Interplay between many-body correlations, strain and lattice relaxation in twisted bilayer graphene

Abstract

In twisted bilayer graphene, a unified understanding of the mechanisms governing temperature-dependent electronic spectra and thermodynamic properties remains controversial despite extensive theoretical efforts. Here, we present a comprehensive theoretical framework that quantitatively accounts for scanning tunneling spectroscopy, quantum twisting microscopy, and thermodynamic properties of magic angle twisted bilayer graphene. We demonstrate that the observed behavior arises from the interplay between electron correlations and external symmetry-breaking induced by strain and lattice relaxation. These effects act cooperatively to shape the emergent electronic behavior, leaving characteristic signatures across spectroscopy, compressibility and entropy.

Figures (15)

• Figure 1: a Sketch of strained twisted bilayer graphene lattice structure. The red arrows represent the moiré lattice vectors, while the shaded area is the strained unit cell. b Non-interacting dispersion of the unperturbed (dashed) and strained and relaxed (solid) THF models for the $K$ valley. c Occupation of the $f_{+}$ and $f_{-}$ orbitals as a function of filling. d Local (mBZ-averaged) spectral function. e Spectral function at the $K_{M}$-point and f at the $\Gamma_{M}$-point for fillings $\nu \in [-4, 4]$ with $0.15\%$ uniaxial heterostrain and lattice relaxation. All data are in the symmetric phase and for $T=11.6$ K. The black dotted line in f is the $\-\mu(\nu)$ curve. The dashed vertical lines are drawn at $\pm M_f \epsilon_-$ which is the magnitude of the strain-induced splitting in the non-interacting model.
• Figure 2: Momentum-resolved $f$-projected spectral function with lattice relaxation and $0.15\%$ strain at filling $\nu=-0.8$ and $T=11.6 K$, projected onto the strain split $f_{+}$ (orange) and $f_{-}$ (blue) orbitals. On the h-doped side ($\nu<0$), the persistent feature at around $10$ meV is made up of unoccupied $f_{+}$ spectral weight.
• Figure 3: a Sketch of the bare (zero-hybridization) dispersion of the $f$- and $c$-electrons in the relaxed THF model (left) and the corresponding density of states (right), b Inverse charge compressibility $\partial\mu/\partial\nu$ as a function fo filling in TBLG with and without lattice relaxation and $0.15\%$ strain and $T=11.6$ K, compared with experimental data pierceUnconventionalSequenceCorrelated2021zondinerCascadePhaseTransitions2020saitoIsospinPomeranchukEffect2021. P-symmetry breaking due to lattice relaxation results in stronger peaks and troughs in the inverse compressibility on the electron-doped side.
• Figure 4: Entropy as a function of filling of unperturbed TBLG (orange lines) compared to that of strained ($0.15\%$) and relaxed TBLG (blue lines). The error bars (shaded area) are obtained by propagating the relative mean square deviation of a sample of DMFT-CTQMC iterations after convergence. In the unstrained case, the entropy on the hole-doping side is not calculated directly, since it is is determined by $P$-symmetry. It is denoted by thin lines without error bars.
• Figure 5: Development of the strain-induced resonance splitting in the local spectral function for three values of doping: (a)$\nu = -0.8$, fractional filling, where in the unstrained case a pinned resonance at the Fermi level is observed, (b)$\nu = -0.0$, the charge neutrality point, where two Hubbard peaks are observed, and (c)$\nu = 2.0$, where in the unstrained case a coherent spectral peak is present at $\omega\approx -10 meV$. The grey shaded area represents the energy splitting of the $f$-orbitals in the noninteracting model. These have been shifted to be centered around the frequency of the noniteracting spectral maximum in panels (a,c) so as to offer a comparison between the interacting and noninteracting splitting magnitude.