title: Topological Winding Number Change and Broken Inversion Symmetry in a Hofstadter's Butterfly.
abstract: Graphene's quantum Hall features are associated with a π Berry's phase due to its odd topological pseudospin winding number. In nearly aligned graphene-hexagonal BN heterostructures, the lattice and orientation mismatch produce a superlattice potential, yielding secondary Dirac points in graphene's electronic spectrum, and under a magnetic field, a Hofstadter butterfly-like energy spectrum. Here we report an additional π Berry's phase shift when tuning the Fermi level past the secondary Dirac points, originating from a change in topological winding number from odd to even when the Fermi-surface electron orbit begins to enclose the secondary Dirac points. At large hole doping inversion symmetry breaking generates a distinct hexagonal pattern in the longitudinal resistivity versus magnetic field and charge density. Major Hofstadter butterfly features persist up to ∼100 K, demonstrating the robustness of the fractal energy spectrum in these systems.
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Peng
authors.initials: P
authors.lastname: Wang
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Bin
authors.initials: B
authors.lastname: Cheng
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Oleg
authors.initials: O
authors.lastname: Martynov
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Tengfei
authors.initials: T
authors.lastname: Miao
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Lei
authors.initials: L
authors.lastname: Jing
authors.affiliation: Advanced Materials Laboratory, National Institute for Materials Science , Tsukuba, Ibaraki 305-0044, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Taniguchi
authors.affiliation: Advanced Materials Laboratory, National Institute for Materials Science , Tsukuba, Ibaraki 305-0044, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Watanabe
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Vivek
authors.initials: V
authors.lastname: Aji
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Chun Ning
authors.initials: CN
authors.lastname: Lau
authors.affiliation: Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
authors.forename: Marc
authors.initials: M
authors.lastname: Bockrath
keywords: Hofstadter butterfly; boron nitride; graphene; moiré superlattice; quantum Hall effect; topological