Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene
Abstract
The recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($$d$$ + i$$d$$ mixed with $$p$$-i$$p$$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three $$M$$ points in the Brillouin Zone, and a 2 × 2 pattern in real space. In simple treatments though, this leads to a full gap at fillings ± (1/2 + 1/8), slightly away from half-filling. The selection of spin-singlet or spin triplet orders, both for the IVCW and the superconductor, arise fcase corresponds to the Hundsrom SO(4) symmetry breaking terms. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1559263
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- npj Quantum Materials
- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2397-4648
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
You, Yi-Zhuang, and Vishwanath, Ashvin. Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene. United States: N. p., 2019.
Web. doi:10.1038/s41535-019-0153-4.
You, Yi-Zhuang, & Vishwanath, Ashvin. Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene. United States. https://doi.org/10.1038/s41535-019-0153-4
You, Yi-Zhuang, and Vishwanath, Ashvin. Mon .
"Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene". United States. https://doi.org/10.1038/s41535-019-0153-4. https://www.osti.gov/servlets/purl/1559263.
@article{osti_1559263,
title = {Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene},
author = {You, Yi-Zhuang and Vishwanath, Ashvin},
abstractNote = {The recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($d$ + i$d$ mixed with $p$-i$p$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three $M$ points in the Brillouin Zone, and a 2 × 2 pattern in real space. In simple treatments though, this leads to a full gap at fillings ± (1/2 + 1/8), slightly away from half-filling. The selection of spin-singlet or spin triplet orders, both for the IVCW and the superconductor, arise fcase corresponds to the Hundsrom SO(4) symmetry breaking terms. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.},
doi = {10.1038/s41535-019-0153-4},
journal = {npj Quantum Materials},
number = 1,
volume = 4,
place = {United States},
year = {Mon Apr 29 00:00:00 EDT 2019},
month = {Mon Apr 29 00:00:00 EDT 2019}
}
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