Speaker
Description
The recent discovery of superconductivity in quasiperiodic twisted trilayer graphene (tTLG) underscores the complex interplay between quasiperiodicity and interactions in moiré materials [1]. Furthermore, previous work by the authors [2] has shown that quasiperiodicity can lead to an enhancement of superconductivity in one-dimensional quasiperiodic models. However, a proper theoretical description of superconductivity in quasiperiodic moiré materials is still lacking, due to the lack of translational invariance that implies that real-space numerical methods must be necessarily employed to study moiré systems such as twisted bilayer graphene (tBLG), requiring the simulation of system sizes in the order of millions of atoms [3].
We propose a real‐space tensor network approach to study s‐wave superconductivity in two‐dimensional quasicrystals with eightfold rotational symmetry. Building on the tensor network kernel polynomial method combined with the quantics tensor cross interpolation method (QTCI) to represent ultra-large real-space Hamiltonians [4, 5], we can obtain real-space mean-field solutions for on-site pairing across systems exceeding one million sites. This scalable approach enables computation of the local density of states and the spatially resolved superconducting pairing, revealing how eightfold symmetry and the quasiperiodic structure of the system shapes the texture of s-wave order. Our work opens a path towards quantitative real-space characterization of superconductivity in quasiperiodic moiré systems that require large-scale simulations.
References
[1] A. Uri et al., Nature 620 (2023) 762–767
[2] R. Oliveira et al., arXiv preprint (2023) 2303.17656
[3] Miguel Gonçalves et al., 2D Mater 9 (2021) 011001
[4] Yitao Sun et al., arXiv preprint (2025) 2503.04373
[5] Tiago V. C. Antão et al., arXiv preprint (2025) 2506.05230