Magic-Angle Semimetals with Chiral Symmetry

Understand

We construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation.

• In real space, this is realized with a quasiperiodic hopping term.
• This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states and sub-diffusive transport when the quasiperiodic hopping is strongest.
• We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique "unfreezing" transition.