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arXiv 2011.05720cond-mat.mes-hall
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二维拓扑绝缘体中的硬壁边缘限制和Dirac点的能量

Hard wall edge confinement in 2D topological insulators and the energy of the Dirac Point

P. C. Klipstein

摘要:

在二维拓扑绝缘体(TI)中,如HgTe/CdTe或InAs/GaSb/AlSb量子阱,自旋极化边缘态具有无质量的类狄拉克色散.在基于4 × 4 BHZ哈密顿量和开边界条件(OBC)的硬壁处理中,波函数被弱限制在边缘附近,与边缘不接触。相比之下,标准的边界条件的波函数和其衍生物(SBC)导致强限制与峰值振幅的边缘。不幸的是,弱约束表现出与OBC波函数中包含的假间隙解相关的非物理行为。这是证实了由父多带哈密顿量的间隙解决方案,从其中较小的哈密顿量是派生出来的,表现出物理行为,不满足OBCs。与OBCs或其他基于唯象边界条件的方法不同,SBCs明确地处理壁。使用空晶体自由电子状态的真空具有相同的对称性作为TI状态的基础上,它表明,一个大的壁带隙重叠的TI只能通过包括一个薄的钝化层来实现。对于诸如二氧化硅的钝化材料,其中中间带隙能量几乎与TI的能量简并,狄拉克点非常接近中间带隙,并且实际上与TI带不对称性无关。处理还表明,一个显着的位移的分散可能会引入界面带混合。位移在狄拉克点处最大,并随边缘态波矢单调减小,当边缘态与体带边缘合并时消失。

英文摘要:

In 2D topological insulators (TIs) based on semiconductor quantum wells such as HgTe/CdTe or InAs/GaSb/AlSb, spin polarized edge states have been predicted with a massless Dirac like dispersion. In a hard wall treatment based on the 4 x 4 BHZ Hamiltonian and open boundary conditions (OBCs), the wave function is weakly confined near the edge, with which it makes no contact. In contrast, standard boundary conditions for the wave function and its derivative (SBCs) lead to strong confinement with a peak amplitude at the edge. Unfortunately, weak confinement exhibits unphysical behavior related to a spurious gap solution that is included in the OBC wave function. This is confirmed by the gap solutions of the parent multiband Hamiltonian from which the smaller Hamiltonian is derived, which exhibit physical behavior and do not satisfy OBCs. Unlike OBCs or other approaches based on phenomenological boundary conditions, SBCs treat the wall explicitly. Using a basis of empty crystal free electron states for the vacuum with the same symmetry as the TI states, it is shown that a large wall band gap overlapping that of the TI can only be achieved by including a thin passivation layer. For passivation materials such as silicon dioxide where the mid gap energy is nearly degenerate with that of the TI, the Dirac point is very close to mid gap and virtually independent of the TI band asymmetry. The treatment also demonstrates that a significant shift of the dispersion may be introduced by interface band mixing. The shift is largest at the Dirac point and decreases monotonically with edge state wave vector, vanishing when the edge states merge with the bulk band edges.

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