拓扑绝缘体表面态调控的第一性原理研究
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摘要
本文采用基于密度泛函理论的第一性原理方法，从理论上研究了拓扑绝缘体材料表面态的相关性质,为设计纳米尺度的物性调控提供了有益的理论指导和依据，得到了如下主要研究成果：
1.应变引起的拓扑相变。基于第一性原理计算，我们研究了具有各向异性相互作用的Bi_2Se_3类材料的拓扑相变。通过施加不同的应变来改变Bi_2Se_3类物质中的相互作用，我们发现QL内的横向相互作用对它们的拓扑相影响很小，而QL间的纵向相互作用能够有效的调制它们的拓扑相。在我们研究的这类材料中，施加的纵向应变对它们的影响是非均匀的，即在QL内与QL间引起的相互作用效果不同。我们的研究表明决定Bi_2Se_3类材料拓扑相的自旋轨道相互作用主要来至于QL间相互作用。Sb2Se3的QL间距比Bi_2Se_3大，自旋轨道相互作用弱，前者是拓扑平庸的，后者是拓扑非平庸的。这使我们弄清楚了为什么具有同样晶体结构，且都含有重元素、小带隙的Sb2Se3和Bi_2Se_3的能带存在拓扑结构上的差别。我们提出了通过应变调节这类材料的拓扑相的方法，发现通过施加c轴方向的纵向压应变减小Sb2Se3的QL间间距，增大自旋轨道耦合强度，使得它由普通绝缘转变成拓扑绝缘体；而施加纵向拉应变可以增大Bi_2Se_3的QL间间距，减弱自旋轨道耦合强度，使Bi_2Se_3由拓扑绝缘体转变成普通绝缘体。类似的相变情形也发生在两类材料的薄膜上。
2.拓扑绝缘体薄膜的表面和界面尺寸效应。基于范德瓦尔斯修正的密度泛函理论计算，我们研究了1QL～6QL厚度的拓扑绝缘体Bi_2Se_3和Bi_2Te_3薄膜的表面和界面效应。我们的计算表明，薄膜表层QL间间距弛豫显著，达到20%；内层QL间距弛豫不明显。随薄膜厚度增加，QL间间距逐渐趋于块体值。对于厚度较小的Bi_2Se_3薄膜（2QL～4QL），存在明显的表面态带隙，随厚度的增加薄膜的表面态带隙逐渐减小并最终闭合，这与实验观测符合的很好。我们还研究了石墨烯衬底对Bi_2Se_3薄膜表面态的影响，发现衬底会诱导显著的Rashba劈裂，随厚度增加劈裂效果越明显，并且与无衬底的情形相比，狄拉克点相对于费米能级发生了移动。Bi_2Te_3薄膜有相对较小的QL间间距弛豫效应和较强自旋轨道耦合作用，2QL的薄膜已经开始显现出无能隙的拓扑表面态，与实验观测一致。
3.半导体衬底对拓扑绝缘体表面与界面态的调控。目前，由于拓扑绝缘体的费米能级难以调控至狄拉克点，它的许多重要且新奇的表面电子与自旋输运性质尚未在实验中得到观测。从实验的迫切需要出发，以Bi_2Se_3和Bi_2Te_3为对象，采用半导体异质节能带调整理论和第一性原理计算，研究常规半导体硅和砷化镓与拓扑绝缘体表面和界面态的作用，寻找调节拓扑绝缘体费米能级至狄拉克点的关键参数。通过第一性原理计算，我们研究了半导体对拓扑绝缘体表面与界面效应。首先，我们计算了不同厚度的拓扑绝缘体薄膜和半导体衬底的功函数。我们的计算发现当半导体衬底的功函数小于拓扑绝缘体薄膜的功函数时，拓扑绝缘体薄膜会从衬底得到电子，更高的能级将被填充，费米能级向上移动，费米能级相对于狄拉克点移动的幅度随薄膜厚度增加而减小。由半导体衬底引起的拓扑绝缘体薄膜费米能级的移动能够用功函数和电荷转移得到解释。随着薄膜厚度的增加，拓扑绝缘体薄膜的态密度也在增加，转移相同数目的电荷引起费米能级的移动幅度较小。
In this thesis, we have investigated theoretically the properties of the surface states oftopological insulators(TI) by using first-principles calculations based on the densityfunctional theory, which will provide a guidance for designing tunable TI-basednano-devices. The main results are summarized as follows:
1. Strain induced topological phase transition: Based on first-principles calculations, westudy the dependence of topological phase on anisotropic interactions in Bi2Se3-typematerials. By applying different strains in order to vary interactions, we reveal that thetopological phase is insensitive to lateral interaction but can be effectively tuned bylongitudinal interaction. Longitudinal strain is inhomogeneous in the studied systems. Theinterquintuple interaction plays a dominant role in determining the topological phase. Theinter-quintuple separation in Sb2Se3is larger than that of Bi2Se3so that the spin-orbitcoupling of the former is weaker than the latter. Therefore Sb2Se3is a normal insulatorwhile Bi2Se3is a topological insulator. We explain the puzzling band-topology differencebetween Sb2Se3and Bi2Se3and propose an approach to tuning the topological phase bystrain. It is found that Sb2Se3can be converted into a topological insulator by applyingcompressive longitudinal strain to reduce the inter-quintuple separation and increase thespin-orbit coupling. A tensile strain will have an opposite tuning effect on theinter-quintuple separation and spin-orbit coupling and turn Bi2Se3into a normal insulator.We have studied thin films of Sb2Se3and Bi2Se3and also observed a strain-inducedtopological phase transition.
