Buckling and flat bands in twisted bilayer graphene

TL;DR

This study addresses engineering flatter bands in twisted bilayer graphene (TBG) beyond the conventional magic-angle by imposing periodic buckling to generate a pseudomagnetic field. Using a Slater-Koster tight-binding model with interlayer coupling up to sixth neighbors and a rigorously defined moiré unit cell, the authors show that large-angle TBG can experience enhanced band flattening under buckling due to reduced in-plane kinetic energy and gap opening at Dirac points from inversion-symmetry breaking, with the effect dampened at strong buckling. Near the magic angle, buckling and moiré flattening compete and are not additive, as buckling induces sublattice polarization and a gap that can make bands more dispersive, though higher-energy buckled bands can become exceptionally flat. Across a wide range of twist angles, buckling can substantially increase the integrated DOS near zero energy (IDOS) and even rival pristine magic-angle TBG in flat-band hosting, offering a robust route to stabilize correlated states and demonstrating experimental feasibility through substrate-induced buckling.

Abstract

Magic-angle twisted bilayer graphene (TBG) with its flat bands provides a rich platform for exploring emergent electronic orders. Similarly, periodically buckled monolayer graphene has been proposed as a tunable alternative for realizing flat bands. Here, we investigate the combined effect of buckling and twisting in bilayer graphene. We find that periodic buckling in large-angle TBG initially enhances band flattening compared to monolayer graphene, but for sufficiently strong buckling, it instead increases the band dispersion. This occurs both because of the presence of interlayer coupling, which reduces the in-plane kinetic energy, and due to the opening of a gap at the Dirac point resulting from inversion-symmetry breaking. Additionally, we find that buckling-induced band flattening competes with twist-induced band flattening. While the former breaks sublattice symmetry, generating a sublattice polarization, the latter prefers to preserve it. This prevents buckling from generating even flatter bands at the magic angle. Nevertheless, we find that buckled TBG can exhibit flatter bands than pristine TBG over a wide range of twist angles, with a flatness similar to that of pristine magic-angle TBG.

Figures (7)

• Figure 1: Band structure of magic-angle TBG (a), with zoom-in on moiré bands highlighted in red (b), charge density of the moiré bands (c), and the buckling-induced PMF of Eq. \ref{['eq:tripmf']} projected over the moiré unit cell (d). Indicated in (d) are the different stacking regions of TBG.
• Figure 2: Low-energy band structure of buckled monolayer graphene (a) and large-angle TBG at $\theta = 3.15 \degree$ (b) for different PMF strengths, with the same moiré unit cell in (a,b).
• Figure 3: Low-energy band structure for pristine and buckled AA-stacked bilayer graphene with $B_0=10000$ T and $L_m= a$ (a), AB-stacked bilayer graphene with $B_0= 10000$ T and $L_m= a$ (b), and large-angle TBG at $\theta = 3.15\degree$, corresponding to $L_m\approx18.2\,a$, with $B_0= 100$ T (c) to keep that the product $L_m B_0$ roughly constant. Red bands are the moiré bands. Dotted bands correspond to pristine, non-buckled bands. Note in (c) the smaller scale on the y-axis.
• Figure 4: Low-energy band structures (a-c) and corresponding top layer sublattice-resolved (A, B) moiré charge densities $n_m$ (d-f) for buckled magic-angle TBG with buckle centered in the AA-stacked region (${\bf r}_0 = 0$), indicated with pink crosses in (d), and buckling strengths $B_0 = 10$ T (a,d), 25 T (b,e), and 35 T (c,f). Red bands are the four energy bands that most resemble the moiré bands, gray bands in (a) are those of pristine magic-angle TBG.
• Figure 5: Same as \ref{['fig:AAmagicband']}, but with buckle centered on the AB-stacked region, indicated with pink cross in (d).