On the quantization of AB phase in nonlinear systems

TL;DR

This paper investigates how the Aharonov-Bohm phase behaves in nonlinear systems with energy band structures, revealing a unique phase jump at critical nonlinearity levels specifically for Kerr nonlinearity.

Contribution

It systematically analyzes the AB phase in nonlinear Dirac cones using the Qi-Wu-Zhang model, highlighting the special phase jump phenomenon for Kerr nonlinearity.

Findings

AB phase jumps by π at critical Kerr nonlinearity

AB phase varies continuously for other nonlinear powers

Results aid experimental measurement of nonlinear effects

Abstract

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of $\pi$ at the critical nonlinearity at which the Dirac cone appears or disappears, whereas for all other powers of nonlinearity the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.