Valley-kink in bilayer graphene at $\nu = 0$: A charge density signature for quantum Hall ferromagnetism

We investigate interaction-induced valley domain walls in bilayer graphene in the $\nu = 0$ quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a double-gated suspended sample, where the electric field changes sign across a line in the middle. The noninteracting energy spectrum of the ground state is characterized by a sharp domain wall between two valley-polarized regions. Using the Hartree-Fock approximation, we find that the Coulomb interaction opens a gap between the two lowest-lying states near the Fermi level, yielding a smooth domain wall with a kink configuration in the valley index. Our results suggest the possibility to visualize the domain wall via measuring the charge density difference between the two graphene layers, which we find exhibits a characteristic pattern. The width of the kink and the resulting pattern can be tuned by the interplay between the magnetic field and the gate electric fields