Topological frequency shift of quantum oscillation in CaFeAsF

TL;DR

This study measures quantum oscillations in CaFeAsF, confirming that Dirac fermions exhibit a temperature-dependent frequency shift proportional to T^2, validating theoretical predictions and demonstrating a method to identify topological fermions.

Contribution

The paper provides experimental evidence for the topological frequency shift in Dirac fermions, aligning with theoretical models and highlighting its use in identifying topological electronic states.

Findings

Dirac electron frequency shifts with T^2 dependence at higher temperatures.

Schrödinger hole frequency remains unaffected by temperature.

Experimental results agree with theoretical predictions within accuracy.

Abstract

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 $\alpha$ Dirac electron exhibits a negative shift with increasing $T$, while that of the $\beta$ Schr\"odinger hole does not. For $T \geqslant 5$ K where $\beta$ is negligible, the $\alpha$-frequency shift is proportional to $T^2$ and its rate agrees with the theoretical prediction within experimental accuracy. At lower temperatures, the shifts of $\alpha$ and $\beta$ 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.