanotechnol. 10, 497–502 (2015).

    CAS  Article  Google Scholar 

  118. 118.

    Koperski, M. et al. Single photon emitters in exfoliated WSe2 structures. Nat. Nanotechnol 10, 503–506 (2015).

    CAS  Article  Google Scholar 

  119. 119.

    Palacios-Berraquero, C. et al. Atomically thin quantum light-emitting diodes. Nat. Commun. 7, 12978 (2016).

    CAS  Article  Google Scholar 

  120. 120.

    Wang, G. et al. Valley dynamics probed through charged and neutral exciton emission in monolayer WSe2. Phys. Rev. B 90, 075413 (2014).

    Article  CAS  Google Scholar 

  121. 121.

    Kumar, S. et al. Resonant laser spectroscopy of localized excitons in monolayer WSe2. Optica 3, 882–886 (2016).

    CAS  Article  Google Scholar 

  122. 122.

    Branny, A. et al. Discrete quantum dot like emitters in monolayer MoSe2: Spatial mapping, magneto-optics, and charge tuning. Appl. Phys. Lett. 108, 142101 (2016).

    Article  CAS  Google Scholar 

  123. 123.

    Liu, X., Balla, I., Bergeron, H. & Hersam, M. C. Point defects and grain boundaries in rotationally commensurate MoS2 on epitaxial graphene. J. Phys. Chem. C 120, 20798–20805 (2016).

    CAS  Article  Google Scholar 

  124. 124.

    Peng, J.-P. et al. Molecular beam epitaxy growth and scanning tunneling microscopy study of TiSe2 ultrathin films. Phys. Rev. B 91, 121113 (2015).

    Article  CAS  Google Scholar 

  125. 125.

    KC, S., Longo, R. C., Addou, R., Wallace, R. M. & Cho, K. Impact of intrinsic atomic defects on the electronic structure of MoS2 monolayers. Nanotechnol. 25, 375703 (2014).

    Article  CAS  Google Scholar 

  126. 126.

    Hildebrand, B. et al. Doping nature of native defects in 1T–TiSe2. Phys. Rev. Lett. 112, 197001 (2014).

    CAS  Article  Google Scholar 

  127. 127.

    Hong, J. et al. Exploring atomic defects in molybdenum disulphide monolayers. Nat. Commun. 6, 6293 (2015).

    CAS  Article  Google Scholar 

  128. 128.

    Noh, J.-Y., Kim, H. & Kim, Y.-S. Stability and electronic structures of native defects in single-layer MoS2. Phys. Rev. B 89, 205417 (2014).

    Article  CAS  Google Scholar 

  129. 129.

    Clark, G. et al. Single defect light-emitting diode in a van der Waals heterostructure. Nano Lett. 16, 3944–3948 (2016).

    CAS  Article  Google Scholar 

  130. 130.

    Li, H. et al. Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide. Nat. Commun. 6, 7381 (2015).

    CAS  Article  Google Scholar 

  131. 131.

    Feng, J., Qian, X., Huang, C.-W. & Li, J. Strain-engineered artificial atom as a broad-spectrum solar energy funnel. Nat. Photonics 6, 866–872 (2012).

    CAS  Article  Google Scholar 

  132. 132.

    Branny, A., Kumar, S., Proux, R. & Gerardot, B. D. Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor. Nat. Commun. 8, 15053 (2017).

    CAS  Article  Google Scholar 

  133. 133.

    Palacios-Berraquero, C. et al. Large-scale quantum-emitter arrays in atomically thin semiconductors. Nat. Commun. 8, 15093 (2017).

    CAS  Article  Google Scholar 

  134. 134.

    Rosenberger, M. R. et al. Quantum calligraphy: Writing single-photon emitters in a two-dimensional materials platform. ACS Nano 13, 904–912 (2019).

    CAS  Article  Google Scholar 

  135. 135.

    Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric loss. Phys. Rev. Lett. 95, 210503 (2005).

    Article  CAS  Google Scholar 

  136. 136.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    CAS  Article  Google Scholar 

  137. 137.

    Kang, K. et al. Layer-by-layer assembly of two-dimensional materials into wafer-scale heterostructures. Nature 550, 229–233 (2017).

    Article  CAS  Google Scholar 

  138. 138.

    Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

    Article  Google Scholar 

  139. 139.

    Scherer, H. & Camarota, B. Quantum metrology triangle experiments: a status review. Meas. Sci. Technol. 23, 124010 (2012).

    CAS  Article  Google Scholar 

  140. 140.

    Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 101–159 (1979).

    Article  Google Scholar 

  141. 141.

    Williams, J. R. et al. Unconventional Josephson effect in hybrid superconductor-topological insulator devices. Phys. Rev. Lett. 109, 056803 (2012).

    CAS  Article  Google Scholar 

  142. 142.

    Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  CAS  Google Scholar 

  143. 143.

    Larsen, T. W. et al. Semiconductor-nanowire-based superconducting qubit. Phys. Rev. Lett. 115, 127001 (2015).

    CAS  Article  Google Scholar 

  144. 144.

    Shim, Y.-P. & Tahan, C. Semiconductor-inspired design principles for superconducting quantum computing. Nat. Commun. 7, 11059 (2016).

    CAS  Article  Google Scholar 

  145. 145.

    Casparis, L. et al. Superconducting gatemon qubit based on a proximitized two-dimensional electron gas. Nat. Nanotechnol. 13, 915–919 (2018).

    CAS  Article  Google Scholar 

  146. 146.

    Ben Shalom, M. et al. Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene. Nat. Phys. 12, 318–322 (2016).

    Article  CAS  Google Scholar 

  147. 147.

    Heersche, H. B., Jarillo-Herrero, P., Oostinga, J. B., Vandersypen, L. M. K. & Morpurgo, A. F. Bipolar supercurrent in graphene. Nature 446, 56–59 (2007).

    CAS  Article  Google Scholar 

  148. 148.

    Rickhaus, P., Weiss, M., Marot, L. & Schönenberger, C. Quantum Hall effect in graphene with superconducting electrodes. Nano Lett. 12, 1942–1945 (2012).

    CAS  Article  Google Scholar 

  149. 149.

    Chen, J.-H. et al. Diffusive charge transport in graphene on SiO2. Solid State Commun. 149, 1080–1086 (2009).

    CAS  Article  Google Scholar 

  150. 150.

    Mizuno, N., Nielsen, B. & Du, X. Ballistic-like supercurrent in suspended graphene Josephson weak links. Nat. Commun. 4, 2716 (2013).

    Article  CAS  Google Scholar 

  151. 151.

    Lee, G.-H., Kim, S., Jhi, S.-H. & Lee, H.-J. Ultimately short ballistic vertical graphene Josephson junctions. Nat. Commun. 6, 6181 (2015).

    CAS  Article  Google Scholar 

  152. 152.

    Island, J. O., Steele, G. A., Zant, H. S. J. van der & Castellanos-Gomez, A. Thickness dependent interlayer transport in vertical MoS2 Josephson junctions. 2D Mater. 3, 031002 (2016).

    Article  CAS  Google Scholar 

  153. 153.

    Kim, M. et al. Strong proximity Josephson coupling in vertically stacked NbSe2–graphene–NbSe2 van der Waals junctions. Nano Lett. 17, 6125–6130 (2017).

    CAS  Article  Google Scholar 

  154. 154.

    Frindt, R. F. Superconductivity in ultrathin NbSe2 layers. Phys. Rev. Lett. 28, 299–301 (1972).

    CAS  Article  Google Scholar 

  155. 155.

    Yabuki, N. et al. Supercurrent in van der Waals Josephson junction. Nat. Commun. 7, 10616 (2016).

    CAS  Article  Google Scholar 

  156. 156.

    Liu, K. et al. Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5, 4966 (2014).

    CAS  Article  Google Scholar 

  157. 157.

    Jarillo-Herrero, P., van Dam, J. A. & Kouwenhoven, L. P. Quantum supercurrent transistors in carbon nanotubes. Nature 439, 953–956 (2006).

    CAS  Article  Google Scholar 

  158. 158.

    Nanda, G. et al. Current-phase relation of ballistic graphene Josephson junctions. Nano Lett. 17, 3396–3401 (2017).

    CAS  Article  Google Scholar 

  159. 159.

    Calado, V. E. et al. Ballistic Josephson junctions in edge-contacted graphene. Nat. Nanotechnol. 10, 761–764 (2015).

