  We calculate the band structures of kesterite and stannite Cu2ZnSnS4 and
Cu2ZnSnSe4, using a state-of-the-art self-consistent GW approach. Our accurate
quasiparticle states allow to discuss: the dependence of the gap on the anion
displacement; the key-role of the non-locality of the exchange-correlation
potential to obtain good structural parameters; the reliability of less
expensive hybrid functional and GGA+U approaches. In particular, we show that
even if the band gap is correctly reproduced by hybrid functionals, the
band-edge corrections are in disagreement with self-consistent GW results,
which has decisive implications for the positioning of the defect levels in the
band gap.
