  Experiments and simulations in solid-state high harmonic generation often
make use of the distinction between interband and intraband currents. These two
contributions to the total current have been associated with qualitatively
different processes, as well as physically measurable signatures, for example
in the spectral phase of harmonic emission. However, it was recently argued [P.
F\"oldi, Phys. Rev. B 96, 035112 (2017)] that these quantities can depend on
the gauge employed in calculations. Since physical quantities are expected to
have gauge-independent values, this raises the question of whether the
decomposition of the total current into interband and intraband contributions
is physically meaningful, or merely a feature of a particular mathematical
representation of nature. In this article, we explore this apparent ambiguity.
We show that a closely related issue arises when calculating instantaneous band
populations. In both the case of inter/intraband currents and in the case of
instantaneous band populations, we propose definitions which are
gauge-invariant, and thus allow these quantities to be calculated consistently
in any gauge.
