Quasiperiodicity enabled quasi-fractal order in narrow-band moir'e systems

The observation of correlated phenomena and unconventional superconductivity in twisted bilayer graphene (tBLG), a moiré system, is one of the most interesting findings in condensed matter physics in recent years. However, twisted bilayer graphene, even in a pristine form, is extremely peculiar: for most twist angles it lacks translational invariance, having instead a quasiperiodic structure. Quasiperiodicity in 1D is known to strongly impact the electronic properties. However, the role of quasiperiodicity in twisted bilayer graphene and other moiré materials has been mostly ignored so far.

In this talk, we will present recent theoretical efforts towards the understanding of the role played by quasiperiodity in moiré electron systems. We have theoretically demonstrated that quasiperiodicity in tBLG leads to the emergence of narrow band single-particle critical states (delocalized in both real and momentum space) with subbalistic transport properties [1].

To unveil the interplay between interactions and quasiperiodicity, we resort to a 1D illustrative example to demonstrate that quasiperiodicity can radically change the ground state properties of moiré systems [2]. While narrow bands play a significant role in enhancing interactions both for commensurate and incommensurate structures, only quasiperiodicity concomitant with critical states is able to extend the ordered phase down to an infinitesimal interaction strength. In this regime, the quasiperiodic-enabled state has contributions from infinitely many wave vectors. This quasi-fractal regime cannot be stabilized in the commensurate case even in the presence of a narrow band.

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

Miguel Gonçalves, Hadi Z. Olyaei, Bruno Amorim, Rubem Mondaini, Pedro Ribeiro, and Eduardo V. Castro

2D Mater. 9 011001 (2022)

doi: 10.1088/2053-1583/ac3259

[2] Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems

Miguel Gonçalves, Bruno Amorim, Flávio Riche, Eduardo V. Castro, and Pedro Ribeiro

arXiv: 2305.03800

https://arxiv.org/abs/2305.03800