  Unlike the local density approximation (LDA) and the generalized gradient
approximation (GGA), calculations with meta-generalized gradient approximations
(meta-GGA) are usually done according to the generalized Kohn-Sham (gKS)
formalism. The exchange-correlation potential of the gKS equation is
non-multiplicative, which prevents systematic comparison of meta-GGA
bandstructures to those of the LDA and the GGA. We implement the optimized
effective potential (OEP) of the meta-GGA for periodic systems, which allows us
to carry out meta-GGA calculations in the same KS manner as for the LDA and the
GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional
[Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band
structures of meta-GGAs are close to those of GGAs. They are smaller than the
more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic
gaps in the band structure of the exact KS potential, as can be seen by
comparing with the gaps of the EXX+RPA OEP potential. The well-known grid
sensitivity of meta-GGAs is much more severe in OEP calculations.
