Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing

Bernevig, B. Andrei; Lian, Biao; Cowsik, Aditya; Xie, Fang; Regnault, Nicolas; Song, Zhi-Da

doi:10.1103/physrevb.103.205415

Title: Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing

Journal Article · Tue May 11 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.205415· OSTI ID:1852146

Bernevig, B. Andrei ^[1]; Lian, Biao ^[1]; Cowsik, Aditya ^[1]; Xie, Fang ^[1]; Regnault, Nicolas ^[2];

^[1]

Princeton Univ., NJ (United States)
Princeton Univ., NJ (United States); Sorbonne Univ., Paris (France); University Paris-Diderot (France)

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 A A and A B / B A 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^-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.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0016239

OSTI ID:: 1852146

Journal Information:: Physical Review. B, Vol. 103, Issue 20; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Strange Metal in Magic-Angle Graphene with near Planckian Dissipation Cao, Yuan; Chowdhury, Debanjan; Rodan-Legrain, Daniel Physical Review Letters, Vol. 124, Issue 7 https://doi.org/10.1103/PhysRevLett.124.076801	journal	February 2020
Landau levels in twisted bilayer graphene and semiclassical orbits Hejazi, Kasra; Liu, Chunxiao; Balents, Leon Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevB.100.035115	journal	July 2019

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