Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture
Abstract
Flat bands amplify interactions into correlated phases, and topological bound states are robust by principle; combining the two in a model that is both exactly analyzable and experimentally accessible is therefore especially desirable. Here we show that a square-lattice model with a slowly modulated Dirac mass texture, m(x)=m+m0cos(2πx/L) with L up to hundreds of sites, provides such a setting, without engineered geometries, lattice-scale textures, or long-range hoppings. Exact nesting reduces the problem, independently at each transverse momentum ky, to a 1+1 dimensional Dirac Hamiltonian with a position-dependent mass: every simple zero of m(x) binds Jackiw-Rebbi zero modes, and the two walls of a period form an effective Su-Schrieffer-Heeger ring. The model interpolates between a chirally pinned flat band at large L, a helical miniband whose nodes are enforced by a boundary phase of the ring, and a bias-dimerized regime in which the sign of the bias sets a winding number. A central result is that the miniband bandwidth is not a single scale: a max-min measurement conflates three widths of different origin, the helical height WJR exponential in the period, the zone-edge upturn Wedge∝ L−2/3 dominating at large L, and a bias bump exponential in L, so the flat band is robust against bias in the thermodynamic limit. We analyze two lattice realizations, a two-orbital model with modulated inter-orbital hybridization and a single-orbital bond-order texture sharing the nodal physics while leaving the van Hove points gapless, and propose experiments on cold-atom superlattices, Kekule-ordered graphene, STM designer lattices, and microwave arrays.
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BibTeX
@misc{zhou2026chirally,
title = {{Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture}},
author = {Tao Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16183},
eprint = {2610.16183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16183},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture
AU - Tao Zhou
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16183
UR - https://arxiv.org/abs/2610.16183
AB - Flat bands amplify interactions into correlated phases, and topological bound states are robust by principle; combining the two in a model that is both exactly analyzable and experimentally accessible is therefore especially desirable. Here we show that a square-lattice model with a slowly modulated Dirac mass texture, m(x)=m+m_0cos(2πx/L) with L up to hundreds of sites, provides such a setting, without engineered geometries, lattice-scale textures, or long-range hoppings. Exact nesting reduces the problem, independently at each transverse momentum k_y, to a 1+1 dimensional Dirac Hamiltonian with a position-dependent mass: every simple zero of m(x) binds Jackiw-Rebbi zero modes, and the two walls of a period form an effective Su-Schrieffer-Heeger ring. The model interpolates between a chirally pinned flat band at large L, a helical miniband whose nodes are enforced by a boundary phase of the ring, and a bias-dimerized regime in which the sign of the bias sets a winding number. A central result is that the miniband bandwidth is not a single scale: a max-min measurement conflates three widths of different origin, the helical height W_JR exponential in the period, the zone-edge upturn W_edge∝ L^−2/3 dominating at large L, and a bias bump exponential in L, so the flat band is robust against bias in the thermodynamic limit. We analyze two lattice realizations, a two-orbital model with modulated inter-orbital hybridization and a single-orbital bond-order texture sharing the nodal physics while leaving the van Hove points gapless, and propose experiments on cold-atom superlattices, Kekule-ordered graphene, STM designer lattices, and microwave arrays.
ER -