Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions

Abstract

Flat-bands play a central role in the presence of correlated phases in Moiré and other modulated two dimensional systems. In this work, flat-bands are shown to exist in uniaxially periodic strained graphene. Such strain should be produced for example by a substrate. The model is thus mapped into a one-dimensional effective Hamiltonian and this allows to find the conditions for having flat-bands, i.e., a long-wavelength modulation only on each one of the bipartite graphene sublattices, while having a tagged strain field between neighboring carbon atoms. The origin of such flat-bands is thus tracked down to the existence of topological localized wavefunctions at domain walls separating different regions, each with a non-uniform Su-Schriffer-Hegger model (SSH) type of coupling. Thereafter, the system is mapped into a continuum model allowing to explain the numerical results in terms of the Jackiw-Rebbi model and of pseudo-Landau levels. Finally, the interplay between the obtained flat-bands and electron-electron interaction is explored through the Hubbard model. The numerical results within the mean-field approximation indicate that the flat-bands induce Néel antiferromagnetic and ferromagnetic domains even for a very weak Hubbard interaction. The present model thus provides a simple platform to understand the physical origin of flat-bands, pseudo-Landau levels and the effects of the electron-electron interaction.

arXiv comment10 pages, 9 figures

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• Absence of edge states at armchair edges in inhomogeneously strained graphene under a pseudomagnetic field
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Quantum percolation on Lieb Lattices
• Flat bands without twists: periodic holey graphene
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices
• Protected Fermionic Zero Modes in Periodic Gauge Fields
• Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates
• Interaction-driven charge textures and unconventional superconductivity in strained monolayer graphene
• Dislocation Patterning as a Mechanism for Flat Band Formation