In the presence of the Hubbard interaction, graphene zigzag nanoribbons have spontaneous edge magnetism with anti-parallel configuration, whose amplitude can be tuned by a transversal electric field. As the electric field increases or decreases across a critical value, the edges are demagnetized or re-magnetized, respectively. A magnetic field at each edge determines the orientation of the re-magnetization. Thus, a combination of a slowly varying transversal electric field and magnetic field in monolayer graphene zigzag nanoribbons can drive the quantum system into a bistability loop. The same phenomenon can be induced in a bilayer/monolayer zigzag nanoribbon without the magnetic field, because the non-symmetry superexchange interaction controls the orientation of the re-magnetization. In this way, the quantum system is switched between ground state and quasi-stable excited state with different magnetism, band structures and conductance. This feature could be used to develop graphene-based spintronic nano-devices without magnetic field.

在哈伯德相互作用的存在下，石墨烯之字形纳米带具有反平行构型的自发边缘磁性，其振幅可以通过横向电场进行调节。随着电场在临界值上增加或减少，边缘分别被退磁或重新磁化。每个边缘的磁场决定了再磁化的方向。因此，单层石墨烯之字形纳米带中缓慢变化的横向电场和磁场的组合可以将量子系统驱动到双稳态回路中。在没有磁场的双层/单层锯齿形纳米带中也可以诱发相同的现象，因为非对称超交换相互作用控制了再磁化的方向。这样，量子系统在基态和准稳定激发态之间切换，具有不同的磁性、能带结构和电导。此功能可用于开发无磁场的基于石墨烯的自旋电子纳米器件。