On the Quantization of AB Phase in Nonlinear Systems

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 and disappears (thus yielding pi-quantization of the AB phase so long as the nonlinear Dirac cone exists), 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.

Automated summary

In this paper, we study the self-intersecting energy band structures induced by nonlinearity at the mean-field level, specifically focusing on the intriguing consequence of nonlinear Dirac cones. Our systematic analysis using the Qi-Wu-Zhang model and power law nonlinearity reveals that the Aharonov-Bohm phase associated with an adiabatic process in the momentum space exhibits a jump of pi only at critical nonlinearity, known as Kerr nonlinearity, where the Dirac cone appears and disappears. This result suggests pi-quantization of the Aharonov-Bohm phase as long as the nonlinear Dirac cone exists, while for other powers of nonlinearity, the phase changes continuously with the nonlinear strength. These findings have important implications for experimental measurement of power-law nonlinearity and further exploration of geometric phase and adiabatic following in nonlinear systems.