Abstract
Symmetry breaking in 2D layered materials plays a significant role in their macroscopic electrical, optical, magnetic and topological properties, including, but not limited to, spin-polarization effects, valley-contrasting physics, nonlinear Hall effects, nematic order, ferroelectricity, Bose–Einstein condensation and unconventional superconductivity. Engineering symmetry breaking of 2D layered materials not only offers extraordinary opportunities to tune their physical properties but also provides unprecedented possibilities to introduce completely new physics and technological innovations in electronics, photonics and optoelectronics. Indeed, over the past 15 years, a wide variety of physical, structural and chemical approaches have been developed to engineer the symmetry breaking of 2D layered materials. In this Technical Review, we focus on the recent progress on engineering the breaking of inversion, rotational, time-reversal and gauge symmetries in 2D layered materials, and present our perspectives on how these may lead to new physics and applications.
Key points
-
Most of the fascinating physical phenomena in 2D materials are dictated by their underlying symmetry breaking, namely, the breaking of inversion, rotational, time-reversal and gauge symmetries.
-
The symmetry breaking in 2D materials can be engineered by a wide variety of physical and chemical approaches. This opens the possibilities to manipulate the internal quantum degrees of freedom (such as spin, valley and layer pseudospin) for the emerging fields of spintronics, valleytronics and twistronics.
-
Engineering symmetry breaking in 2D materials can create unique opportunities to integrate different broken symmetries within one system, providing an unprecedented path to underpin new physics and transform the landscape of technological innovations.
-
Through engineering spontaneous symmetry breaking in magic-angle moiré superlattices, semimetallic graphene can be turned into a series of quantum states (such as a band insulator, Mott-like correlated insulator, quantum anomalous Hall insulator or superconductor), potentially offering new insights into strongly correlated physics, such as high-temperature unconventional superconductors and quantum spin liquids.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$99.00 per year
only $8.25 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
Novoselov, K., Mishchenko, A., Carvalho, A. & Neto, A. C. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).
Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nat. Photonics 10, 227–238 (2016).
Mak, K. F., Xiao, D. & Shan, J. Light–valley interactions in 2D semiconductors. Nat. Photonics 12, 451–460 (2018).
Gong, C. & Zhang, X. Two-dimensional magnetic crystals and emergent heterostructure devices. Science 363, eaav4450 (2019).
Sun, Z. et al. Giant nonreciprocal second-harmonic generation from antiferromagnetic bilayer CrI3. Nature 572, 497–501 (2019). This paper demonstrated the nonreciprocal second-order nonlinear optical effect in 2D materials enabled by the inversion symmetry breaking of the magnetic point group.
Xu, S.-Y. et al. Spontaneous gyrotropic electronic order in a transition-metal dichalcogenide. Nature 578, 545–549 (2020).
Autere, A. et al. Nonlinear optics with 2D layered materials. Adv. Mater. 30, 1705963 (2018).
Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).
Huang, B. et al. Tuning inelastic light scattering via symmetry control in the two-dimensional magnet CrI3. Nat. Nanotechnol. 15, 212–216 (2020).
Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019). This work represents one of the earliest experimental studies of nonlinear Hall effect enabled by the combination of inversion symmetry breaking and C3 rotational symmetry breaking.
Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).
Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019).
Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).
Langer, F. et al. Lightwave valleytronics in a monolayer of tungsten diselenide. Nature 557, 76–80 (2018).
Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).
Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).
Song, P. et al. Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature. Nat. Mater. 19, 292–298 (2020).
Shi, Y. et al. Imaging quantum spin Hall edges in monolayer WTe2. Sci. Adv. 5, eaat8799 (2019).
Zhu, H. et al. Observation of chiral phonons. Science 359, 579–582 (2018).
Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155–1160 (2016).
Belopolski, I. et al. Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points. Nat. Commun. 8, 942 (2017).
Lv, B. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Wu, W. et al. Piezoelectricity of single-atomic-layer MoS2 for energy conversion and piezotronics. Nature 514, 470–474 (2014).
Zhu, H. et al. Observation of piezoelectricity in free-standing monolayer MoS2. Nat. Nanotechnol. 10, 151–155 (2015).
Ares, P. et al. Piezoelectricity in monolayer hexagonal boron nitride. Adv. Mater. 32, 1905504 (2020).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). This paper engineered the spontaneous gauge symmetry breaking through creating flat bands in moiré superlattices and demonstrated the unconventional superconductivity.
