Fig. 5
From: Orbital Hall conductivity in a Graphene Haldane and Haldane Haldane bilayers
(a,b): Orbital magnetic moment of the valence bands (Valence band-1, 2) of AA stacked and AB stacked \(\textrm{G}/\tilde{\textrm{G}}\) bilayers with highlighted \(K-\)valley distribution, where \(M=0\), \(\gamma =0.2t_g\), \(\phi =\pi /2\) and \(t_g=-2.7\) eV. The \(m_z\) distribution at the \(K'-\)valley has identical as \(K-\) valley. (c,d): \(\tilde{\textrm{G}}/\tilde{\textrm{G}}\) bilayer system, where \(M_l=M_u=0\), \(\gamma =0.2t_g\), \(\phi _l=\phi _u=\pi /2\), \(t_g=-2.7\) eV, and \(t_{2l}=t_{2u}=t_2\) for two different NNN hopping strengths: \(t_2=0.01t_g\)(red line) and \(t_2=0.1t_g\)(blue line). The valley dependent \(m_z\) of the \({\textrm{AB}}(\textrm{G}/\tilde{\textrm{G}})\) and valley independent \(m_z\) of \({\textrm{AB}}(\tilde{\textrm{G}}/\tilde{\textrm{G}})\) are highlighted in each plots.