2. The effects of the surface and interface on the TI films: Based on van der Waalsdensity functional calculations, we have studied few-quintuple-layer (QL) films of Bi2Se3and Bi_2Te_3. The inter-QL separation near the surface is found to have an up to about20%increase, while the inner QL separation is smaller and approaches the bulk value as thethickness grows. Accordingly, the surface Dirac cone of Bi2Se3film is evidently gappedfor small thickness (2~4QLs) and the gap is reduced and finally closed with the increasingthickness, agreeing well with the experiments. We further studied the substrate effect byinvestigating the Bi2Se3/graphene system. It is found that the underlying graphene inducesgiant thickness-dependent Rashba splitting and Dirac point shift with respect to the Fermi level. Because Bi_2Te_3films have smaller relative inter-QL expansion and strongerspin-orbit coupling, the gapless topological surface states emerge in the film as thin as2QL, in good accord with the experiments.
3. The tuning of the surface and interface states by semiconductor substrate: We haveinvestigated the heterostructures of Bi_2Te_3/Si and Bi_2Se_3/GaAs by first-principlescalculations. It is found that the semiconductor substrate plays an important role in tuningthe Fermi level with respect to the Dirac point of topological insulators (TIs). Theworkfunctions of Bi_2Te_3and Bi_2Se_3are larger than that of the semiconductor substrate,leading to charge transfer from the substrate to TI and the upward Fermi level shift, whichis proportional to the difference of the workfunctions of the two interfaced materials.Thicker TI films have larger density of the states and hence the charge transferred to TIwill give rise to a smaller Fermi level shift. We also studied Bi_2Se_3on polarsemiconductor GaAs. It is found that different termination of GaAs at the interfacecorresponds to different work functions and will result in different Fermi level shift inBi_2Se_3.
1.应变引起的拓扑相变。基于第一性原理计算，我们研究了具有各向异性相互作用的Bi_2Se_3类材料的拓扑相变。通过施加不同的应变来改变Bi_2Se_3类物质中的相互作用，我们发现QL内的横向相互作用对它们的拓扑相影响很小，而QL间的纵向相互作用能够有效的调制它们的拓扑相。在我们研究的这类材料中，施加的纵向应变对它们的影响是非均匀的，即在QL内与QL间引起的相互作用效果不同。我们的研究表明决定Bi_2Se_3类材料拓扑相的自旋轨道相互作用主要来至于QL间相互作用。Sb2Se3的QL间距比Bi_2Se_3大，自旋轨道相互作用弱，前者是拓扑平庸的，后者是拓扑非平庸的。这使我们弄清楚了为什么具有同样晶体结构，且都含有重元素、小带隙的Sb2Se3和Bi_2Se_3的能带存在拓扑结构上的差别。我们提出了通过应变调节这类材料的拓扑相的方法，发现通过施加c轴方向的纵向压应变减小Sb2Se3的QL间间距，增大自旋轨道耦合强度，使得它由普通绝缘转变成拓扑绝缘体；而施加纵向拉应变可以增大Bi_2Se_3的QL间间距，减弱自旋轨道耦合强度，使Bi_2Se_3由拓扑绝缘体转变成普通绝缘体。类似的相变情形也发生在两类材料的薄膜上。
2.拓扑绝缘体薄膜的表面和界面尺寸效应。基于范德瓦尔斯修正的密度泛函理论计算，我们研究了1QL～6QL厚度的拓扑绝缘体Bi_2Se_3和Bi_2Te_3薄膜的表面和界面效应。我们的计算表明，薄膜表层QL间间距弛豫显著，达到20%；内层QL间距弛豫不明显。随薄膜厚度增加，QL间间距逐渐趋于块体值。对于厚度较小的Bi_2Se_3薄膜（2QL～4QL），存在明显的表面态带隙，随厚度的增加薄膜的表面态带隙逐渐减小并最终闭合，这与实验观测符合的很好。我们还研究了石墨烯衬底对Bi_2Se_3薄膜表面态的影响，发现衬底会诱导显著的Rashba劈裂，随厚度增加劈裂效果越明显，并且与无衬底的情形相比，狄拉克点相对于费米能级发生了移动。Bi_2Te_3薄膜有相对较小的QL间间距弛豫效应和较强自旋轨道耦合作用，2QL的薄膜已经开始显现出无能隙的拓扑表面态，与实验观测一致。
3.半导体衬底对拓扑绝缘体表面与界面态的调控。目前，由于拓扑绝缘体的费米能级难以调控至狄拉克点，它的许多重要且新奇的表面电子与自旋输运性质尚未在实验中得到观测。从实验的迫切需要出发，以Bi_2Se_3和Bi_2Te_3为对象，采用半导体异质节能带调整理论和第一性原理计算，研究常规半导体硅和砷化镓与拓扑绝缘体表面和界面态的作用，寻找调节拓扑绝缘体费米能级至狄拉克点的关键参数。通过第一性原理计算，我们研究了半导体对拓扑绝缘体表面与界面效应。首先，我们计算了不同厚度的拓扑绝缘体薄膜和半导体衬底的功函数。我们的计算发现当半导体衬底的功函数小于拓扑绝缘体薄膜的功函数时，拓扑绝缘体薄膜会从衬底得到电子，更高的能级将被填充，费米能级向上移动，费米能级相对于狄拉克点移动的幅度随薄膜厚度增加而减小。由半导体衬底引起的拓扑绝缘体薄膜费米能级的移动能够用功函数和电荷转移得到解释。随着薄膜厚度的增加，拓扑绝缘体薄膜的态密度也在增加，转移相同数目的电荷引起费米能级的移动幅度较小。
In this thesis, we have investigated theoretically the properties of the surface states oftopological insulators(TI) by using first-principles calculations based on the densityfunctional theory, which will provide a guidance for designing tunable TI-basednano-devices. The main results are summarized as follows:
