Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25 T ($2\pi$ Flux)

Twisted bilayer graphene (TBG) is remarkable for its topological flat bands, which drive strongly interacting physics at integer fillings, and its simple theoretical description facilitated by the Bistritzer-MacDonald Hamiltonian, a continuum model coupling two Dirac fermions. Because of the large moiré unit cell, TBG offers the unprecedented opportunity to observe reentrant Hofstadter phases in laboratory-strength magnetic fields near 25 T. This Letter is devoted to magic angle TBG at $2\pi$ flux where the magnetic translation group commutes. We use a newly developed gauge-invariant formalism to determine the exact single-particle band structure and topology. We find that the characteristic TBG flat bands reemerge at $2\pi$ flux, but, due to the magnetic field breaking $C_{2z}\mathcal{T}$, they split and acquire Chern number $\pm 1$. We show that reentrant correlated insulating states appear at $2\pi$ flux driven by the Coulomb interaction at integer fillings, and we predict the characteristic Landau fans from their excitation spectrum.

Figure 1

TBG in flux. (a) The band structure and density of states at $\varphi =2\pi$, $w_0/w_1=0.8$, and $\theta =1.05°$ reveal $\sim 1.5\mathrm{meV}$ flat bands with a 40 meV gap. (b) The Hofstadter spectrum shows the flat bands remain gapped at all flux. (c) The Wilson loop of the two flat bands is trivial due to $C_2\mathcal{T}$ breaking when particle-hole symmetry is intact. (d) The flat bands at $2\pi$ flux.

Figure 2

$\frac{1}{2}{R}_{\pm }^{\eta }(\mathbf{k})$ spectra at $w_0/w_1=0.71$. (a) At $\nu =0$, the charge $\pm 1$ excitations are identical and feature a quadratic (massive) dispersion at the $\mathrm{\Gamma }$ point. (b) At $\nu =2$, the charge $-1$ excitation (red) has a large mass, strongly suppressing the Landau fans pointing toward charge neutrality, while the $+1$ excitation (blue) is lighter by a factor of 3. The $+1$ charge gap at $\nu =2$ is $\sim 0.5\mathrm{meV}$ or roughly 5 K.