Magic angle conditions for twisted 3D topological insulators

Abstract

We derive a general low-energy theory for twisted moiré heterostructures comprised of Dirac materials. We apply our theory to heterostructures on the surface of a three dimensional topological insulator (3D TI). First, we consider the interface between two 3D TIs arranged with a relative twist angle. We prove that if the two TIs are identical, then a necessary condition for a magic angle where the Dirac cone velocity vanishes is to have an interlayer spin-flipping hopping term. Without this term, the Dirac cone velocities can still be significantly renormalized, decreasing to less than half of their original values, but they will not vanish. Second, we consider graphene on the surface of a TI arranged with a small twist angle. Again, a magic angle is only achievable with a spin-flipping hopping term. Without this term, the Dirac cone is renormalized, but not significantly. In both cases, our perturbative results are verified by computing the band structure of the continuum model. The enhanced density of states that results from decreasing the surface Dirac cone velocity provides a tunable route to realizing interacting topological phases.

References in corpus (13)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Flat Bands in Slightly Twisted Bilayer Graphene
• Continuum Model of the Twisted Bilayer
• Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity
• Designer Meron Lattice on the Surface of a Topological Insulator
• Magic continuum in twisted bilayer square lattice with staggered flux
• Magnetic moiré surface states and flat chern band in topological insulators
• Density Waves Instability and a Skyrmion Lattice on the Surface of Strong Topological Insulators
• Strong correlations at topological insulator surfaces and the breakdown of the bulk-boundary correspondence
• Band manipulation and spin texture in interacting moiré helical edges
• Transmission in graphene-topological insulator heterostructures
• Quantum spin Hall effect from multi-scale band inversion in twisted bilayer Bi${}_2$(Te${}_{1-x}$Se${}_x$)${}_3$

Cited by in corpus (13)

• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• High-order Van Hove singularities and their connection to flat bands
• Multilayer graphene with a superlattice potential
• Symmetries as the guiding principle for flattening bands of Dirac fermions
• Designer Meron Lattice on the Surface of a Topological Insulator
• Chiral model of twisted bilayer graphene realized in a monolayer
• ${\mathbb{Z}}_2$-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures
• Intrinsically-multilayer moiré heterostructures
• Kagome and honeycomb flat bands in moiré graphene
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Band theory for heterostructures with interface superlattices
• Sliding Luttinger Liquid and Topological Flat Bands in Symmetry Mismatched Moiré Interfaces
• Preservation of Topological Surface States in Millimeter-Scale Transferred Membranes