Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene

Abstract

We study the electronic structure and band topology of fully relaxed twisted multi-layer graphene (TMLG). Isolated flat bands emerge in TMLG with the number of layers [$M+N$ with $M$ the layer number of the bottom few-layer graphene (FLG)] up to 10 and with various stacking orders, and most of them are on the hole side. The touched bands of FLGs around the Fermi level are split by the moiré coupling through the electron-hole asymmetry in low-energy bands of FLGs and by the vertical hopping between next-nearest layers. The full structural relaxation leads to global gaps that completely isolate a flat band. For TMLG with given $M$ and $N$, the highest magnitude of Chern numbers ($|C|$) of the separable flat bands reaches $M+N-1$ and can be hosted by certain isolated bands. The $|C|=9$ occurs in the isolated flat valence band of several configurations with 10 layers. Such high $|C|$ originates from the lifting of the band-state degeneracy in the weak regime of moiré coupling or from the topological phase transitions induced by the strong moiré coupling. Moreover, large orbital magnetic moments arise in isolated flat bands with high $|C|$ and depend on the structural configurations of TMLG.

10 pages, 7 figures

References in corpus (20)

• Graphene Bilayers with a Twist
• Continuum Model of the Twisted Bilayer
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Band Structure of ABC-Stacked Graphene Trilayers
• Electrical switching of magnetic order in an orbital Chern insulator
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Flatbands in twisted double bilayer graphene
• Band structure and topological property of twisted double bilayer graphenes
• The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta \sim 1.08^{\circ }$
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Voltage-Controlled Magnetic Reversal in Orbital Chern Insulators
• Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
• Band structure of twisted bilayer graphene on hexagonal boron nitride
• Electronic structure calculations of twisted multi-layer graphene superlattices
• Quasiperiodicity, band topology, and moiré graphene
• Pressure induced gap modulation and topological transitions in twisted bilayer and double bilayer graphene
• Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
• $\text{Ab initio}$ four-band Wannier tight-binding model for generic twisted graphene systems
• Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride

Cited by in corpus (3)

• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
• Moiré Flat Bands of Twisted Few-layer Graphite