In a recent paper, Ibanez-Azpiroz et al. [Phys. Rev. B 97, 245143 (2018)] derive a band-truncation-error-free formula for calculating the generalized derivative of the interband dipole matrix using Wannier interpolation. In practice, the denominators involving intermediate states are regularized by introducing a finite broadening parameter. In this Comment, I show that when a finite broadening parameter is used, a correction term must be added to the generalized derivative to obtain results that are independent of the phase convention for the Bloch sums.

We show that the key formula in the works of Ding et al. [K.-H. Ding, Z.-G. Zhu, and J. Berakdar, Phys. Rev. B 79, 045405 (2009); 84, 115433 (2011); K.-H. Ding, Z.-G. Zhu, Z.-H. Zhang, and J. Berakdar, Phys. Rev. B 82, 155143 (2010)] is invalid in the extended graphene system they investigated. The correct formalism in the extended infinite system is also presented in this Comment.

By using high magnetic field data to estimate the background conductivity, Rullier-Albenque and coworkers have recently published [Phys. Rev. B 84, 014522 (2011)] experimental evidence that the in-plane paraconductivity in cuprates is almost independent of doping. In this Comment we also show that, in contrast with their claims, these useful data may be explained at a quantitative level in terms of the Gaussian-Ginzburg-Landau approach for layered superconductors, extended by Carballeira and coworkers to high reduced temperatures by introducing a total-energy cutoff [Phys. Rev. B 63, 144515 (2001)]. When combined, these two conclusions further suggest that the paraconductivity in cuprates is conventional, i.e., associated with fluctuating superconducting pairs above the mean-field critical temperature.