AUTHOR=Vidarte Kevin J. U. , Lewenkopf Caio 

TITLE=Quasicrystalline 30° twisted bilayer graphene: fractal patterns and electronic localization properties

JOURNAL=Frontiers in Carbon

VOLUME=3

YEAR=2024

URL=https://www.frontiersin.org/journals/carbon/articles/10.3389/frcrb.2024.1496179

DOI=10.3389/frcrb.2024.1496179

ISSN=2813-4192

ABSTRACT=<p>The recently synthesized <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>30</mml:mn><mml:mo>°</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> twisted bilayer graphene (<inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>30</mml:mn><mml:mo>°</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. We employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach we employ is very efficiency for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow us to address a broad class of multilayer two-dimensional crystal with incommensurate configurations, particularly TBGs. Our results reveal that the <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>30</mml:mn><mml:mo>°</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>-TBG electronic spectrum consist of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.</p>