Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing
| Autor: | Biao Lian, Zhida Song, Fang Xie, Aditya Cowsik, B. Andrei Bernevig, Nicolas Regnault |
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| Přispěvatelé: | Department of Physics, Princeton University (DPPU), Princeton University, Théorie de la Matière Condensée, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Phonon Binding energy Charge (physics) 02 engineering and technology 021001 nanoscience & nanotechnology Kinetic energy 7. Clean energy 01 natural sciences [PHYS.COND.CM-S]Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con] Quantum mechanics 0103 physical sciences Coulomb Cooper pair [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] 010306 general physics 0210 nano-technology Bilayer graphene Wave function ComputingMilieux_MISCELLANEOUS [PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] |
| Zdroj: | Physical Review B Physical Review B, American Physical Society, 2021, 103 (20), pp.205415. ⟨10.1103/PhysRevB.103.205415⟩ |
| ISSN: | 2469-9950 2469-9969 |
| Popis: | We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of $AA$ and $AB/BA$ tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since Vafek and Kang [Phys. Rev. Lett. 125, 257602 (2020)] showed that the kinetic energy bounds on the superexchange energy are less ${10}^{\ensuremath{-}3}$ in Coulomb units, the phonon mechanism becomes then very likely. If nonetheless the superconductivity is due to kinetic terms which render the bands nonflat, one prediction of our theory is that the highest ${T}_{c}$ would not occur at the highest DOS. |
| Databáze: | OpenAIRE |
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