  The phase offset of quantum oscillations is commonly used to experimentally
diagnose topologically non-trivial Fermi surfaces. This methodology, however,
is inconclusive for spin-orbit-coupled metals where $\pi$-phase-shifts can also
arise from non-topological origins. Here, we show that the linear dispersion in
topological metals leads to a $T^2$-temperature correction to the oscillation
frequency that is absent for parabolic dispersions. We confirm this effect
experimentally in the Dirac semi-metal Cd$_3$As$_2$ and the multiband Dirac
metal LaRhIn$_5$. Both materials match a tuning-parameter-free theoretical
prediction, emphasizing their unified origin. For topologically trivial
Bi$_2$O$_2$Se, no frequency shift associated to linear bands is observed as
expected. However, the $\pi$-phase shift in Bi$_2$O$_2$Se would lead to a false
positive in a Landau-fan plot analysis. Our frequency-focused methodology does
not require any input from ab-initio calculations, and hence is promising for
identifying correlated topological materials.
