扭曲拓扑绝缘体的杂化和场驱动相变
Hybridization and Field Driven Phase Transitions in Hexagonally Warped Topological Insulators
摘要：
本文讨论了量子相变中材料参数和外场效应对薄膜拓扑绝缘体（TI）的影响。首先，我们考虑一个面内倾斜的磁场，并确定表面态的能带结构作为倾斜角的函数。我们发现，存在的杂交项或六方翘曲或两者的组合导致半金属到绝缘体的相变，这是由它们的${\cal PT}$对称性破缺字符促进。然后我们注意到，虽然电场的引入不允许这种QPT，因为它不破坏${\cal PT}$对称性，但它可以与隧穿元件结合使用以有效地达到相变。相应的临界点则非平凡地依赖于电场，这是在这里指出的。然后，我们证明，包括一个六边形的翘曲项导致立即${\cal PT}$对称违反QPT。
英文摘要：
In this paper we discuss the role of material parameters and external field effects on a thin film topological insulator(TI) in the context of quantum phase transition(QPT). First, we consider an in-plane tilted magnetic field and determine the band structure of the surface states as a function of the tilt angle. We show that the presence of either a hybridization term or hexagonal warping or a combination of both leads to a semi-metal to insulator phase transition which is facilitated by their ${\cal PT}$ symmetry breaking character. We then note that while the introduction of an electric field does not allow for this QPT since it doesn't break ${\cal PT}$ symmetry, it can be used in conjunction with a tunneling element to reach a phase transition efficiently. The corresponding critical point is then non-trivially depend on the electric field, which is pointed out here. Then, we demonstrate that including a hexagonal warping term leads to an immediate ${\cal PT}$ symmetry violating QPT.
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