Abstract Moiré superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moiré systems has been at the foreground. However, the implications of moiré band topology within the single-particle framework are little explored experimentally. An outstanding problem is understanding the effect of band topology on Hofstadter physics, which does not require electron correlations. Our work experimentally studies Chern state switching in the Hofstadter regime using twisted double bilayer graphene (TDBG), which offers electric field tunable topological bands, unlike twisted bilayer graphene. Here we show that the nontrivial topology reflects in the Hofstadter spectra, in particular, by displaying a cascade of Hofstadter gaps that switch their Chern numbers sequentially while varying the perpendicular electric field. Our experiments together with theoretical calculations suggest a crucial role of charge polarization changing concomitantly with topological transitions in this system. Layer polarization is likely to play an important role in the topological states in few-layer twisted systems. Moreover, our work establishes TDBG as a novel Hofstadter platform with nontrivial magnetoelectric coupling.
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Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle
Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θ m1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θ m2 ∼ 0.5°, which cannot be explained without considering electron–election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.
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- Award ID(s):
- 1643312
- NSF-PAR ID:
- 10288459
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 30
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- e2100006118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Engineering moiré superlattices by twisting layers in van der Waals (vdW) heterostructures has uncovered a wide array of quantum phenomena. We constructed a vdW heterostructure that consists of three graphene layers stacked with alternating twist angles ±θ. At the average twist angle θ ~ 1.56°, a theoretically predicted “magic angle” for the formation of flat electron bands, we observed displacement field–tunable superconductivity with a maximum critical temperature of 2.1 kelvin. By tuning the doping level and displacement field, we found that superconducting regimes occur in conjunction with flavor polarization of moiré bands and are bounded by a van Hove singularity (vHS) at high displacement fields. Our findings display inconsistencies with a weak coupling description, suggesting that the observed moiré superconductivity has an unconventional nature.
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At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θGr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.more » « less
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Dirac Fermion Cloning, Moiré Flat Bands, and Magic Lattice Constants in Epitaxial Monolayer Graphenemore » « less
Abstract Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D material, enhance electron correlations, and give rise to novel condensed‐matter phases such as superconductors, Mott insulators, Wigner crystals, and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. In this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moiré flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the supercell of graphene. The results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many‐body quantum phases arising from interactions between Dirac electrons.
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Collective excitations contain key information regarding the electronic order of the ground state of strongly correlated systems. Various collective modes in the spin and valley isospin channels of magic-angle graphene moiré bands have been alluded to by a series of recent experiments. However, a direct observation of collective excitations has been impossible due to the lack of a spin probe. Here we observe low-energy collective excitations in twisted bilayer graphene near the magic angle, using a resistively detected electron spin resonance technique. Two independent observations show that the generation and detection of microwave resonance relies on the strong correlations within the flat moiré energy band. First, the onset of the resonance response coincides with the spontaneous flavour polarization at moiré half-filling, but is absent in the isospin unpolarized density range. Second, we perform the same measurement on various systems that do not have flat bands and observe no indication of a resonance response in these samples. Our explanation is that the resonance response near the magic angle originates from Dirac revivals and the resulting isospin order.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2100006118