Xi, X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).
Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).
Lu, J. et al. Evidence for two-dimensional Ising superconductivity in gated MoS2. Science 350, 1353–1357 (2015).
Manchon, A., Koo, H. C., Nitta, J., Frolov, S. & Duine, R. New perspectives for Rashba spin–orbit coupling. Nat. Mater. 14, 871–882 (2015).
Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).
Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science 361, 690–693 (2018).
Liu, Y. et al. Van der Waals heterostructures and devices. Nat. Rev. Mater. 1, 16042 (2016).
Jariwala, D., Marks, T. J. & Hersam, M. C. Mixed-dimensional van der Waals heterostructures. Nat. Mater. 16, 170–181 (2017).
Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).
Wu, S. et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nat. Phys. 9, 149–153 (2013).
Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).
Finney, N. R. et al. Tunable crystal symmetry in graphene–boron nitride heterostructures with coexisting moiré superlattices. Nat. Nanotechnol. 14, 1029–1034 (2019).
Sui, M. et al. Gate-tunable topological valley transport in bilayer graphene. Nat. Phys. 11, 1027–1031 (2015).
Castro, E. V. et al. Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007). This study represents one of the earliest reports to engineer inversion symmetry breaking through out-of-plane electric fields.
McCann, E. & Fal’ko, V. I. Landau-level degeneracy and quantum Hall effect in a graphite bilayer. Phys. Rev. Lett. 96, 086805 (2006).
Oostinga, J. B., Heersche, H. B., Liu, X., Morpurgo, A. F. & Vandersypen, L. M. Gate-induced insulating state in bilayer graphene devices. Nat. Mater. 7, 151–157 (2008).
Weitz, R. T., Allen, M., Feldman, B., Martin, J. & Yacoby, A. Broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812–816 (2010).
Velasco, J. et al. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. Nat. Nanotechnol. 7, 156–160 (2012).
Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Controlling the electronic structure of bilayer graphene. Science 313, 951–954 (2006).
Shimazaki, Y. et al. Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat. Phys. 11, 1032–1036 (2015).
Mak, K. F., Lui, C. H., Shan, J. & Heinz, T. F. Observation of an electric-field-induced band gap in bilayer graphene by infrared spectroscopy. Phys. Rev. Lett. 102, 256405 (2009).
Taychatanapat, T. & Jarillo-Herrero, P. Electronic transport in dual-gated bilayer graphene at large displacement fields. Phys. Rev. Lett. 105, 166601 (2010).
Yan, J. et al. Dual-gated bilayer graphene hot-electron bolometer. Nat. Nanotechnol. 7, 472–478 (2012).
Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).
Ju, L. et al. Tunable excitons in bilayer graphene. Science 358, 907–910 (2017).
Ju, L. et al. Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene. Nat. Commun. 11, 2941 (2020).
Cao, T., Wu, M. & Louie, S. G. Unifying optical selection rules for excitons in two dimensions: Band topology and winding numbers. Phys. Rev. Lett. 120, 087402 (2018).
Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).
Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).
Martin, I., Blanter, Y. M. & Morpurgo, A. Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008).
Li, J. et al. Gate-controlled topological conducting channels in bilayer graphene. Nat. Nanotechnol. 11, 1060–1065 (2016).
Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018).
You, J.-S., Fang, S., Xu, S.-Y., Kaxiras, E. & Low, T. Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109 (2018).
Lee, J., Mak, K. F. & Shan, J. Electrical control of the valley Hall effect in bilayer MoS2 transistors. Nat. Nanotechnol. 11, 421–425 (2016).
Lui, C. H., Li, Z., Mak, K. F., Cappelluti, E. & Heinz, T. F. Observation of an electrically tunable band gap in trilayer graphene. Nat. Phys. 7, 944–947 (2011).
Khodkov, T., Khrapach, I., Craciun, M. F. & Russo, S. Direct observation of a gate tunable band gap in electrical transport in ABC-trilayer graphene. Nano Lett. 15, 4429–4433 (2015).
Zhang, Y., van den Brink, J., Felser, C. & Yan, B. Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2. 2D Mater. 5, 044001 (2018).
Yuan, H. et al. Zeeman-type spin splitting controlled by an electric field. Nat. Phys. 9, 563–569 (2013).
Klein, J. et al. Electric-field switchable second-harmonic generation in bilayer MoS2 by inversion symmetry breaking. Nano Lett. 17, 392–398 (2016).
