Bilayer graphene (BLG) offers a rich platform for broken-symmetry states stabilized by interactions. In this work, we study the phase diagram of BLG in the quantum Hall regime at filling factor ν = 0 within the Hartree-Fock approximation. In the simplest noninteracting situation, this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer polarized, canted antiferromagnetic, Kekule, a “spin-valley entangled” state, and a “broken U(1) × U(1)” phase. This last phase involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias D and perpendicular magnetic field B⊥ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed.
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We are grateful to J. Zhu, J. Li, A. Young, M. Zaletel, and J. Ramon de Nova for illuminating conversations, and to the Aspen Center for Physics (NSF Grant No. 1066293), where this work was begun and completed. G.M. thanks the NSF (Grant No. DMR-1306897) and the Gordon and Betty Moore Foundation for financial support. H.A.F. acknowledges the support of the NSF through Grants No. DMR-1506263 and No. DMR-1506460. E.S. thanks support of the Israel Science Foundation (ISF) via Grant No. 231/14, of the Simons Foundation, and thanks the hospitaliy of the Kavli Institute for Theoretical Physics (NSF Grant No. PHY-11-25915). Finally, we would like to acknowledge support for all the present authors by the US-Israel Binational Science Foundation (Grant No. BSF-2012120).
Murthy, Ganpathy; Shimshoni, Efrat; and Fertig, H. A., "Spin-Valley Coherent Phases of the v = 0 Quantum Hall State in Bilayer Graphene" (2017). Physics and Astronomy Faculty Publications. 516.