Topological phases in a multi-band 2D electron gas.

Recent experiments have established the phase diagrams of mono-, bilayer and ABC-stacked trilayer graphene at the charge neutrality, but that in more complex cases of graphene multiband structures such as ABA-stacked trilayer graphene (TLG) have not been thoroughly investigated. We report transport studies in ABA-TLG where the effect of Coulomb interactions plays a crucial role in formation of the different orbital/spin/valley symmetries. We explore theoretically and experimentally the effect of magnetic and displacement fields on these symmetries within the $\nu {\rm g}=$ 0 quantum Hall state. Our experimental results indicate at least 5 different phases arise from multiband nature of TLG, with conductance ranging from 0.1e$^{\mathrm{2}}$/h, 2e$^{\mathrm{2}}$/h to 4e$^{\mathrm{2}}$/h, reflecting the rich interplay between crystal symmetry and Coulomb interactions.