Woods, C. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).
Yankowitz, M., Ma, Q., Jarillo-Herrero, P. & LeRoy, B. J. van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).
Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
Gorbachev, R. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014).
Giovannetti, G., Khomyakov, P. A., Brocks, G., Kelly, P. J. & Van Den Brink, J. Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Phys. Rev. B 76, 073103 (2007).
Stepanov, E. A. et al. Direct observation of incommensurate–commensurate transition in graphene-hBN heterostructures via optical second harmonic generation. ACS Appl. Mater. Interfaces 12, 27758–27764 (2020).
Wang, E. et al. Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride. Nat. Phys. 12, 1111–1115 (2016).
Zhu, M. J. et al. Edge currents shunt the insulating bulk in gapped graphene. Nat. Commun. 8, 14552 (2017).
Chen, Z.-G. et al. Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures. Nat. Commun. 5, 4461 (2014).
Jung, J., DaSilva, A. M., MacDonald, A. H. & Adam, S. Origin of band gaps in graphene on hexagonal boron nitride. Nat. Commun. 6, 6308 (2015).
Yankowitz, M. et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure. Nature 557, 404–408 (2018).
Yankowitz, M., Watanabe, K., Taniguchi, T., San-Jose, P. & LeRoy, B. J. Pressure-induced commensurate stacking of graphene on boron nitride. Nat. Commun. 7, 13168 (2016).
Zhou, S. Y. et al. Substrate-induced bandgap opening in epitaxial graphene. Nat. Mater. 6, 770–775 (2007). This study represents one of the earliest reports to engineer inversion symmetry breaking through staggered sublattice potential.
Pletikosić, I. et al. Dirac cones and minigaps for graphene on Ir(111). Phys. Rev. Lett. 102, 056808 (2009).
Varykhalov, A. et al. Intact Dirac cones at broken sublattice symmetry: photoemission study of graphene on Ni and Co. Phys. Rev. X 2, 041017 (2012).
Lin, C.-L. et al. Substrate-induced symmetry breaking in silicene. Phys. Rev. Lett. 110, 076801 (2013).
Xu, X. et al. Interfacial engineering in graphene bandgap. Chem. Soc. Rev. 47, 3059–3099 (2018).
Jiang, T. et al. Valley and band structure engineering of folded MoS2 bilayers. Nat. Nanotechnol. 9, 825–829 (2014).
Hsu, W.-T. et al. Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers. ACS Nano 8, 2951–2958 (2014). This study represents one of the earliest reports to engineer inversion symmetry breaking through interlayer twist angle.
Carr, S. et al. Twistronics: manipulating the electronic properties of two-dimensional layered structures through their twist angle. Phys. Rev. B 95, 075420 (2017).
Du, L., Dai, Y. & Sun, Z. Twisting for tunable nonlinear optics. Matter 3, 987–988 (2020).
Yang, F. et al. Tunable second harmonic generation in twisted bilayer graphene. Matter 3, 1361–1376 (2020).
Kim, C.-J. et al. Stacking order dependent second harmonic generation and topological defects in h-BN bilayers. Nano Lett. 13, 5660–5665 (2013).
Yasuda, K., Wang, X., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Stacking-engineered ferroelectricity in bilayer boron nitride. Preprint at arXiv https://arxiv.org/abs/2010.06600 (2020).
Suzuki, R. et al. Valley-dependent spin polarization in bulk MoS2 with broken inversion symmetry. Nat. Nanotechnol. 9, 611–617 (2014).
Scuri, G. et al. Electrically tunable valley dynamics in twisted WSe2/WSe2 bilayers. Phys. Rev. Lett. 124, 217403 (2020).
Du, L. et al. Robust circular polarization of indirect Q-K transitions in bilayer 3R–WS2. Phys. Rev. B 100, 161404 (2019).
Yao, K. et al. Nonlinear twistoptics at symmetry-broken interfaces. Preprint at arXiv https://arxiv.org/abs/2006.13802 (2020).
Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016). This paper demonstrated the ‘tear-and-stack’ technique to control the interlayer twist angle to within 0.1° accuracy.
Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).
Du, L. et al. Modulating PL and electronic structures of MoS2/graphene heterostructures via interlayer twisting angle. Appl. Phys. Lett. 111, 263106 (2017).
Liao, M. et al. Precise control of the interlayer twist angle in large scale MoS2 homostructures. Nat. Commun. 11, 2153 (2020).
Manzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A. 2D transition metal dichalcogenides. Nat. Rev. Mater. 2, 17033 (2017).
Yang, H., Kim, S. W., Chhowalla, M. & Lee, Y. H. Structural and quantum-state phase transitions in van der Waals layered materials. Nat. Phys. 13, 931–937 (2017).
Du, L. et al. Giant valley coherence at room temperature in 3R WS2 with broken inversion symmetry. Research 2019, 6494565 (2019).
Li, Y., Duerloo, K.-A. N., Wauson, K. & Reed, E. J. Structural semiconductor-to-semimetal phase transition in two-dimensional materials induced by electrostatic gating. Nat. Commun. 7, 10671 (2016).
Wang, Y. et al. Structural phase transition in monolayer MoTe2 driven by electrostatic doping. Nature 550, 487–491 (2017). This study represents one of the earliest reports to control the crystal phase through electrostatic doping.
Kappera, R. et al. Phase-engineered low-resistance contacts for ultrathin MoS2 transistors. Nat. Mater. 13, 1128–1134 (2014).
Lin, Y.-C., Dumcenco, D. O., Huang, Y.-S. & Suenaga, K. Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS2. Nat. Nanotechnol. 9, 391–396 (2014).
Zhu, J. et al. Argon plasma induced phase transition in monolayer MoS2. J. Am. Chem. Soc. 139, 10216–10219 (2017).
Zhang, K. et al. Raman signatures of inversion symmetry breaking and structural phase transition in type-II Weyl semimetal MoTe2. Nat. Commun. 7, 13552 (2016).
Keum, D. H. et al. Bandgap opening in few-layered monoclinic MoTe2. Nat. Phys. 11, 482–486 (2015).
Chen, S.-Y., Goldstein, T., Venkataraman, D., Ramasubramaniam, A. & Yan, J. Activation of new Raman modes by inversion symmetry breaking in type II Weyl semimetal candidate T′-MoTe2. Nano Lett. 16, 5852–5860 (2016).
Duerloo, K.-A. N., Li, Y. & Reed, E. J. Structural phase transitions in two-dimensional Mo- and W-dichalcogenide monolayers. Nat. Commun. 5, 4214 (2014).
Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019).
Cho, S. et al. Phase patterning for ohmic homojunction contact in MoTe2. Science 349, 625–628 (2015).
Wang, J., Zhu, B.-F. & Liu, R.-B. Second-order nonlinear optical effects of spin currents. Phys. Rev. Lett. 104, 256601 (2010).
Werake, L. K. & Zhao, H. Observation of second-harmonic generation induced by pure spin currents. Nat. Phys. 6, 875–878 (2010).
Balog, R. et al. Bandgap opening in graphene induced by patterned hydrogen adsorption. Nat. Mater. 9, 315–319 (2010).
Gibertini, M., Koperski, M., Morpurgo, A. & Novoselov, K. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 14, 408–419 (2019).
Burch, K. S., Mandrus, D. & Park, J.-G. Magnetism in two-dimensional van der Waals materials. Nature 563, 47–52 (2018).
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).
Jiang, S., Shan, J. & Mak, K. F. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater. 17, 406–410 (2018).
Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotechnol. 13, 544–548 (2018).
Jiang, S., Li, L., Wang, Z., Mak, K. F. & Shan, J. Controlling magnetism in 2D CrI3 by electrostatic doping. Nat. Nanotechnol. 13, 549–553 (2018).
Zhang, Y. et al. Switchable magnetic bulk photovoltaic effect in the two-dimensional magnet CrI3. Nat. Commun. 10, 3783 (2019).
Klein, D. R. et al. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science 360, 1218–1222 (2018).
Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 360, 1214–1218 (2018).
Wang, Z. et al. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3. Nat. Commun. 9, 2516 (2018).
Xia, F., Wang, H., Hwang, J. C. M., Neto, A. H. C. & Yang, L. Black phosphorus and its isoelectronic materials. Nat. Rev. Phys. 1, 306–317 (2019).
Li, L. et al. Emerging in-plane anisotropic two-dimensional materials. InfoMat 1, 54–73 (2019).
Autere, A. et al. Rapid and large-area characterization of exfoliated black phosphorus using third-harmonic generation microscopy. J. Phys. Chem. Lett. 8, 1343–1350 (2017).
