Direct measurement of discrete valley and orbital quantum numbers in a multicomponent quantum Hall system B.M. Hunt1;2;3, J.I.A. Li2, A.A. Zibrov4, L. Wang5, T. Taniguchi6, K. Watanabe6, J. Hone5, C. R. Dean2, M. Zaletel7, R.C. Ashoori1, A.F. Young1;4;∗ 1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 2Department of Physics, Columbia University, New York, NY 10027, USA 3Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 5Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA 6Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan 7Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA 4Department of Physics, University of California, Santa Barbara CA 93106 USA ∗
[email protected] Strongly interacting two dimensional electron systems ence of internal degeneracy. The Bernal bilayer graphene (B- (2DESs) host a complex landscape of broken symmetry BLG) zero energy Landau level (ZLL) provides an extreme states. The possible ground states are further expanded by example of such degeneracy. In B-BLG, LLs jξNσi are la- internal degrees of freedom such as spin or valley-isospin. beled by their electron spin σ ="; #, valley ξ = +; −, and While direct probes of spin in 2DESs were demonstrated “orbital” index N 2 Z. Electrons in valley +=− are local- two decades ago1, the valley quantum number has only ized near points K=K0 of the hexagonal Brillouin zone, while been probed indirectly in semiconductor quantum wells2, the index N is closely analogous to the LL-index of conven- graphene mono-3,4 and bilayers5–13, and, transition metal tional LL systems.