Intrinsic quantized anomalous Hall effect in a moiré heterostructure

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

July 2, 2019 | M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, A. F. Young
A quantum anomalous Hall (QAH) effect has been observed in twisted bilayer graphene (tBLG) with a flat band structure, showing Hall resistance quantized to within 0.1% of the von Klitzing constant $ h/e^2 $ at zero magnetic field. The effect arises from intrinsic strong correlations, which polarize the electron system into a single spin and valley resolved moiré miniband with Chern number $ C = 1 $. Unlike extrinsic systems, the measured transport energy gap $ \Delta/k_B \approx 27 $ K is larger than the Curie temperature $ T_C \approx 9 $ K, and Hall quantization persists to several Kelvin. Electrical currents as small as 1 nA can be used to switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory. Two-dimensional insulators are classified by the topology of their filled energy bands. In the absence of time reversal symmetry, nontrivial band topology manifests as a quantized Hall conductivity $ \sigma_{xy} = C \frac{e^2}{\hbar} $, where $ C \neq 0 $ is the total Chern number of the filled bands. The QAH effect has been observed in a narrow class of materials, including transition metal doped $ (\mathrm{Bi}, \mathrm{Sb})_2\mathrm{Te}_3 $, where magnetic ordering breaks time reversal symmetry. However, these materials are limited by inhomogeneous magnetic dopant distribution, leading to disorder. Moiré graphene heterostructures provide the necessary ingredients for intrinsic QAH effects, including topological bands and strong correlations. In tBLG with a twist angle $ \theta \approx 1.1^\circ $, the bandwidth of these Chern bands can be made exceptionally small, favoring correlation-driven states that break spin, valley, or lattice symmetries. Experiments have found correlation-driven low temperature phases at integer band fillings when these bands are sufficiently flat. States showing magnetic hysteresis indicative of time-reversal symmetry breaking have been reported in tBLG and ABC/hBN heterostructures at commensurate filling. The QAH effect in flat-band tBLG is observed with robust zero magnetic field quantization. The electronic structure of flat-band tBLG is described by two distinct bands per spin and valley projection, isolated from higher energy dispersive bands by an energy gap. The total capacity of the flat bands is eight electrons per unit cell, spanning $ -4 < \nu < 4 $, where $ \nu = n A_m $ with $ n $ the electron density and $ A_m \approx 130 \, nm^2 $ the area of the moiré unit cell. The Hall resistance $ R_{xy} $ approaches $ h/e^2 $ in a narrow range of density near $ \nu =A quantum anomalous Hall (QAH) effect has been observed in twisted bilayer graphene (tBLG) with a flat band structure, showing Hall resistance quantized to within 0.1% of the von Klitzing constant $ h/e^2 $ at zero magnetic field. The effect arises from intrinsic strong correlations, which polarize the electron system into a single spin and valley resolved moiré miniband with Chern number $ C = 1 $. Unlike extrinsic systems, the measured transport energy gap $ \Delta/k_B \approx 27 $ K is larger than the Curie temperature $ T_C \approx 9 $ K, and Hall quantization persists to several Kelvin. Electrical currents as small as 1 nA can be used to switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory. Two-dimensional insulators are classified by the topology of their filled energy bands. In the absence of time reversal symmetry, nontrivial band topology manifests as a quantized Hall conductivity $ \sigma_{xy} = C \frac{e^2}{\hbar} $, where $ C \neq 0 $ is the total Chern number of the filled bands. The QAH effect has been observed in a narrow class of materials, including transition metal doped $ (\mathrm{Bi}, \mathrm{Sb})_2\mathrm{Te}_3 $, where magnetic ordering breaks time reversal symmetry. However, these materials are limited by inhomogeneous magnetic dopant distribution, leading to disorder. Moiré graphene heterostructures provide the necessary ingredients for intrinsic QAH effects, including topological bands and strong correlations. In tBLG with a twist angle $ \theta \approx 1.1^\circ $, the bandwidth of these Chern bands can be made exceptionally small, favoring correlation-driven states that break spin, valley, or lattice symmetries. Experiments have found correlation-driven low temperature phases at integer band fillings when these bands are sufficiently flat. States showing magnetic hysteresis indicative of time-reversal symmetry breaking have been reported in tBLG and ABC/hBN heterostructures at commensurate filling. The QAH effect in flat-band tBLG is observed with robust zero magnetic field quantization. The electronic structure of flat-band tBLG is described by two distinct bands per spin and valley projection, isolated from higher energy dispersive bands by an energy gap. The total capacity of the flat bands is eight electrons per unit cell, spanning $ -4 < \nu < 4 $, where $ \nu = n A_m $ with $ n $ the electron density and $ A_m \approx 130 \, nm^2 $ the area of the moiré unit cell. The Hall resistance $ R_{xy} $ approaches $ h/e^2 $ in a narrow range of density near $ \nu =
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