Fig. 4: Bulk and surface band structure for Mn₃Sn.

In (a), we show the bulk band structure, for an energy window corresponding to the frequency of the laser. In (b), we show the same plot, but with the colour and opacity of the bands indicating the value of \(\mathop{\min }\limits_{m}\{{E}_{n}({{{{{{{\boldsymbol{k}}}}}}}})-({E}_{m}({{{{{{{\boldsymbol{k}}}}}}}})\pm \hslash \omega )\}\) for band n, with ± indicating whether the band is above/below the Fermi surface. This is a rough indicator of the possibility of a vertical transition from band n occurring. The flat bands around K may also allow non-vertical transitions. In (c, d), we show the surface band structure for the c-directed top and bottom surface respectively, with the colour indicating how well-localised the states are on the surface.