Sturman, B. I. & Fridkin, V. M. Photovoltaic and Photo-refractive Effects in Noncentrosymmetric Materials Vol. 8 (CRC Press, 1992).
Zhang, Y. et al. Enhanced intrinsic photovoltaic effect in tungsten disulfide nanotubes. Nature 570, 349–353 (2019). This study represents one of the earliest reports to engineer C3 rotational symmetry breaking through reducing the effective dimensionality.
Osterhoudt, G. B. et al. Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater. 18, 471–475 (2019).
Yuan, H. et al. Polarization-sensitive broadband photodetector using a black phosphorus vertical p–n junction. Nat. Nanotechnol. 10, 707–713 (2015).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015). This study predicted the nonlinear Hall effect and Berry curvature dipole in materials where both inversion and C3 rotational symmetries are broken.
Lee, J., Wang, Z., Xie, H., Mak, K. F. & Shan, J. Valley magnetoelectricity in single-layer MoS2. Nat. Mater. 16, 887–891 (2017).
Son, J., Kim, K.-H., Ahn, Y. H., Lee, H.-W. & Lee, J. Strain engineering of the Berry curvature dipole and valley magnetization in monolayer MoS2. Phys. Rev. Lett. 123, 036806 (2019).
Zelisko, M. et al. Anomalous piezoelectricity in two-dimensional graphene nitride nanosheets. Nat. Commun. 5, 4284 (2014).
Ho, S.-C. et al. Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene. Preprint at arXiv https://arxiv.org/abs/1910.07509 (2019).
Alexeev, E. M. et al. Emergence of highly linearly polarized interlayer exciton emission in MoSe2/WSe2 heterobilayers with transfer-induced layer corrugation. ACS Nano 14, 11110–11119 (2020).
Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).
Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).
Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).
Frisenda, R. et al. Symmetry breakdown in franckeite: spontaneous strain, rippling, and interlayer moiré. Nano Lett. 20, 1141–1147 (2020).
Guinea, F., Katsnelson, M. & Geim, A. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30–33 (2010).
Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).
Yang, R., Shi, Z., Zhang, L., Shi, D. & Zhang, G. Observation of Raman g-peak split for graphene nanoribbons with hydrogen-terminated zigzag edges. Nano Lett. 11, 4083–4088 (2011).
Wu, J. B. et al. Monolayer molybdenum disulfide nanoribbons with high optical anisotropy. Adv. Opt. Mater. 4, 756–762 (2016).
Cui, X. et al. Rolling up transition metal dichalcogenide nanoscrolls via one drop of ethanol. Nat. Commun. 9, 1301 (2018).
Cook, A. M., Fregoso, B. M., De Juan, F., Coh, S. & Moore, J. E. Design principles for shift current photovoltaics. Nat. Commun. 8, 14176 (2017).
Thiel, L. et al. Probing magnetism in 2D materials at the nanoscale with single-spin microscopy. Science 364, 973–976 (2019).
Song, T. et al. Switching 2D magnetic states via pressure tuning of layer stacking. Nat. Mater. 18, 1298–1302 (2019).
Li, T. et al. Pressure-controlled interlayer magnetism in atomically thin CrI3. Nat. Mater. 18, 1303–1308 (2019).
Yan, J. et al. Stacking-dependent interlayer coupling in trilayer MoS2 with broken inversion symmetry. Nano Lett. 15, 8155–8161 (2015).
Jiang, P. et al. Stacking tunable interlayer magnetism in bilayer CrI3. Phys. Rev. B 99, 144401 (2019).
Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2, 177–180 (2006).
Taychatanapat, T., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene. Nat. Phys. 7, 621–625 (2011).
Li, L. et al. Quantum Hall effect in black phosphorus two-dimensional electron system. Nat. Nanotechnol. 11, 593–597 (2016).
Bandurin, D. A. et al. High electron mobility, quantum Hall effect and anomalous optical response in atomically thin InSe. Nat. Nanotechnol. 12, 223–227 (2016).
Aivazian, G. et al. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys. 11, 148–152 (2015).
Srivastava, A. et al. Valley Zeeman effect in elementary optical excitations of monolayer WSe2. Nat. Phys. 11, 141–147 (2015).
Zhang, X.-X. et al. Zeeman-induced valley-sensitive photocurrent in monolayer MoS2. Phys. Rev. Lett. 122, 127401 (2019).
Li, Y. et al. Valley splitting and polarization by the Zeeman effect in monolayer MoSe2. Phys. Rev. Lett. 113, 266804 (2014).
