Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.