Two-dimensional (2D) massless Dirac fermions (MDF), which represent a type of quasiparticles with linear energy-momentum dispersions only in 2D momentum space, provide a fertile ground for realizing novel quantum phenomena. However, 2D MDF were seldom observed in the superconducting bulk states of 3D materials. Furthermore, as a cornerstone for accurately tuning the quantum phenomena based on 2D MDF, a quantitative relationship between 2D MDF and a structural parameter has rarely been revealed so far. Here, we report magnetoinfrared spectroscopy studies of the iron-arsenide-superconductor systems NaFeAs and $A{\mathrm{Fe}}_2{\mathrm{As}}_2(A=\mathrm{Ca},\mathrm{Ba})$ at temperature $T\sim 4.2$ K and at magnetic fields ($B$) up to 17.5 T. Our results demonstrate the existence of 2D MDF in the superconducting bulk state of NaFeAs. Moreover, the 2D-MDF Fermi velocities in NaFeAs and $A{\mathrm{Fe}}_2{\mathrm{As}}_2(A=\mathrm{Ca},\mathrm{Ba})$, which are extracted from the slopes of the linear $\sqrt{B}$ dependences of the Landau-level transition energies, scale linearly with the Fe-As bond lengths. The linear scaling between the 2D-MDF Fermi velocities and the Fe-As bond lengths is supported by (i) the linear relationship between the square root of the effective mass of the $d_{xy}$ electrons and the Fe-As bond length and (ii) the linear dependence of the square root of the calculated tight-binding hopping energy on the Fe-As bond length. Our results open up avenues for exploring and tuning quantum phenomena based on 2D MDF in the superconducting bulk states of 3D materials.

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• Landau levels
• Iron-based superconductors
• Fourier transform infrared spectroscopy