Incommensurability effects in low-dimensional Quantum Materials

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (FCT_CPCA_2020_01), grant CPCA/A00/7343/2020. Funded amount: EUR 308, as stated by the source. Runs 2021-01-01 to 2021-12-31. Keywords: twisted bilayer graphene, inverse participation ratio, sub-ballistic transport, incommensurability, exact diagonalization., Exact sciences. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-07-19); national funding data, not CORDIS. Abstract given by the source: The discovery of correlated insulating phases and superconductivity in twisted bilayer graphene (tBLG), has sparked the interest in these materials. By changing the twist angle between the two graphene layers a strong renormalization of the Fermi velocity can be achieved, with small velocities occurring for smaller angles. In the small-angle regime, extremely narrow bands appear at low energies, with the Fermi velocity vanishing at specific magic angles when the bands become flat. Recently, [see preprint arXiv:2008.07542] we have shown that often neglected incommensurability effects, arising at small irrational angles, can lead to sub-ballistic states that radically change the transport properties of the tBLG. In this project, we propose to continue the study of the importance of incommensurability effects in the narrow-band regime in graphene and other low-dimensional materials. Incommensurate quantum lattice models systems are hard to study since the lack of translational invariance prohibits a simplifying momentum-space treatment. One then has to resort to large scale exact diagonalizations of the Hamiltonian for increasing systems and finite size scaling to obtain results that are valid for macroscopic systems. This is a CPU and memory intensive task. Our code uses parallelisation of matrix-vector multiplication implemented in PETSc.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Fundação para a Ciência e a Tecnologia, I.P. (FCT). Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Incommensurability effects in low-dimensional Quantum Materials" is funded by FCT with a grant of EUR 308, running from January 1 to December 31, 2021. It focuses on twisted bilayer graphene and its transport properties influenced by incommensurability effects. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.