Fig. 6: Transformation of pseudovectors and polar vectors under different symmetry operation and ferroelectric switching of LPGE and CPGE nonlinear current. | npj Computational Materials

Fig. 6: Transformation of pseudovectors and polar vectors under different symmetry operation and ferroelectric switching of LPGE and CPGE nonlinear current.

From: Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2

Fig. 6

a Transformation of Berry curvature, spin polarization, shift vector, BCD and SD as well as LPGE and CPGE nonlinear current under different symmetry operation between two ferroelectric states in time-reversal invariant few-layer WTe2. Berry curvature and spin polarization transform as time-reversal antisymmetric pseudovectors. Under a mirror symmetry operation \({\cal{M}}_{z}\) for the ferroelectric states in bilayer WTe2, most quantities remain invariant, except in-plane spin and Berry curvature component. Under inversion symmetry operation \({\cal{I}}\) for the −iFE and +iFE state states in trilayer WTe2, all quantities, including Berry curvature, spin polarization, shift vector, BCD and SD, flip the sign in the presence of time-reversal symmetry, giving rise to FNAHE in trilayer WTe2. b, c Ferroelectric switching of nonlinear current in the −iFE and +iFE state of trilayer WTe2, respectively. Upon the polarization Pz switching, nonlinear anomalous Hall current \(j_{x}^{L}\) from LPGE switches between −x and +x direction under external field with in-plane linear polarization, while nonlinear anomalous Hall current \(j_{y}^{C}\) from CPGE switches between −y and +y direction under circularly-polarized light with normal incidence.

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