Department of Physics and Astronomy, University of California , Riverside, California 92521, United States.
Advanced Materials Laboratory, National Institute for Materials Science , Tsukuba, Ibaraki 305-0044, Japan.
Nano Lett. 2015 Oct 14;15(10):6395-9. doi: 10.1021/acs.nanolett.5b01568. Epub 2015 Oct 1.
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.
当费米能级越过二次狄拉克点时，石墨烯的电子能谱中会出现一个额外的π Berry 相移，这是由拓扑涡旋数从奇数变为偶数引起的，此时费米面电子轨道开始包围二次狄拉克点。
