It is a well-known fact that the disorder has its most dramatic effects on the conventional quantum transport in one-dimensional systems. In flat-band (FB) systems, it is revealed that the conductivity at the FB energy is robust against the disorder and can even be tremendously boosted. Here, the disorder is due to randomly distributed vacancies. Furthermore, challenging our understanding of the physical phenomena, the giant increase occurs in the limit of low FB state density. The singular behavior of the quantum metric of the FB eigenstates is found to be at the heart of these unexpected and puzzling features. Additionally, it is shown that the compact localized eigenstates should extend over at least two unit cells to allow a boost. Our findings should have interesting fallout for other physical systems, and may as well open up engineering strategies to boost the critical temperature in two-dimensional superconducting FB materials.

• Received 12 May 2022
• Revised 1 August 2022
• Accepted 1 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.125125