Ferroelectric Band Twinning from Pair-State Symmetry
Ferroelectric switching provides a nonvolatile way to control electronic structures, but a general symmetry rule connecting the full Bloch bands of two switchable polarization states is still lacking. Here, we introduce ferroelectric band twinning, a pair-state relation in which the bands of two opposite-polarization states are mapped onto each other by a non-inversion state-exchange symmetry. Using dichromatic groups, we derive the band-twinning rule and identify 11 ferroelectric band-twinning point-group classes. Screening the Ferroelectric Materials Database yields 16 candidate compounds, of which the two lattice-metric-preserving candidates, bulk gamma-Ag3SI and BaAl2O4, are selected for first-principles validation. For gamma-Ag3SI, we further show that the same pair-state symmetry controls the transformation of shift-current tensor components under polarization reversal. These results establish ferroelectric band twinning as a general symmetry framework for nonvolatile control of momentum-dependent electronic structures in ferroelectrics.