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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2312.00986 |
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| _version_ | 1866917780775763968 |
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| author | Khaetskii, Alexander Golovach, Vitaly Kiefer, Arnold |
| author_facet | Khaetskii, Alexander Golovach, Vitaly Kiefer, Arnold |
| contents | We consider surface states in semiconductors with inverted-band structures, such as $α$-Sn and HgTe. The main interest is the interplay of the effect of a strain of an arbitrary sign and that of the sample finite size. We consider, in particular, a model system comprised of a gapless semiconductor (e.g. HgTe or $α$-Sn) of finite-width sandwiched between layers of a regular-band semiconductor (e.g. CdTe or InSb). We clarify the origin of various transitions that happen at a given strain with the change of the sample thickness, in particular the transition between the Dirac semimetal and quasi-3D (quantized) topological insulator. Our conclusion opposes those reached recently by the majority of researchers. We show that near the transition point the surface state cannot be treated as a truly topological one since the parameters of the problem are such that an appreciable overlap of the surface states' wave functions located at opposite boundaries occur. As a result, a spin-conserving, elastic impurity scattering between the states located at opposite boundaries will induce substantial backscattering and destroy the robustness of the surface state. For the k-p Kane model we derive hard-wall boundary conditions in the case when the regular-band materials form high barriers for the carriers of the inner inverted-band semiconductor (for example, CdTe/HgTe/CdTe and CdTe/$α$-Sn/CdTe cases). We show that in this case the boundary conditions have universal and simple form and allow investigation of the realistic case of finite mass of the heavy-hole band, and comparison of the results obtained within the Kane and Luttinger models. In particular, a new type of surface states (wing states) developes with application of strain in the Kane model and is absent in the Luttinger model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00986 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Interplay between strain and size quantization in a class of topological insulators based on inverted-band semiconductors Khaetskii, Alexander Golovach, Vitaly Kiefer, Arnold Mesoscale and Nanoscale Physics We consider surface states in semiconductors with inverted-band structures, such as $α$-Sn and HgTe. The main interest is the interplay of the effect of a strain of an arbitrary sign and that of the sample finite size. We consider, in particular, a model system comprised of a gapless semiconductor (e.g. HgTe or $α$-Sn) of finite-width sandwiched between layers of a regular-band semiconductor (e.g. CdTe or InSb). We clarify the origin of various transitions that happen at a given strain with the change of the sample thickness, in particular the transition between the Dirac semimetal and quasi-3D (quantized) topological insulator. Our conclusion opposes those reached recently by the majority of researchers. We show that near the transition point the surface state cannot be treated as a truly topological one since the parameters of the problem are such that an appreciable overlap of the surface states' wave functions located at opposite boundaries occur. As a result, a spin-conserving, elastic impurity scattering between the states located at opposite boundaries will induce substantial backscattering and destroy the robustness of the surface state. For the k-p Kane model we derive hard-wall boundary conditions in the case when the regular-band materials form high barriers for the carriers of the inner inverted-band semiconductor (for example, CdTe/HgTe/CdTe and CdTe/$α$-Sn/CdTe cases). We show that in this case the boundary conditions have universal and simple form and allow investigation of the realistic case of finite mass of the heavy-hole band, and comparison of the results obtained within the Kane and Luttinger models. In particular, a new type of surface states (wing states) developes with application of strain in the Kane model and is absent in the Luttinger model. |
| title | Interplay between strain and size quantization in a class of topological insulators based on inverted-band semiconductors |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2312.00986 |