The protected surface states of topological insulators (TIs) form gapless Dirac cones corresponding nondegenerate eigenstates with helical spin polarization. The presence of a warping term deforms the isotropic cone of the most simple model into snowflake Fermi surfaces as in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Their features have been identified in STM quasiparticle interference (QPI) experiments on isolated surfaces. Here we investigate the QPI spectrum for the TI thin film geometry with a finite tunneling between the surface states. This leads to a dramatic change of spectrum due to gapping and a change in spin texture that should leave distinct signatures in the QPI pattern. We consider both normal and magnetic exchange scattering from the surface impurities and obtain the scattering $t$ matrix in Born approximation as well as the general closed solution. We show the expected systematic variation of QPI snowflake intensity features by varying film thickness and study, in particular, the influence on backscattering processes. We predict the variation of QPI spectrum for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films using the observed gap dependence from ARPES results.

中文翻译：

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薄膜拓扑绝缘体中带间隙的狄拉克锥和自旋纹理

拓扑绝缘体（TI）的受保护表面态形成无间隙Dirac锥，对应于具有螺旋自旋极化的非简并本征态。翘曲项的存在将最简单模型的各向同性圆锥变形为雪花费米曲面，如下${双}_2{硒}_3$ 和 ${双}_2{特}_3$。它们的特征已在隔离表面上的STM准粒子干涉（QPI）实验中确定。在这里，我们通过表面状态之间的有限隧穿来研究TI薄膜几何形状的QPI光谱。由于间隙和自旋纹理的变化，这会导致频谱发生巨大变化，这应该在QPI模式中留下明显的特征。我们考虑了来自表面杂质的正态和磁交换散射，并获得了散射$Ť$Born近似中的矩阵以及一般的封闭解。我们通过改变膜厚度和研究，特别是对反向散射过程的影响，显示了预期的QPI雪花强度特征的系统变化。我们预测QPI频谱的变化${双}_2{硒}_3$ 薄膜使用ARPES结果观察到的间隙依赖性。