# Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene

June 5, 2014**Fractional quantum Hall states in bilayer graphene:** (**A** and **C**) Inverse compressibility as a function of filling factor and magnetic field. The color scales are the same in both panels. (**B** and **D**) Average inverse compressibility between *B* = 7.9 and 11.9 T as a function of filling factor. Colors indicate regions of similar behavior in the background inverse compressibility. (**E** and **F**) Inverse compressibility as a function of filling factor and magnetic field near ν = *–*7/5 and 3/5. (**G**) Diagram highlighting the differences in background inverse compressibility between ν = 2*p* and ν = 2*p* + 1 in purple and ν = 2*p* + 1 and ν = 2*p* in blue. [From A. Kou, B. E. Feldman, A. J. Levin, B. I. Halperin, K. Watanabe, T. Taniguchi, A. Yacoby, "Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene," *Science* 345 (4 July 2014) | DOI: 10.1126/science.1250270. Reprinted with permission from AAAS.]

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. In a recent Report in *Science*, Professors Bertrand Halperin and Amir Yacoby, with a team of scientists from Harvard, Yale, and National Institute for Materials Science, Tsukuba, Japan, presented local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. They observed incompressible FQH states at filling factors ν = 2*p* + 2/3 with hints of additional states appearing at ν = 2*p* + 3/5, where *p* = *–*2, *–*1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a *ν *→* ν* + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.