AI 中文总结
该研究借助黎曼-布洛赫态评估晶体中电子态的贝里相位，利用复平面正则化程序与准对称性，解释了准周期性导致贝里相位随绕数或GTO展宽出现不连续跳变的机制。
AI 中文摘要
借助黎曼-布洛赫态在整个布里渊区提供的一致描述，针对倒空间中不同积分路径，评估孤立电子态的贝里相位；针对开路贝里相位，研究其与有界位置算符的关系，以及与构成原子轨道高斯型（GTO）不同形状因子的关系。当对倒空间中的闭合回路评估贝里相位时，采用复平面中的正则化程序，首次利用额外准对称性解释非解析跳变的出现，该跳变是绕数或GTO展宽的函数。
英文摘要
The Berry phase of an isolated electronic state is evaluated for different integration paths in reciprocal space, thanks to Riemann-Bloch states providing a consistent description in the whole Brillouin zone. The relationship with the bounded position operator is investigated for the open-path Berry phase and with different form factors of the constituent Gaussian type atomic orbitals (GTOs). When the Berry phase is evaluated over a closed loop in reciprocal space, a regularisation procedure in the complex plane is adopted and additional \textit{quasi}-symmetries are exploited here for the first time in order to rationalise the occurrence of non-analytical jumps as a function of the winding number or of the GTO broadening.
