Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours—such as spin or valley—that the electrons can possess and the excitation spectrum of the broken-symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with fourfold spin–valley degeneracy is a model system for such investigations, but the nature of its broken-symmetry states—particularly at partial fillings—is still not understood. Here we demonstrate a non-invasive spectroscopic technique with a scanning tunnelling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of the Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken-symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat-band platform, which is applicable to other graphene-based electronic systems.
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This content will become publicly available on June 1, 2024
Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride
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.
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- Award ID(s):
- 1904442
- NSF-PAR ID:
- 10465740
- Date Published:
- Journal Name:
- Low Temperature Physics
- Volume:
- 49
- Issue:
- 6
- ISSN:
- 1063-777X
- Page Range / eLocation ID:
- 655 to 661
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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