Disorder-induced nonlinear Hall effect with time-reversal symmetry

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Transport Phenomena

Background:

• The nonlinear Hall effect is crucial for understanding topological states of matter.
• Disorder is known to influence various linear Hall effects, including quantized, anomalous, spin, and valley Hall effects.
• Unlike linear effects, disorder influences the nonlinear Hall effect from the outset.

Purpose of the Study:

• To derive formulas for nonlinear Hall conductivity considering disorder scattering.
• To investigate the nonlinear Hall response in a minimal model (tilted 2D Dirac model).
• To establish a general scaling law for the nonlinear Hall effect to aid experimental interpretation.

Main Methods:

• Derivation of theoretical formulas for nonlinear Hall conductivity in the presence of disorder.
• Application of derived formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model.
• Construction of a general scaling law for the nonlinear Hall effect.

Main Results:

• Formulas for nonlinear Hall conductivity with disorder scattering have been successfully derived.
• The nonlinear Hall response of the tilted 2D Dirac model was calculated using these formulas.
• A general scaling law for the nonlinear Hall effect was established.

Conclusions:

• Disorder plays a fundamental role in the nonlinear Hall effect, entering at the leading order.
• The tilted 2D Dirac model serves as a minimal, versatile model for studying these effects.
• The developed scaling law provides a framework for experimentally distinguishing disorder-induced nonlinear Hall effects.