Topological frequency shift of quantum oscillation in CaFeAsF

Guo, Alexandradinata, \textit{et al.} have recently proposed that quantum-oscillation frequencies from Dirac/Weyl fermions exhibit a negative shift proportional to $T^2$ because of the energy dependence of the effective mass peculiar to a linear band-dispersion. We have measured Shubnikov--de Haas oscillation in CaFeAsF up to $T$ = 9 K. The frequency of the $α$ Dirac electron exhibits a negative shift with increasing $T$, while that of the $β$ Schrödinger hole does not. For $T \geqslant 5$ K where $β$ is negligible, the $α$-frequency shift is proportional to $T^2$ and its rate agrees with the theoretical prediction within experimental accuracy. At lower temperatures, the shifts of $α$ and $β$ deviate from theoretical expectations, which we ascribe to the inaccuracy in the frequency determination due to unfavorable interference between frequencies. Our results confirm that the topological frequency shift can be utilized to identify Dirac/Weyl fermions when quantum-oscillation frequencies can be determined accurately.

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