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]. Similar critical states can also occur in 1D quasiperiodic models, and we have identified several such models using a recently developed approach based on real space – momentum space dualities [2, 3, 4].
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 [5]. 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. We will also present preliminary results indicating that quasiperiodicity can enhance superconductivity in 1D quasiperiodic models with critical phases [6].
References:
[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] Hidden dualities in 1D quasiperiodic lattice models
Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro
SciPost Phys. 13, 046 (2022)
doi: 10.21468/SciPostPhys.13.3.046
[3] Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro
Phys. Rev. B 108, L100201 (2023)
doi: 10.1103/PhysRevB.108.L100201
[4] Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models
Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro
Phys. Rev. Lett. 131, 186303 (2023)
doi: 10.1103/PhysRevLett.131.186303
[5] 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
[6] Incommensurability-Induced Enhancement of Superconductivity in One Dimensional Critical Systems
Ricardo Oliveira, Miguel Gonçalves, Pedro Ribeiro, Eduardo V. Castro, Bruno Amorim
arXiv:2303.17656
https://doi.org/10.48550/arXiv.2303.17656
Paulo Brás, Paulo Silva, Jaime Silva