Nonlinear Hall Effect and Berry Curvature Memory in Emergent 2D Ferroelectric Materials

Classical Hall effect requires the broken time-reversal symmetry via external magnetic field or internal magnetization. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear Hall current in time-reversal invariant materials – an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles approaches, we present a theory of ferroelectric nonlinear Hall effect in time-reversal invariant few-layer ferroelectric WTe₂ [1] and discuss the first experimental demonstration of Berry curvature memory based on the predicted ferroelectric nonlinear Hall effect [2]. Nonlinear Hall current switches in odd-layer WTe₂ except 1T′ monolayer while remaining invariant in even-layer WTe₂ upon interlayer-sliding induced ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe₂. Our work establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials, and suggests that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics. This work was supported the National Science Foundation (NSF) under award number DMR-1753054. References: [1] npj Computational Materials 5, 119 (2019). [2] Nature Physics 16, 1028-1034 (2020).