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Electromagnetic absorption and Kerr effect in quantum Hall ferromagnetic states of bilayer graphene

In a quantizing magnetic field, the chiral two-dimensional electron gas in Landau level $N=0$ of bilayer graphene goes through a series of phase transitions at integer filling factors $ν\in \left[ -3,3\right] $ when the strength of an electric field applied perpendicularly to the layers is increased. At filling factor $ν=3,$ the electron gas can described by a simple two-level system where layer and spin degrees of freedom are frozen. The gas then behaves as an orbital quantum Hall ferromagnet. A Coulomb-induced Dzyaloshinskii-Moriya term in the orbital pseudospin Hamiltonian is responsible for a series of transitions first to a Wigner crystal state and then to a spiral state as the electric field is increased. Both states have a non trivial orbital pseudospin texture. In this work, we study how the phase diagram at $ν=3$ is modified by an electric field applied in the plane of the layers and then derive several experimental signatures of the uniform and nonuniform states in the phase diagram. In addition to the transport gap, we study the electromagnetic absorption and the Kerr rotation due to the excitations of the orbital pseudospin-wave modes in the broken-symmetry states.