Dichotomy of Electron-Phonon Coupling in Graphene Moir\'e Flat Bands

Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands

Young Woo Choi and Hyoung Joon Choi

Phys. Rev. Lett. 127, 167001 – Published 11 October 2021

Abstract

Graphene moiré superlattices are outstanding platforms to study correlated electron physics and superconductivity with exceptional tunability. However, robust superconductivity has been measured only in magic-angle twisted bilayer graphene (MA-TBG) and magic-angle twisted trilayer graphene (MA-TTG). The absence of a superconducting phase in certain moiré flat bands raises a question on the superconducting mechanism. In this work, we investigate electronic structure and electron-phonon coupling in graphene moiré superlattices based on atomistic calculations. We show that electron-phonon coupling strength $λ$ is dramatically different among graphene moiré flat bands. The total strength $λ$ is very large ( $λ > 1$ ) for MA-TBG and MA-TTG, both of which display robust superconductivity in experiments. However, $λ$ is an order of magnitude smaller in twisted double bilayer graphene (TDBG) and twisted monolayer-bilayer graphene (TMBG) where superconductivity is reportedly rather weak or absent. We find that the Bernal-stacked layers in TDBG and TMBG induce sublattice polarization in the flat-band states, suppressing intersublattice electron-phonon matrix elements. We also obtain the nonadiabatic superconducting transition temperature $T_{c}$ that matches well with the experimental results. Our results clearly show a correlation between strong electron-phonon coupling and experimental observations of robust superconductivity.

Received 8 April 2021
Accepted 3 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.167001

Physics Subject Headings (PhySH)

Electron-phonon coupling Electronic structure Superconductivity

Graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Young Woo Choi and Hyoung Joon Choi ^*

Department of Physics, Yonsei University, Seoul 03722, Korea

^*h.j.choi@yonsei.ac.kr

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Vol. 127, Iss. 16 — 15 October 2021

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Figure 1
Atomic relaxation patterns of (a) TBG with $θ = 1.0 8 °$ , (b) TTG with an alternating twist angle $θ = 1.6 1 °$ , (c) TDBG with $θ = 1.3 5 °$ , and (d) TMBG with $θ = 1.2 5 °$ . $δ z$ is the deviation of atomic positions in the out-of-plane direction from the average value within each layer. Topmost two layers in (c) and bottom two layers in (c) and (d) are Bernal-stacked without twist.
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Figure 2
(a) Band structure and density of states (DOS) per spin and (b) electron-phonon coupling strength $λ$ as a function of the Fermi energies $E_{F}$ in (upper left) TBG with $θ = 1.0 8 °$ , (upper right) TTG with $θ = 1.6 1 °$ , (lower left) TDBG with $θ = 1.3 5 °$ , and (lower right) TMBG with $θ = 1.2 5 °$ . In (a), colored circles represent sublattice polarization (SP). TBG and TTG have exactly zero sublattice polarization. In (b), black lines show the total coupling strength. Red (blue) lines represent contributions of the inter- (intra-) sublattice electron-phonon coupling. In each case, the inset shows the average electron-phonon matrix element $V_{ep} = λ / N_{F}$ , where $N_{F}$ is the DOS per spin at $E_{F}$ . (c),(d) Illustrations of how sublattice polarization suppresses intersublattice electron-phonon matrix elements. Blue arrows indicate electron-phonon matrix elements induced by phonon displacements denoted by green arrows. When sublattice polarization is nonzero in (d), the nearest-neighbor electron-phonon matrix elements are weakened.
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Figure 3
(a) Eliashberg function $α^{2} F (ω)$ , shown in red, at the half-filling energy of the hole-side in (upper left) TBG and (upper right) TTG, and the electron-side in (lower left) TDBG and (lower right) TMBG. Dashed blue lines denote frequency-integrated electron-phonon coupling strength $λ (ω) = 2 \int_{0}^{ω} α^{2} F (ω^{'}) / ω^{'} d ω^{'}$ . Insets show low-frequency ranges of $α^{2} F (ω)$ . (b) Phonon frequencies and momenta of the characteristic modes.
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Figure 4
(a) Electronic structure and (b) electron-phonon coupling in (upper left) TBG with $θ = 1.0 8 °$ , (upper right) TTG with $θ = 1.6 1 °$ , (lower left) TDBG with $θ = 1.3 5 °$ , and (lower right) TMBG with $θ = 1.2 5 °$ under vertical electric field. The strength of electric field $E_{z}$ is $15 (5) mV / Å$ for TBG and TTG (TDBG and TMBG). The unit of DOS in (a) is $states /spin/ m eV$ . In (a), colors of band lines represent the sublattice polarization. TBG and TTG have exactly zero sublattice polarization. In (b), black lines show the total coupling strength. Red (blue) lines represent contributions of inter- (intra-) sublattice electron-phonon couplings.
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Physical Review Letters

Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands

Young Woo Choi and Hyoung Joon Choi

Phys. Rev. Lett. 127, 167001 – Published 11 October 2021

Abstract

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