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Topological Winding Number Change and Broken Inversion Symmetry in a Hofstadter’s Butterfly
journal contribution
posted on 2015-10-14, 00:00 authored by Peng Wang, Bin Cheng, Oleg Martynov, Tengfei Miao, Lei Jing, Takashi Taniguchi, Kenji Watanabe, Vivek Aji, Chun Ning Lau, Marc BockrathGraphene’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.