We theoretically investigate quantum phase transitions from topologically non-trivial to trivial states in three-dimensional hybridized topological insulator (TI) ultra-thin films. The interplay between the hybridization of the top and bottom surface states (SSs) and Zeeman energy gives rise to topological and normal insulating phases. By tuning the Zeeman energy, we can drive phase transition between these two phases by closing and reopening the band gap. Furthermore, we impinge a Gaussian beam on the surface of the 3D TI to study the Faraday rotation (FR) and magneto-optical Kerr effect (MOKE) in the presence of an external magnetic field, while explicitly taking into account the hybridization between the top and bottom Dirac SSs of the TI film. The FR and MOKE change sign when the polarization is changed from s to p. We demonstrate that giant FR and MOKE can be achieved by tuning the external magnetic field. Furthermore, the MOKE signal takes a sharp anti-phase peak at the charge neutrality point as the system goes from the quantum spin Hall insulator (QSHI) to the semimetallic state. Lastly, the MOKE and FR in the bottom and top SSs can be independently tuned for intra-band and inter-band transitions via n-type and p-type doping respectively.

中文翻译：

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混合拓扑绝缘体薄膜的过渡法拉第和克尔效应

我们从理论上研究了三维杂化拓扑绝缘体（TI）超薄薄膜中从拓扑非平凡状态到平凡状态的量子相变。顶部和底部表面状态（SSs）的混合与塞曼能量之间的相互作用产生了拓扑和正常绝缘阶段。通过调节塞曼能量，我们可以通过关闭和重新打开带隙来驱动这两个相位之间的相变。此外，我们在3D TI的表面上撞击高斯光束，以研究存在外部磁场时的法拉第旋转（FR）和磁光克尔效应（MOKE），同时明确考虑了顶部之间的杂化和TI膜的底部Dirac SS。当极化从s改变时，FR和MOKE改变符号到p。我们证明通过调节外部磁场可以实现巨型FR和MOKE。此外，随着系统从量子自旋霍尔绝缘体（QSHI）变为半金属态，MOKE信号在电荷中性点处出现尖锐的反相峰值。最后，可以分别通过n型和p型掺杂分别针对底部和顶部SS的MOKE和FR进行带内和带间转换的调谐。