Narrow bands in magnetic field and strong-coupling Hofstadter spectra

Abstract

We develop a new, efficient, and general method to determine the Hofstadter spectrum of isolated narrow bands. The method works for topological as well as for trivial narrow bands by projecting the zero $\mathbf{B}$-field hybrid Wannier states -- which are localized in one direction and Bloch extended in another direction -- onto a representation of the magnetic translation group in the Landau gauge. We then apply this method to find, for the first time, the Hofstadter spectrum for the exact single particle charged excitations in the strong coupling limit of the magic angle twisted bilayer graphene at the charge neutrality point and at $|\nu |=2$ down to low magnetic fields when the flux through the moiré unit cell is only $\sim 1/25$ of the electronic flux quantum i.e. $\sim 1$T at the first magic angle. The resulting spectra provide a means to investigate Landau quantization of the quasiparticles even if their dispersion is interaction induced.

arXiv commentVersion 2 with 17 pages and 10 figures. Strong coupling excitation spectra (heavy hole and light electron) at nu=2, and supplementary material added

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• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Extended linear-in-$T$ resistivity due to electron-phason scattering in moiré superlattices
• Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers
• Magic momenta and three dimensional Landau levels from a three dimensional graphite moiré superlattice
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Revisiting Bloch electrons in magnetic field: Hofstadter physics via hybrid Wannier states
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Superconductivity in a Topological Lattice Model with Strong Repulsion