Abstract
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. Furthermore, challenging our understanding of the physical phenomena, the giant increase occurs in the limit of low FB states density. The singular behaviour of the quantum metric of the FB eigenstates is found to be at the heart of these unexpected and puzzling features. 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.
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