Table 1 Magnetoelectric susceptibility pseudotensor \(\alpha \) for D\({}_{6}\), C\({}_{3}\), and C\({}_{1}\) point group.

From: Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene

Point group

\(\alpha \)

Point group

\(\alpha \)

D\({}_{6}\)

\(\left(\begin{array}{lll}{\alpha }_{\parallel }&0&0\\ 0&{\alpha }_{\parallel }&0\\ 0&0&{\alpha }_{zz}\end{array}\right)\)

C\({}_{3}\)

\(\left(\begin{array}{lll}{\alpha }_{\parallel }&-{\alpha }^{-}&0\\ {\alpha }^{-}&{\alpha }_{\parallel }&0\\ 0&0&{\alpha }_{zz}\end{array}\right)\)

C\({}_{1}\)

\(\left(\begin{array}{lll}{\alpha }_{xx}&{\alpha }_{xy}&{\alpha }_{xz}\\ {\alpha }_{yx}&{\alpha }_{yy}&{\alpha }_{yz}\\ {\alpha }_{zx}&{\alpha }_{zy}&{\alpha }_{zz}\end{array}\right)\)

  
  1. \({\alpha }_{ij}\) with \(i,j=x,y,z\) are in general the elements in \(\alpha \). In D\({}_{6}\) and C\({}_{3}\), \({\alpha }_{xx}={\alpha }_{yy}\) is denoted as \({\alpha }_{\parallel }={\alpha }_{xx}={\alpha }_{yy}\). In C\({}_{3}\), the antisymmetric off diagonal element is denoted as \({\alpha }^{-}=-{\alpha }_{xy}={\alpha }_{yx}\).
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