Abstract
Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon–polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin–valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.
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Data availability
The data shown in Figs. 1, 2 and 4 are available from the Harvard Dataverse Repository at https://doi.org/10.7910/DVN/SU00ZW. The datasets generated during and/or analysed during this study are available from the corresponding authors upon reasonable request.
Code availability
The code shown in Fig. 1b–d,f,g to generate band structures is available from the Harvard Dataverse Repository at https://doi.org/10.7910/DVN/SU00ZW.
Change history
15 January 2024
A Correction to this paper has been published: https://doi.org/10.1038/s41565-024-01604-6
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Acknowledgements
We acknowledge helpful discussions with J. Liu, S. Wang, Y. Zhang and F. Wang. This work is supported by the National Key Research Program of China (grant nos. 2020YFA0309000, 2021YFA1400100, 2021YFA1202902 and 2022YFA1402401), NSF of China (grant nos.12174248 and 12074244) and SJTU no. 21X010200846. G.C. acknowledges sponsorship from the Yangyang Development Fund. We acknowledge support from the Korean NRF through grant no. 2020R1A2C3009142 for F.L. and 2020R1A5A1016518 for Y.P. J. Jung acknowledges support from Samsung Science and Technology Foundation (grant no. SSTF-BA1802-06). K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 20H00354, 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. This research used resources of the Center for High Performance Computing at Shanghai Jiao Tong University.
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G.C. supervised the project. K.L. and J.Z. fabricated the devices and performed the transport measurements with the assistance of Y.S. and B.L. K.L. and Z.S. performed the near-field infrared and AFM measurements. K.L., F.L., Y.R., Y.P., W.L. and J. Jung calculated the band structures. K.W. and T.T. grew the hBN single crystals. K.L., J.Z., Y.S., J. Jung and G.C. analysed the data. K.L., Z.S., J. Jung and G.C. wrote the paper with input from all authors.
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Extended data
Extended Data Fig. 1 Wavelength dependent SNOM contrast of ABCA and ABAB regions.
a, Schematic diagram of a scattering-type scanning near-field optical microscope (s-SNOM). The wavelength of quantum cascade laser is tunable from 900 to 1675 cm−1, allowing us to find a best wavelength for the phonon-polariton assisted infrared imaging of graphene under hBN. The beam splitter and lens are both made of ZnSe, and the scattered light signal is collected by an HgCdTe detector working at liquid nitrogen temperature in the far field. b–m, IR-SNOM images of the same tetra-layer graphene sample with that in Fig. 2c–e at different incident wavelength ranging from 1000 to 1600 cm−1. Only when the incident wavelength lies in the hBN Reststrahlen (1370 ~ 1610 cm−1), ABAB and ABCA regions can be clearly distinguished. Between 1500 ~ 1600 cm−1, ABCA is always darker than ABAB (j ~ m), between 1400 ~ 1500 cm−1, ABAB should be darker (Fig. h, i). Below 1350 cm−1 there is no obvious boundary between ABCA and ABAB and the contrast is weak. The hBN thickness is about 35 nm.
Extended Data Fig. 2 Arrhenius plot.
ln(ρxx) versus temperature at different displacement fields. The transport gap Δ in Fig. 3c is extracted according to thermal activation equation ρxx ∝ e−Δ/2kBT. The dashed lines in a to d represent the linear regions to estimate the gap. a and d correspond to LPI, b and c correspond to LAF, e corresponds to IS which shows the metallic behavior when temperature is lower than 14 K.
Extended Data Fig. 3 A possible phase transition.
a, Zoomed-in plot of resistivity ρxx as a function of displacement field D at various temperatures for the device shown in the main text. b, Normalized resistivity \({\rho }_{{\rm{xx}}}/{\rho }_{{\rm{xx}}}^{D=0}\) as a function of D at typical temperatures, where \({\rho }_{{\rm{xx}}}^{D=0}\) is the resistivity when D = 0.
Extended Data Fig. 4 Comparison of the response to the vertical and parallel magnetic field focusing around D = 0.
a, ρxx − D plot at B = 0 T; B⊥ = 0 T, B// = 12 T and B⊥ = 12 T, B// = 0 T. b, ρxx − n plot at B⊥ = 4 T, B// = 11 T and B⊥ = 4 T, B// = 0 T. Both data show parallel magnetic field have little influence on the correlated insulator state around CNP. A rotating probe is used to relatively change the direction of magnetic field. According to the measurement of Hall resistance, pure in-plane or out of plane magnetic field (error within 0.1°) can be applied to sample.
Extended Data Fig. 5 Hopping parameters and spontaneous degeneracy breaking.
a, Illustration of the intralayer and interlayer tight-binding hopping terms of ABCA multilayer graphene used in this work. b, Layer resolved distribution of electrons and holes for charge neutral QAH, LAF, and flavor Fi, and F phases illustrating the layer polarization of the four spin-valley flavors (K ↑ , K′ ↑ , K ↓ , K′↓,). c, k-point mesh grid of the first Brillouin zone where the dense grid near two Dirac points, K and K’, is equivalent to 576 × 576 k points, and the coarse grid for the rest of the area is to 18 × 18 k points. We show electric field dependent variations on d band gap (Δgap), e total energy (Etot), f the sum of band (Eband) and Hartree (EH) energy, and g exchange energy (EX) for each phase.
Extended Data Fig. 6 Illustrations of spontaneous broken-symmetry states at charge neutral point.
Illustrations of layer polarized insulator (LPI, also named as F phase), quantum anomalous Hall insulator (QAH), ALL (Fi) state and quantum spin Hall insulator (QSH). K and K’ indicate two valleys, arrows indicate spin up and down, and black and grey planes indicate graphene layers.
Extended Data Fig. 7 Correlated insulating state at device 2.
a, ρ – n – D color plot of device 2, it shows a log color scale from 4 to 40 kΩ. b, Left axis corresponds to plot of ρxx at different D and fixed n and B of 0 for temperatures ranging from 1.5 K to 160 K. Right axis is the corresponding displacement field dependence of gap Δ. Device 2 gives almost the same gap with device 1 in the main text.
Extended Data Fig. 8 Correlated insulating state and SP & SVP states at device 3.
a, ρ - n - D color plot of device 3 when temperature T = 3.7 K, it shows a log color scale from 50 to 1 MΩ. b, Corresponding R - n - D color plot when B = 5 T. SP and SVP occur at the similar regions with device 1 in the main text.
Extended Data Fig. 9 Phase boundary between IV and V.
n – B// color plot of resistivity at D = −0.33 V/nm between region IV and V. The phase boundary between IV and V doesn’t move under in-plane magnetic field.
Extended Data Fig. 10 Landau level fan of device 1 (the same sample in the main text).
ρ – n – B color plot of device 1 at D = 0.3 V/nm when T = 1.5 K. SP and SVP states are also prominent in the landau level fan diagram which is indicated by blue and red triangles, and their area would develop with magnetic field since the Zeeman energy of spin and orbital should be changed (red and blue dashed lines show the boundary of SP and SVP. above the dashed line, all the degeneracy is open by the large magnetic field). The area of the SP metal indicted by the left hand side red triangle is almost unchanged, we ascribe it as a fully spin polarized region but the SP metal indicted by the right hand side red triangle as a partially spin polarized region.
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Liu, K., Zheng, J., Sha, Y. et al. Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene. Nat. Nanotechnol. 19, 188–195 (2024). https://doi.org/10.1038/s41565-023-01558-1
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DOI: https://doi.org/10.1038/s41565-023-01558-1
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