Wang, Z., Shan, J. & Mak, K. F. Valley- and spin-polarized Landau levels in monolayer WSe2. Nat. Nanotechnol. 12, 144–149 (2017).
Roch, J. G. et al. First-order magnetic phase transition of mobile electrons in monolayer MoS2. Phys. Rev. Lett. 124, 187602 (2020).
Back, P. et al. Giant paramagnetism-induced valley polarization of electrons in charge-tunable monolayer MoSe2. Phys. Rev. Lett. 118, 237404 (2017).
Zhang, J. et al. Enhancing and controlling valley magnetic response in MoS2/WS2 heterostructures by all-optical route. Nat. Commun. 10, 4226 (2019).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Sie, E. J. et al. Large, valley-exclusive Bloch-Siegert shift in monolayer WS2. Science 355, 1066–1069 (2017).
Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).
Kim, J. et al. Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2 monolayers. Science 346, 1205–1208 (2014). This study represents one of the earliest reports to engineer time-reversal symmetry breaking through coherent light–matter interaction.
Ye, Z., Sun, D. & Heinz, T. F. Optical manipulation of valley pseudospin. Nat. Phys. 13, 26–29 (2017).
Scharf, B., Xu, G., Matos-Abiague, A. & Žutić, I. Magnetic proximity effects in transition-metal dichalcogenides: converting excitons. Phys. Rev. Lett. 119, 127403 (2017).
Zhong, D. et al. Layer-resolved magnetic proximity effect in van der Waals heterostructures. Nat. Nanotechnol. 15, 187–191 (2020).
Wang, Z., Tang, C., Sachs, R., Barlas, Y. & Shi, J. Proximity-induced ferromagnetism in graphene revealed by the anomalous Hall effect. Phys. Rev. Lett. 114, 016603 (2015). This study represents one of the earliest reports to engineer time-reversal symmetry breaking through magnetic proximity effects.
Wei, P. et al. Strong interfacial exchange field in the graphene/EuS heterostructure. Nat. Mater. 15, 711–716 (2016).
Zhao, C. et al. Enhanced valley splitting in monolayer WSe2 due to magnetic exchange field. Nat. Nanotechnol. 12, 757–762 (2017).
Zhong, D. et al. Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics. Sci. Adv. 3, e1603113 (2017).
Ciorciaro, L., Kroner, M., Watanabe, K., Taniguchi, T. & Imamoglu, A. Observation of magnetic proximity effect using resonant optical spectroscopy of an electrically tunable MoSe2/CrBr3 heterostructure. Phys. Rev. Lett. 124, 197401 (2020).
Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).
Zhang, J. et al. Topology-driven magnetic quantum phase transition in topological insulators. Science 339, 1582–1586 (2013).
Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).
Zhou, J. et al. Synthesis of co-doped MoS2 monolayers with enhanced valley splitting. Adv. Mater. 32, 1906536 (2020).
Li, B. et al. A two-dimensional Fe-doped SnS2 magnetic semiconductor. Nat. Commun. 8, 1958 (2017).
Han, W., Kawakami, R. K., Gmitra, M. & Fabian, J. Graphene spintronics. Nat. Nanotechnol. 9, 794–807 (2014).
González-Herrero, H. et al. Atomic-scale control of graphene magnetism by using hydrogen atoms. Science 352, 437–441 (2016).
Tilley, D. R. Superfluidity and Superconductivity (Routledge, 2019).
Ye, J. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).
Costanzo, D., Jo, S., Berger, H. & Morpurgo, A. F. Gate-induced superconductivity in atomically thin MoS2 crystals. Nat. Nanotechnol. 11, 339–344 (2016).
Saito, Y. et al. Superconductivity protected by spin–valley locking in ion-gated MoS2. Nat. Phys. 12, 144–149 (2015).
Lu, J. et al. Full superconducting dome of strong Ising protection in gated monolayer WS2. Proc. Natl Acad. Sci. USA 115, 3551–3556 (2018).
Sohn, E. et al. An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe2. Nat. Mater. 17, 504–508 (2018).
Tsen, A. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nat. Phys. 12, 208–212 (2016).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019).
Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).
Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
Zhang, Y.-H., Po, H. C. & Senthil, T. Landau level degeneracy in twisted bilayer graphene: Role of symmetry breaking. Phys. Rev. B 100, 125104 (2019).
