EuCd$_2$As$_2$: a magnetic semiconductor
EuCd$_2$As$_2$ is now widely accepted as a topological semimetal in which a Weyl phase is induced by an external magnetic field. We challenge this view through firm experimental evidence using a combination of electronic transport, optical spectroscopy and excited-state photoemission spectroscopy. We show that the EuCd$_2$As$_2$ is in fact a semiconductor with a gap of 0.77 eV. We show that the externally applied magnetic field has a profound impact on the electronic band structure of this system. This is manifested by a huge decrease of the observed band gap, as large as 125~meV at 2~T, and consequently, by a giant redshift of the interband absorption edge. However, the semiconductor nature of the material remains preserved. EuCd$_2$As$_2$ is therefore a magnetic semiconductor rather than a Dirac or Weyl semimetal, as suggested by {\em ab initio} computations carried out within the local spin-density approximation.