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Temperature dependence of quantum oscillations from non-parabolic dispersions

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 $π$-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 $π$-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.