Chatterjee, S., Bultinck, N. & Zaletel, M. P. Symmetry breaking and skyrmionic transport in twisted bilayer graphene. Phys. Rev. B 101, 165141 (2020).
Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).
Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Preprint at arXiv https://arxiv.org/abs/2004.04148 (2020).
Jin, C. et al. Stripe phases in WSe2/WS2 moiré superlattices. Preprint at arXiv https://arxiv.org/abs/2007.12068 (2020).
Liu, C.-C., Zhang, L.-D., Chen, W.-Q. & Yang, F. Chiral spin density wave and d + id superconductivity in the magic-angle-twisted bilayer graphene. Phys. Rev. Lett. 121, 217001 (2018).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
Zhou, Y. et al. Signatures of bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Preprint at arXiv https://arxiv.org/abs/2010.03037 (2020).
Smoleński, T. et al. Observation of Wigner crystal of electrons in a monolayer semiconductor. Preprint at arXiv https://arxiv.org/abs/2010.03078 (2020).
Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).
Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).
Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).
Delaney, P., Choi, H. J., Ihm, J., Louie, S. G. & Cohen, M. L. Broken symmetry and pseudogaps in ropes of carbon nanotubes. Nature 391, 466–468 (1998).
Chen, Y.-J., Cain, J. D., Stanev, T. K., Dravid, V. P. & Stern, N. P. Valley-polarized exciton–polaritons in a monolayer semiconductor. Nat. Photonics 11, 431–435 (2017).
Sun, Z. et al. Optical control of room-temperature valley polaritons. Nat. Photonics 11, 491–496 (2017).
Lundt, N. et al. Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor. Nat. Nanotechnol. 14, 770–775 (2019).
Lu, J. et al. Observation of topological valley transport of sound in sonic crystals. Nat. Phys. 13, 369–374 (2017).
Li, F., Huang, X., Lu, J., Ma, J. & Liu, Z. Weyl points and Fermi arcs in a chiral phononic crystal. Nat. Phys. 14, 30–34 (2018).
Dong, J.-W., Chen, X.-D., Zhu, H., Wang, Y. & Zhang, X. Valley photonic crystals for control of spin and topology. Nat. Mater. 16, 298–302 (2017).
Noh, J., Huang, S., Chen, K. P. & Rechtsman, M. C. Observation of photonic topological valley Hall edge states. Phys. Rev. Lett. 120, 063902 (2018).
Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).
Ji, S.-C. et al. Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas. Nat. Phys. 10, 314–320 (2014).
Acknowledgements
The authors gratefully acknowledge the financial support by the Academy of Finland (grant nos. 314810, 333982, 336144, 336818 and 333099), the Academy of Finland Flagship Programme (PREIN), the EU H2020-MSCA-RISE-872049 (IPN-Bio), the National Key R&D Program of China (grant nos. 2020YFA0308800), the NSF of China (grants nos. 11734003, 12061131002), the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB30000000), EPSRC (grant no. EP/T014601/1), the European Union’s Horizon 2020 research and innovation programme (grant no. 820423, S2QUIP) and the European Research Council (ERC) (grant no. 834742). C.N.L. acknowledges the support of DOE BES DE-SC0020187, NSF DMR 1807928 and 1922076.
Author information
Authors and Affiliations
Contributions
L.D. and Z.S. conceived the idea and led the writing. T.H. contributed substantially to the discussion of the content. All authors reviewed and edited the manuscript before submission.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information
Nature Reviews Physics thanks Shuyun Zhou and the other, anonymous, reviewers for their contribution to the peer review of this work.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Du, L., Hasan, T., Castellanos-Gomez, A. et al. Engineering symmetry breaking in 2D layered materials. Nat Rev Phys 3, 193–206 (2021). https://doi.org/10.1038/s42254-020-00276-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42254-020-00276-0
This article is cited by
-
Interfacial magnetic spin Hall effect in van der Waals Fe3GeTe2/MoTe2 heterostructure
Nature Communications (2024)
-
Interlayer exciton dynamics of transition metal dichalcogenide heterostructures under electric fields
Nano Research (2024)
-
Superconducting tunnel junctions with layered superconductors
Quantum Frontiers (2024)
-
Reversible non-volatile electronic switching in a near-room-temperature van der Waals ferromagnet
Nature Communications (2024)
-
Sequential order dependent dark-exciton modulation in bi-layered TMD heterostructure
Nature Communications (2023)
