Is MgB$_2$ a superconductor?

Abstract

Hirsch and Marsiglio, in their recent publication (J. Supercond. Nov. Mag. 35, 3141-3145 (2022)), assert that experimental data on the trapping of magnetic flux by hydrogen-rich compounds clearly demonstrate the absence of superconductivity in hydrides at high pressures. We argue that this assertion is incorrect, as it relies on the wrong model coupled with selective manipulations (hide/delete) of calculated datasets and ignores the reference measurements after the release of pressure. A critical examination of the authors' claim of having performed fitting of experimental data to the model reveals that, in fact, the authors conducted simulations where all free parameters were fixed. Importantly, an application of the Hirsch-Marsiglio model to MgB$_2$ leads to the conclusion that it is not a superconductor.