Ising quantum Hall ferromagnetic states in bilayer graphene

We present a study of the phase diagram of the chiral two-dimensional electron gas (C2DEG) in the higher Landau levels, $\left\vert N\right\vert\geq 1,$ of a chirally stacked bilayer graphene as a function of magnetic field $B$ and interlayer electrical bias $\Delta _{B}$. In the Hartree-Fock approximation, the ground states of the C2DEG are respectively valley-pseudospin or spin Ising quantum Hall ferromagnets at odd or even filling factors of the quartet of states in levels $\left\vert N\right\vert\geq 1$ [1]. Changing the magnetic field or the bias introduces first order phase transitions between the different Ising ground states that are characterized by a discontinuity in the transport gap $\Delta _{t}$. The C2DEG shows an hysteretic behavior with respect to the bias $\Delta _{B}$ with a marked difference between positive $N>0$ and negative $N<0$ Landau levels [2]. We discuss the relevance of our results with recent experimental measurements of broken-symmetry gaps in bilayer graphene [3].\\[4pt] [1] Wenchen Luo, R. C\^{o}t\'{e}, and Alexandre B\'{e}dard-Vall\'{e}e, Phys. Rev. B \textbf{90}, 075425 (2014). \\[0pt] [2] Wenchen Luo and R. C\^{o}t\'{e}, arXiv:1410.4232 (2014). \\[0pt] [3] Kayoung Lee et al., Science \textbf{345}, 58 (2014).