Speaker
Description
Moiré materials represent one of the richest fields in condensed matter physics, with twisted bilayer graphene (TBG) serving as a prime example. TBG exhibits exotic physical properties, including unconventional superconductivity and delocalized eigenstates in both momentum and real space near the flat-band regime. Recent experiments on hBN/TBG and twisted trilayer graphene (TTG) have uncovered a new, intrinsically quasiperiodic regime driven by competing incommensurate moirés, dubbed moiré quasicrystals. Because these phases also host robust correlated states, understanding the exact role of quasiperiodicity is essential to determine whether such phenomena are driven by correlation, topology, or the explicit breaking of translational invariance.
To address this, we perform real-space atomistic tight-binding simulations of 2D moiré materials containing up to 10 million atoms. By comparing quasiperiodic and commensurate (unit cell = 1 moiré cell) TBG, we conduct a multifractal analysis of the local density of states to extract the singularity spectrum, a quantity directly accessible to experimentalists via STS maps. Our results show that incommensurate magic-angle TBG, the flat band is strictly multifractal, whereas commensurate structures remain monofractal. In contrast, the remote bands exhibit perfect monofractal behavior across both regimes.