Unconventional ferroelectricity in moiré heterostructures

Keimer, B. & Moore, J. E. The physics of quantum materials. Nat. Phys. 13, 1045–1055 (2017).
Tokura, Y., Kawasaki, M. & Nagaosa, N. Emergent functions of quantum materials. Nat. Phys. 13, 1056–1068 (2017).
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Suárez Morell, E., Correa, J., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).
Li, G. et al. Observation of van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020); correction 581, E3 (2020).
Burg, G. W. et al. Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett. 123, 197702 (2019).
Liu, X. et al. Spin-polarized correlated insulator and superconductor in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020); correction 583, 215–220 (2020).
Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Nandkishore, R. & Levitov, L. Dynamical screening and excitonic instability in bilayer graphene. Phys. Rev. Lett. 104, 156803 (2010).
Fradkin, E., Kivelson, S. A., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).
Fu, L. Parity-breaking phases of spin–orbit-coupled metals with gyrotropic, ferroelectric, and multipolar orders. Phys. Rev. Lett. 115, 026401 (2015).
Fernandes, R. M. & Venderbos, J. W. Nematicity with a twist: rotational symmetry breaking in a moiré superlattice. Sci. Adv. 6, eaba8834 (2020).
Kozii, V. & Fu, L. Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin–orbit-coupled systems. Phys. Rev. Lett. 115, 207002 (2015).
Mishra, A. & Lee, S. Topological multiferroic phases in the extended Kane–Mele–Hubbard model in the Hofstadter regime. Phys. Rev. B 98, 235124 (2018).
Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Preprint at https://arxiv.org/abs/2004.04148 (2020).
Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
Choi, Y. et al. Imaging electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019); correction 15, 1205 (2019).
Zhang, Y.-H., Mao, D., Cao, Y., Jarillo-Herrero, P. & Senthil, T. Nearly flat Chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019).
McCann, E. & Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 76, 056503 (2013).
Li, J., Martin, I., Büttiker, M. & Morpurgo, A. F. Topological origin of subgap conductance in insulating bilayer graphene. Nat. Phys. 7, 38–42 (2011).
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).
Sui, M. et al. Gate-tunable topological valley transport in bilayer graphene. Nat. Phys. 11, 1027–1031 (2015).
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).
Ju, L. et al. Tunable excitons in bilayer graphene. Science 358, 907–910 (2017).
Maher, P. et al. Evidence for a spin phase transition at charge neutrality in bilayer graphene. Nat. Phys. 9, 154–158 (2013).
Hunt, B. et al. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. Nat. Commun. 8, 948 (2017).
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).
Bao, W. et al. Evidence for a spontaneous gapped state in ultraclean bilayer graphene. Proc. Natl Acad. Sci. USA 109, 10802–10805 (2012).
Freitag, F., Trbovic, J., Weiss, M. & Schönenberger, C. Spontaneously gapped ground state in suspended bilayer graphene. Phys. Rev. Lett. 108, 076602 (2012).
Nam, Y., Ki, D.-K., Soler-Delgado, D. & Morpurgo, A. F. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 362, 324–328 (2018).
Fei, Z. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336–339 (2018).
Zhang, Y., Yuan, N. F. & Fu, L. Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices. Preprint at https://arxiv.org/abs/1910.14061 (2019).
Katayama, Y., Tsui, D., Manoharan, H., Parihar, S. & Shayegan, M. Charge transfer at double-layer to single-layer transition in double-quantum-well systems. Phys. Rev. B 52, 14817–14824 (1995).
Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).
Young, A. F. & Levitov, L. S. Capacitance of graphene bilayer as a probe of layer-specific properties. Phys. Rev. B 84, 085441 (2011).
Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013).
Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).
Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).
Ponomarenko, L. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).
Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
Finney, N. R. et al. Tunable crystal symmetry in graphene–boron nitride heterostructures with coexisting moiré superlattices. Nat. Nanotechnol. 14, 1029–1034 (2019).
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2, 177–180 (2006).
Craciun, M. et al. Trilayer graphene is a semimetal with a gate-tunable band overlap. Nat. Nanotechnol. 4, 383–388 (2009).
Jhang, S. H. et al. Stacking-order dependent transport properties of trilayer graphene. Phys. Rev. B 84, 161408 (2011).
Wang, H., Wu, Y., Cong, C., Shang, J. & Yu, T. Hysteresis of electronic transport in graphene transistors. ACS Nano 4, 7221–7228 (2010).
McGilly, L. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).