    CAS  Article  Google Scholar 

  160. 160.

    Wang, J. I.-J. et al. Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures. Nat. Nanotechnol. 14, 120–125 (2019).

    CAS  Article  Google Scholar 

  161. 161.

    Lee, G.-H. et al. Inducing superconducting correlation in quantum Hall edge states. Nat. Phys. 13, 693–698 (2017).

    CAS  Article  Google Scholar 

  162. 162.

    Amet, F. et al. Supercurrent in the quantum Hall regime. Science 352, 966–969 (2016).

    CAS  Article  Google Scholar 

  163. 163.

    Pribiag, V. S. et al. Edge-mode superconductivity in a two-dimensional topological insulator. Nat. Nanotechnol. 10, 593–597 (2015).

    CAS  Article  Google Scholar 

  164. 164.

    Schmidt, F. E., Jenkins, M. D., Watanabe, K., Taniguchi, T. & Steele, G. A. A ballistic graphene superconducting microwave circuit. Nat. Commun. 9, 4069 (2018).

    Article  CAS  Google Scholar 

  165. 165.

    Kroll, J. G. et al. Magnetic field compatible circuit quantum electrodynamics with graphene Josephson junctions. Nat. Commun. 9, 4615 (2018).

    CAS  Article  Google Scholar 

  166. 166.

    Walsh, E. D. et al. Graphene-based Josephson-junction single-photon detector. Phys. Rev. Applied 8, 024022 (2017).

    Article  Google Scholar 

  167. 167.

    Wilczek, F. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982).

    CAS  Article  Google Scholar 

  168. 168.

    Leinaas, J. M. & Myrheim, J. On the theory of identical particles. Nuovo Cim. B 37, 1–23 (1977).

    Article  Google Scholar 

  169. 169.

    Stern, A. Non-Abelian states of matter. Nature 464, 187–193 (2010).

    CAS  Article  Google Scholar 

  170. 170.

    Kitaev, A. Yu. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

    CAS  Article  Google Scholar 

  171. 171.

    Teo, J. C. Y. & Kane, C. L. Majorana fermions and non-Abelian statistics in three dimensions. Phys. Rev. Lett. 104, 046401 (2010).

    Article  CAS  Google Scholar 

  172. 172.

    Moore, G. & Read, N. Nonabelions in the fractional quantum hall effect. Nucl. Phys. B 360, 362–396 (1991).

    Article  Google Scholar 

  173. 173.

    Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).

    CAS  Article  Google Scholar 

  174. 174.

    Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, E. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).

    CAS  Article  Google Scholar 

  175. 175.

    Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    CAS  Article  Google Scholar 

  176. 176.

    Feldman, B. E., Krauss, B., Smet, J. H. & Yacoby, A. Unconventional sequence of fractional quantum Hall states in suspended graphene. Science 337, 1196–1199 (2012).

    CAS  Article  Google Scholar 

  177. 177.

    Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 350, 1231–1234 (2015).

    CAS  Article  Google Scholar 

  178. 178.

    Kim, Y. et al. Even denominator fractional quantum Hall states in higher Landau levels of graphene. Nat. Phys. 15, 154–158 (2019).

    CAS  Article  Google Scholar 

  179. 179.

    Zibrov, A. A. et al. Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene. Nat. Phys. 14, 930–935 (2018).

    CAS  Article  Google Scholar 

  180. 180.

    Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017).

    CAS  Article  Google Scholar 

  181. 181.

    Sanchez-Yamagishi, J. D. et al. Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer. Nat. Nanotechnol. 12, 118–122 (2017).

    CAS  Article  Google Scholar 

  182. 182.

    Li, J. I. A. et al. Even-denominator fractional quantum Hall states in bilayer graphene. Science 358, 648–652 (2017).

    CAS  Article  Google Scholar 

  183. 183.

    Lin, X., Du, R. & Xie, X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Nat. Sci. Rev. 1, 564–579 (2014).

    CAS  Article  Google Scholar 

  184. 184.

    Das Sarma, S., Nayak, C. & Tewari, S. Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortices in a px + ipy superconductor. Phys. Rev. B 73, 220502 (2006).

    Article  CAS  Google Scholar 

  185. 185.

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    Article  CAS  Google Scholar 

  186. 186.

