Liu Xi, Wang Qing-Hai, Gong Jiangbin
NUS Graduate School-Integrative Sciences and Engineering Programme (ISEP), National University of Singapore, Singapore 119077, Singapore.
Department of Physics, National University of Singapore, Singapore 117551, Singapore.
Entropy (Basel). 2022 Dec 16;24(12):1835. doi: 10.3390/e24121835.
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 π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-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.
在平均场水平下，动量空间中的自相交能带结构可由非线性诱导产生，所谓的非线性狄拉克锥就是一个有趣的结果。本文使用祁-吴-张模型加幂律非线性，系统地研究了与动量空间中绝热过程相关的阿哈罗诺夫-玻姆（AB）相位，其中两条绝热路径围绕一个非线性狄拉克锥盘旋。有趣的是，且仅对于克尔非线性，AB相位在狄拉克锥出现和消失的临界非线性处经历π的跃变（因此只要非线性狄拉克锥存在，AB相位就会产生π量子化），而对于所有其他幂次的非线性，AB相位总是随非线性强度连续变化。我们的结果可能有助于幂律非线性的实验测量，并将激发对非线性系统中几何相位和绝热跟随方面的进一步基础研究兴趣。
