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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2502.06938 |
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| _version_ | 1866917935507832832 |
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| author | Vorobev, Dmitrii Chen, Yiheng Tarnopolsky, Grigory M. |
| author_facet | Vorobev, Dmitrii Chen, Yiheng Tarnopolsky, Grigory M. |
| contents | We consider a general model of two atomic chains forming a moiré pattern due to a small mismatch in their lattice spacings, given by $θ= (a_{1} - a_{2})/a_{2}$. Assuming arbitrary single-band dispersion relations $\varepsilon_{1}(p)$ and $\varepsilon_{2}(q)$ for the chains, along with an arbitrary inter-chain coupling term $T(x)$, we show that the entire spectrum of such a one-dimensional moiré superchain is governed by a single three-term recurrence (TTR) relation. We analyze this TTR relation using the discrete WKB method and demonstrate how the entire structure of the spectrum as well as emergence of flat bands can be easily identified from a pair of upper and lower potential functions of the TTR relation. We also comment on the chiral limit of the moiré superchain, which can be viewed, in some sense, as a 1D analog of the chiral limit of Twisted Bilayer Graphene. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Entire Structure of the Energy Bands of 1D Moiré Superchain Vorobev, Dmitrii Chen, Yiheng Tarnopolsky, Grigory M. Strongly Correlated Electrons Mesoscale and Nanoscale Physics We consider a general model of two atomic chains forming a moiré pattern due to a small mismatch in their lattice spacings, given by $θ= (a_{1} - a_{2})/a_{2}$. Assuming arbitrary single-band dispersion relations $\varepsilon_{1}(p)$ and $\varepsilon_{2}(q)$ for the chains, along with an arbitrary inter-chain coupling term $T(x)$, we show that the entire spectrum of such a one-dimensional moiré superchain is governed by a single three-term recurrence (TTR) relation. We analyze this TTR relation using the discrete WKB method and demonstrate how the entire structure of the spectrum as well as emergence of flat bands can be easily identified from a pair of upper and lower potential functions of the TTR relation. We also comment on the chiral limit of the moiré superchain, which can be viewed, in some sense, as a 1D analog of the chiral limit of Twisted Bilayer Graphene. |
| title | On the Entire Structure of the Energy Bands of 1D Moiré Superchain |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2502.06938 |