Magic fermions: Carroll and flat bands

The Carroll algebra is constructed as the $c\to0$ limit of Poincare and associated to symmetries on generic null surfaces. In this paper, we begin investigations Carrollian fermions or defined Due availability two different (degenerate) metrics spacetimes, there possibility versions Clifford algebras. We consider both possibilities construct explicit representations gamma matrices show how build higher spacetime dimensional out lower ones. Actions for are with these properties actions investigated. that in condensed matter systems where dispersion relation becomes trivial i.e. energy not dependent momentum bands flatten out, symmetry generically appears. give examples including twisted bi-layer graphene, superconductivity appears at so called magic angles connect fermions.