1. Strain induced topological phase transition: Based on first-principles calculations, westudy the dependence of topological phase on anisotropic interactions in Bi2Se3-typematerials. By applying different strains in order to vary interactions, we reveal that thetopological phase is insensitive to lateral interaction but can be effectively tuned bylongitudinal interaction. Longitudinal strain is inhomogeneous in the studied systems. Theinterquintuple interaction plays a dominant role in determining the topological phase. Theinter-quintuple separation in Sb2Se3is larger than that of Bi2Se3so that the spin-orbitcoupling of the former is weaker than the latter. Therefore Sb2Se3is a normal insulatorwhile Bi2Se3is a topological insulator. We explain the puzzling band-topology differencebetween Sb2Se3and Bi2Se3and propose an approach to tuning the topological phase bystrain. It is found that Sb2Se3can be converted into a topological insulator by applyingcompressive longitudinal strain to reduce the inter-quintuple separation and increase thespin-orbit coupling. A tensile strain will have an opposite tuning effect on theinter-quintuple separation and spin-orbit coupling and turn Bi2Se3into a normal insulator.We have studied thin films of Sb2Se3and Bi2Se3and also observed a strain-inducedtopological phase transition.
2. The effects of the surface and interface on the TI films: Based on van der Waalsdensity functional calculations, we have studied few-quintuple-layer (QL) films of Bi2Se3and Bi_2Te_3. The inter-QL separation near the surface is found to have an up to about20%increase, while the inner QL separation is smaller and approaches the bulk value as thethickness grows. Accordingly, the surface Dirac cone of Bi2Se3film is evidently gappedfor small thickness (2~4QLs) and the gap is reduced and finally closed with the increasingthickness, agreeing well with the experiments. We further studied the substrate effect byinvestigating the Bi2Se3/graphene system. It is found that the underlying graphene inducesgiant thickness-dependent Rashba splitting and Dirac point shift with respect to the Fermi level. Because Bi_2Te_3films have smaller relative inter-QL expansion and strongerspin-orbit coupling, the gapless topological surface states emerge in the film as thin as2QL, in good accord with the experiments.
3. The tuning of the surface and interface states by semiconductor substrate: We haveinvestigated the heterostructures of Bi_2Te_3/Si and Bi_2Se_3/GaAs by first-principlescalculations. It is found that the semiconductor substrate plays an important role in tuningthe Fermi level with respect to the Dirac point of topological insulators (TIs). Theworkfunctions of Bi_2Te_3and Bi_2Se_3are larger than that of the semiconductor substrate,leading to charge transfer from the substrate to TI and the upward Fermi level shift, whichis proportional to the difference of the workfunctions of the two interfaced materials.Thicker TI films have larger density of the states and hence the charge transferred to TIwill give rise to a smaller Fermi level shift. We also studied Bi_2Se_3on polarsemiconductor GaAs. It is found that different termination of GaAs at the interfacecorresponds to different work functions and will result in different Fermi level shift inBi_2Se_3.
引文
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