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On the Quantization of AB Phase in Nonlinear Systems
Xi Liu1, Qing-Hai Wang2, Jiangbin Gong2,3
1NUS Graduate School-Integrative Sciences and Engineering Programme (ISEP), National University of Singapore, Singapore 119077, Singapore.
Entropy (Basel, Switzerland)
|December 23, 2022
Summary
For Kerr nonlinearity, the Aharonov-Bohm phase jumps by π at the critical point where nonlinear Dirac cones appear and disappear. Other nonlinearities show continuous phase changes.
Area of Science:
- Condensed matter physics
- Nonlinear dynamics
- Quantum mechanics
Background:
- Nonlinearity can induce self-intersecting energy bands in momentum space.
- Nonlinear Dirac cones are an intriguing consequence of such phenomena.
Purpose of the Study:
- Investigate the Aharonov-Bohm (AB) phase in nonlinear systems.
- Analyze the impact of power-law nonlinearity on the AB phase around nonlinear Dirac cones.
Main Methods:
- Utilized the Qi-Wu-Zhang model with power-law nonlinearity.
- Studied the AB phase via adiabatic paths in momentum space.
Main Results:
- Kerr nonlinearity leads to a π-jump in the AB phase at critical nonlinearity.
- This π-quantization occurs when nonlinear Dirac cones emerge or vanish.
- Other nonlinearities result in a continuous AB phase change with nonlinear strength.
Conclusions:
- The study reveals unique π-quantization of the AB phase for Kerr nonlinearity.
- Results offer potential for experimental measurement of power-law nonlinearity.
- Motivates further research into geometric phases in nonlinear systems.
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