Background Electrical Hall effect HE requires magnetic field

Background • Electrical Hall effect (HE)– requires magnetic field. • Hall effect without magnetic fields – “anomalous Hall Effect” (AHE). • Role of an internal magnetization for AHE – ‘quantum magnets’. • Studies on HE have lead to important discoveries of Berry curvature and topological Chern invariants.

Background • Electrical Hall effect (HE)– requires magnetic field. • Hall effect without magnetic fields – “anomalous Hall Effect” (AHE). • Role of an internal magnetization for AHE – ‘quantum magnets’. • Studies on HE have lead to important discoveries of Berry curvature and topological Chern invariants. • HE requires breaking of time reversal symmetry – linear regime. • HE in non-linear regime is not subject to such symmetry constraints. • This paper: reports observation of non-linear HE under TR symmetric conditions. NEW TYPE OF HALL EFFECT.

Anomalous Hall Effect (AHE) – paradigm • Non-vanishing Hall conductivity that arises from the momentumintegrated Berry curvature (requires breaking TR). • Hall voltage that is linearly proportional to the external electric field. • Hall effects beyond this paradigm are theoretically possible.

Non-linear AHE • Even in a non-magnetic material, inversion-symmetry breaking may segregate the positive and negative Berry curvatures in different momentum regions, leading to a dipole moment. • Berry-curvature dipole should give rise to HE, in the second-order response; a nonlinear Hall effect is induced by an electric field parallel to the Berry-curvature dipole. Berry dipole

Some experimental plots (bilayer WTe 2) First observation of a new type of Hall Effect.

Schematic bands & Berry curvature Tilted DFs Bilayer WTe 2