    Wang, M.-X. et al. The coexistence of superconductivity and topological order in the Bi2Se3 thin films. Science 336, 52–55 (2012).

    CAS  Article  Google Scholar 

  187. 187.

    Xu, J.-P. et al. Experimental detection of a Majorana mode in the core of a magnetic vortex inside a topological insulator-superconductor Bi2Te3/NbSe2 heterostructure. Phys. Rev. Lett. 114, 017001 (2015).

    Article  CAS  Google Scholar 

  188. 188.

    Sun, H.-H. et al. Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor. Phys. Rev. Lett. 116, 257003 (2016).

    Article  CAS  Google Scholar 

  189. 189.

    Xu, J.-P. et al. Artificial topological superconductor by the proximity effect. Phys. Rev. Lett. 112, 217001 (2014).

    Article  CAS  Google Scholar 

  190. 190.

    Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

    Article  CAS  Google Scholar 

  191. 191.

    Chiu, C.-K., Gilbert, M. J. & Hughes, T. L. Vortex lines in topological insulator-superconductor heterostructures. Phys. Rev. B 84, 144507 (2011).

    Article  CAS  Google Scholar 

  192. 192.

    He, J. J., Ng, T. K., Lee, P. A. & Law, K. T. Selective equal-spin Andreev reflections induced by Majorana fermions. Phys. Rev. Lett. 112, 037001 (2014).

    Article  CAS  Google Scholar 

  193. 193.

    Banerjee, A., Sundaresh, A., Ganesan, R. & Kumar, P. S. A. Signatures of topological superconductivity in bulk-insulating topological insulator BiSbTe1.25Se1.75 in proximity with superconducting NbSe2. ACS Nano 12, 12665–12672 (2018).

    CAS  Article  Google Scholar 

  194. 194.

    Sun, H.-H. et al. Coexistence of topological edge state and superconductivity in bismuth ultrathin film. Nano Lett. 17, 3035–3039 (2017).

    CAS  Article  Google Scholar 

  195. 195.

    Ge, J.-F. et al. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3. Nat. Mater. 14, 285–289 (2015).

    CAS  Article  Google Scholar 

  196. 196.

    Wang, Z. F. et al. Topological edge states in a high-temperature superconductor FeSe/SrTiO3(001) film. Nat. Mater. 15, 968–973 (2016).

    CAS  Article  Google Scholar 

  197. 197.

    Yin, J.-X. et al. Observation of a robust zero-energy bound state in iron-based superconductor Fe(Te,Se). Nat. Phys. 11, 543–546 (2015).

    CAS  Article  Google Scholar 

  198. 198.

    Xu, G., Lian, B., Tang, P., Qi, X.-L. & Zhang, S.-C. Topological superconductivity on the surface of Fe-based superconductors. Phys. Rev. Lett. 117, 047001 (2016).

    Article  CAS  Google Scholar 

  199. 199.

    Zhang, P. et al. Observation of topological superconductivity on the surface of an iron-based superconductor. Science 360, 182–186 (2018).

    Article  CAS  Google Scholar 

  200. 200.

    Wang, D. et al. Evidence for Majorana bound states in an iron-based superconductor. Science 362, 333–335 (2018).

    CAS  Article  Google Scholar 

  201. 201.

    Machida, T. et al. Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te). Nat. Mater. 18, 811–881 (2019).

    CAS  Article  Google Scholar 

  202. 202.

    Chen, M. et al. Discrete energy levels of Caroli-de Gennes-Matricon states in quantum limit in FeTe0.55Se0.45. Nat. Commun. 9, 970 (2018).

    Article  CAS  Google Scholar 

  203. 203.

    Massee, F. et al. Imaging atomic-scale effects of high-energy ion irradiation on superconductivity and vortex pinning in Fe(Se,Te). Sci. Adv. 1, e1500033 (2015).

    Article  Google Scholar 

  204. 204.

    Clarke, D. J., Alicea, J. & Shtengel, K. Exotic non-Abelian anyons from conventional fractional quantum Hall states. Nat. Commun. 4, 1348 (2013).

    Article  CAS  Google Scholar 

  205. 205.

    Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8, 2150 (2017).

    Article  CAS  Google Scholar 

  206. 206.

    Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).

    CAS  Article  Google Scholar 

  207. 207.

