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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.02353 |
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| _version_ | 1866916546145681408 |
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| author | Yu, Jiabin Xie, Ming Wu, Fengcheng Sarma, Sankar Das |
| author_facet | Yu, Jiabin Xie, Ming Wu, Fengcheng Sarma, Sankar Das |
| contents | Magic-angle twisted bilayer graphene (MATBG) hosts normal-state nearly-flat bands with nonzero Euler numbers and shows superconductivity. In this work, we study the effects of the nontrivial normal-state band topology on the intervalley $C_{2z}\mathcal{T}$-invariant mean-field Cooper pairing order parameter in MATBG. We show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel in all gauges for the normal-state basis, generalizing the previously-studied channel splitting in the Chern gauge. The nonzero normal-state Euler numbers require the pairing gap function of the Euler obstructed channel to have zeros, while the trivial channel can have a nonvanishing pairing gap function. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. Under the approximation of exactly-flat bands, we find that the mean-field zero-temperature superfluid weight is generally bounded from below, no matter whether the Euler obstructed channel is dominant or not, generalizing the previously-derived bound for the uniform s-wave pairing. We numerically verify these statements for pairings derived from a local attractive interaction. Our work suggests that Euler obstructed Cooper pairing may play an essential role in the superconducting MATBG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02353 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight Yu, Jiabin Xie, Ming Wu, Fengcheng Sarma, Sankar Das Superconductivity Mesoscale and Nanoscale Physics Magic-angle twisted bilayer graphene (MATBG) hosts normal-state nearly-flat bands with nonzero Euler numbers and shows superconductivity. In this work, we study the effects of the nontrivial normal-state band topology on the intervalley $C_{2z}\mathcal{T}$-invariant mean-field Cooper pairing order parameter in MATBG. We show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel in all gauges for the normal-state basis, generalizing the previously-studied channel splitting in the Chern gauge. The nonzero normal-state Euler numbers require the pairing gap function of the Euler obstructed channel to have zeros, while the trivial channel can have a nonvanishing pairing gap function. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. Under the approximation of exactly-flat bands, we find that the mean-field zero-temperature superfluid weight is generally bounded from below, no matter whether the Euler obstructed channel is dominant or not, generalizing the previously-derived bound for the uniform s-wave pairing. We numerically verify these statements for pairings derived from a local attractive interaction. Our work suggests that Euler obstructed Cooper pairing may play an essential role in the superconducting MATBG. |
| title | Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight |
| topic | Superconductivity Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2202.02353 |