When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems)
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2024
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| author | Kwan, Yves H. Wagner, Glenn Yu, Jiabin Dagnino, Andrea Kouta Jiang, Yi Xu, Xiaodong Bernevig, B. Andrei Neupert, Titus Regnault, Nicolas |
| author_facet | Kwan, Yves H. Wagner, Glenn Yu, Jiabin Dagnino, Andrea Kouta Jiang, Yi Xu, Xiaodong Bernevig, B. Andrei Neupert, Titus Regnault, Nicolas |
| contents | Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $θ\approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $ν=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $θ\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $ν=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_02560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems) Kwan, Yves H. Wagner, Glenn Yu, Jiabin Dagnino, Andrea Kouta Jiang, Yi Xu, Xiaodong Bernevig, B. Andrei Neupert, Titus Regnault, Nicolas Strongly Correlated Electrons Mesoscale and Nanoscale Physics Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $θ\approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $ν=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $θ\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $ν=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases. |
| title | When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems) |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2407.02560 |