    Wang, H. et al. High-quality monolayer superconductor NbSe2 grown by chemical vapour deposition. Nat. Commun. 8, 394 (2017).

    Article  CAS  Google Scholar 

  208. 208.

    Mannix, A. J. et al. Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs. Science 350, 1513–1516 (2015).

    CAS  Article  Google Scholar 

  209. 209.

    Liu, X., Zhang, Z., Wang, L., Yakobson, B. I. & Hersam, M. C. Intermixing and periodic self-assembly of borophene line defects. Nat. Mater. 17, 783–788 (2018).

    CAS  Article  Google Scholar 

  210. 210.

    Liu, X. et al. Geometric imaging of borophene polymorphs with functionalized probes. Nat. Commun. 10, 1642 (2019).

    Article  CAS  Google Scholar 

  211. 211.

    Zhu, F.-F. et al. Epitaxial growth of two-dimensional stanene. Nat. Mater. 14, 1020–1025 (2015).

    CAS  Article  Google Scholar 

  212. 212.

    Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl. Acad. Sci. USA 115, 10938–10942 (2018).

    CAS  Article  Google Scholar 

  213. 213.

    Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

    CAS  Article  Google Scholar 

  214. 214.

    Yan Gong, J. G. & Yan Gong, J. G. Experimental realization of an intrinsic magnetic topological insulator. Chin. Phys. Lett. 36, 076801 (2019).

    Article  Google Scholar 

  215. 215.

    Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Sci. Adv. 5, eaaw5685 (2019).

    Article  Google Scholar 

  216. 216.

    Liu, C. et al. Quantum phase transition from axion insulator to Chern insulator in MnBi2Te4. arXiv:1905.00715 [cond-mat.mes-hall] (2019).

  217. 217.

    Deng, Y. et al. Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. arXiv:1904.11468 [cond-mat.mtrl-sci] (2019).

  218. 218.

    Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    CAS  Article  Google Scholar 

  219. 219.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    CAS  Article  Google Scholar 

  220. 220.

    Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science 361, 690–693 (2018).

    CAS  Article  Google Scholar 

  221. 221.

    Liu, X. et al. Scanning probe nanopatterning and layer-by-layer thinning of black phosphorus. Adv. Mater. 29, 1604121 (2017).

    Article  CAS  Google Scholar 

  222. 222.

    Wood, J. D. et al. Effective passivation of exfoliated black phosphorus transistors against ambient degradation. Nano Lett. 14, 6964–6970 (2014).

    CAS  Article  Google Scholar 

  223. 223.

    Ryder, C. R. et al. Covalent functionalization and passivation of exfoliated black phosphorus via aryl diazonium chemistry. Nat. Chem. 8, 597–602 (2016).

    CAS  Article  Google Scholar 

  224. 224.

    Wells, S. A. et al. Suppressing ambient degradation of exfoliated InSe nanosheet devices via seeded atomic layer deposition encapsulation. Nano Lett. 18, 7876–7882 (2018).

    CAS  Article  Google Scholar 

  225. 225.

    Shcherbakov, D. et al. Raman spectroscopy, photocatalytic degradation, and stabilization of atomically thin chromium tri-iodide. Nano Lett. 18, 4214–4219 (2018).

    CAS  Article  Google Scholar 

  226. 226.

    Ryder, C. R., Wood, J. D., Wells, S. A. & Hersam, M. C. Chemically tailoring semiconducting two-dimensional transition metal dichalcogenides and black phosphorus. ACS Nano 10, 3900–3917 (2016).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

X.L. and M.C.H. acknowledge support from the Office of Naval Research (ONR N00014-17-1-2993) and the National Science Foundation Materials Research Science and Engineering Center (NSF DMR-1720139). X.L. further acknowledges support from a Ryan Fellowship that is administered through the Northwestern University International Institute for Nanotechnology.

Author information

Affiliations

Authors

Contributions

X.L. researched the data for the article. All authors discussed the contents and provided important contributions to the manuscript.

Corresponding author

Correspondence to Mark C. Hersam.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Hersam, M.C. 2D materials for quantum information science. Nat Rev Mater 4, 669–684 (2019). https://doi.org/10.1038/s41578-019-0136-x

Download citation

Further reading

Search

Quick links

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing