Topological domain-wall states from Umklapp scattering in twisted bilayer graphene

TL;DR

This work addresses the challenge of understanding large-angle twist physics in bilayer graphene, where intervalley Umklapp scattering and structural chirality govern low-energy bands. By building symmetry-constrained $k\cdot p$ models for $D_6$ and $D_3$ tBG at $21.8^{\circ}$ and validating with atomistic simulations, the authors reveal a gapped, BHZ-like topological phase for $D_6$ and a semimetallic quadratic crossing for $D_3$, with chirality reversal across domain walls producing robust, Jackiw–Rebbi-type topological interfacial states. These domain-wall modes persist under various symmetry-breaking perturbations and even in generic, randomly displaced tBG, indicating universal topological channels that can be engineered at chirality interfaces. The results establish a new mechanism to design chiral transport in twisted van der Waals materials and suggest broader applicability to other layered systems via intervalley Umklapp-driven topology.

Abstract

Twistronics, harnessing interlayer rotation to tailor electronic states in van der Waals materials, has predominantly focused on small-angle regime. Here, we unveil the pivotal role of intervalley Umklapp scattering in large-angle twisted bilayer graphene, which governs low-energy physics and drives unconventional band topology. By constructing symmetry-constrained effective $k\cdot p$ models for $\pm 21.8^{\circ}$-twisted bilayers, we demonstrate how structural chirality imprints distinct electronic responses. The $D_6$ configuration exhibits a gapped spectrum with chiral interlayer coupling, while $D_3$ symmetric stacking configuration displays semimetallic behavior. Crucially, chirality inversion creates topological domain-wall states, which manifest as counterpropagating pseudospin modes at interfaces between oppositely twisted regions. These states, absent in untwisted bilayers, emerge from a Jackiw-Rebbi-like mechanism tied to chirality reversal. Atomistic simulations confirm these topological states and demonstrate their robustness against symmetry-breaking perturbations. The interplay between twist-induced chirality and topology opens new pathways for engineering domain-wall states in twisted materials.

Figures (7)

• Figure 1: (a-c) Crystal structures of the $D_6$, $D_3$, and $D_3^\prime$ configurations, respectively. Red/blue colors denote top/bottom layers; solid/hollow markers distinguish $A$/$B$ sublattices. (d) Direct band gap maps of local structures versus in-plane translation vector $\boldsymbol{d}$ of top layer. (e) Brillouin zone schematic of monolayer Dirac points at small twist angles: solid/hollow markers denote $K$/$K^{\prime}$ valleys; red/blue colors indicate top/bottom layers. Layer hybridization is dominated by intravalley channel near the Dirac points (dotted black circles). (f) Brillouin zone schematic for $\theta=21.8^{\circ}$ showing $K$/$K^{\prime}$ points of top layer overlapping with $K^{\prime}$/$K$ points of bottom layer at second-zone corners (dotted green circles). Layer hybridization here is dominated by the intervalley Umklapp processes.
• Figure 2: Comparison of low-energy band structures in large-angle tBG versus untwisted bilayers. (a, d) Bulk bands of the $D_6$ and $D_3$ configurations from atomistic-SKTB method. (b, e) Corresponding $k\cdot p$ effective model results. (c, f) Untwisted $AA$/$AB$-stacked bilayer graphene bands for reference. Color coding denotes $k$-space band geometric quantity $\omega_n(\boldsymbol{k})$. (g, h) Intra- and interlayer chiral term effects in $D_3$$k\cdot p$ model: chiral hoppings restore characteristic trigonal warping in low-energy bands (only topmost valence and bottommost conduction bands are shown).
• Figure 3: Topological domain-wall states induced by structural chirality. (a) Schematic of a domain wall between $\theta = \pm 21.8^\circ$ tBG ($D_6$ configuration). A short length is shown for better representation. (b, c) Corresponding energy spectra.
• Figure 4: Topological robustness against different symmetry-breaking perturbations. (a-d) Energy spectra for the domain walls under $H_s^{(1)}, H_s^{(2)}, H_s^{(3)}$ ($\Delta_s=15$ meV) and $7\%$ uniaxial strain, respectively. (e, f) Crystal structure and domain-wall states for a configuration displaced from $D_6$ structure by $\boldsymbol{L}_1/21$. (g, h) Alternative realization of the topological domain-wall states.
• Figure A1: The atomistic-SKTB band structures of domain walls under three kinds of symmetry-breaking perturbations $(\Delta_s/2)\tau_z\sigma_z$, $(\Delta_s/2)\tau_0\sigma_z$ and $(\Delta_s/2)\tau_z\sigma_0$.