Paper detail

Transport gap and hysteretic behavior of the Ising quantum Hall ferromagnets in Landau levels $\left\vert N\right\vert >0$ of bilayer graphene

The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavior of the Ising quantum Hall ferromagnets. We compute the transport gap due to different excitations: bulk electron-hole pairs, electron-hole pairs confined to the coherent region of a valley-pseudospin domain wall, and spin or valley-pseudospin skyrmion-antiskyrmion pairs. We determine which of these excitations has the lowest energy at a given value of the Zeeman coupling, bias, and magnetic field.