Topological Winding Number Change and Broken Inversion Symmetry in a Hofstadter鈥檚 Butterfly

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• 作者：Peng Wang ; Bin Cheng ; Oleg Martynov ; Tengfei Miao ; Lei Jing ; Takashi Taniguchi ; Kenji Watanabe ; Vivek Aji ; Chun Ning Lau ; Marc Bockrath
• 刊名：Nano Letters
• 出版年：2015
• 出版时间：October 14, 2015
• 年：2015
• 卷：15
• 期：10
• 页码：6395-6399
• 全文大小：327K
• ISSN：1530-6992

文摘

Graphene鈥檚 quantum Hall features are associated with a 蟺 Berry鈥檚 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鈥檚 electronic spectrum, and under a magnetic field, a Hofstadter butterfly-like energy spectrum. Here we report an additional 蟺 Berry鈥檚 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 鈭?00 K, demonstrating the robustness of the fractal energy spectrum in these systems.