Comment on paper: Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)

Abstract

We demonstrate that an absolutely flat band retains the superconducting state at $T_c\to 0$. When $T_c>0$ the flat band disappears, since it must be modified by the superconducting state. Thus, a number of the results on ultra-strong coupling superconductivity in flat band considered in the article ("Evidence for Dirac flat band superconductivity enabled by quantum geometry", Nature 614, 440 (2023)) were predicted and explained many years ago. One has to take into account that at $T_c>0$ the flat band distorts, becoming tilted. As a result, the charge carriers' velocity $v_F\propto T_c$ becomes finite, rather than being extremely slow, as it is stated in the article. Thus, the statement "the charge carriers' group velocity $v_ F$ is extremely slow" is incorrect and leads the authors to the conceptional misunderstanding, confusing the reader.