Capturing magic angles in twisted bilayer graphene from information theory markers

Zero energy eigenstates ψ 0 ( θ ) of the twisted bilayer graphene Hamiltonian at the Dirac point show a high sensitivity to the twist angle θ near the magic angles where the effective Fermi velocity vanishes. We use information theory markers, like fidelity-susceptibility and entanglement entropy of the reduced density matrix to the layer sector, to capture this quantum criticality of zero modes at magic twist angles. • This article contributes to unravel the magic behind the electronic properties and exotic quantum states of twisted bilayer graphene. • The quantum criticality of zero modes at magic twist angles is revealed by fidelity and entanglement measures, as an alternative complement to the usual Fermi velocity, conductivity and band flattening characteristics. • We provide plots of fidelity, entanglement and interlayer hopping probabilities of conduction and valence zero modes as a function of the twist angle, where magic angles are conspicuous.