Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene

Abstract

We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance of samples with fixed width decreases with the system size in the longitudinal direction for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability/quasiperiodicity effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.

Low energy excitation spectrum of magic-angle semimetals

“…Along these lines, recent theoretical work has found that incommensurate effects at moderate (θ = 9 • in the chiral limit) [27] and small twist angles (θ ≈ 1.05 • i.e. the magic-angle) [52] in twisted bilayer graphene can play a significant role when the velocity vanishes at the magic-angle through wavefunction multifractality in momentum space and subballistic transport. These incommensurate effects may also be relevant to limits in the resolution of recent angle resolved photoemission spectroscopy (ARPES) measurements of magic-angle twisted bilayer graphene [53,54].…”

Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors

“…At this transition the Weyl velocity goes to zero continuously, the density of states becomes non-analytic, and the single particle wavefunctions at the Dirac node energy delocalize in momentum space. Studies of similar effects in two-dimensional Dirac semimetal models [46][47][48] have linked this quantum phase transition with the magic-angle phenomena originally discovered in twisted bilayer graphene [49] (and extended to incorporate incommensurate effects [46,50]). Thus, the transition that was originally sought in disordered Weyl semimetals was uncovered in the quasiperiodic limit by removing rare regions from the problem.…”

“…We do so by considering how the avoided transition is connected to the magic-angle condition, of a vanishing velocity, by studying the interplay of disorder and quasiperiodicity on equal footing. A closely related problem has been studied in twodimensional Dirac semimetal models and is pertinent to understand the role of twist disorder in magic-angle graphene experiments [50][51][52][53][54][55], which have attracted a great deal of attention. However, in two dimensions the marginal relevance of disorder removes the AQCP from the problem and does not allow a direct link between the two effects to be exposed.…”

Hidden dualities in 1D quasiperiodic lattice models

“…[20] and references therein). For the latter, effects of quasiperiodicity are often overlooked, but recent studies have shown that in some regimes these may have important consequences to localization and transport [21][22][23][24][25][26].…”