Linear scaling relation between two-dimensional massless Dirac fermion Fermi velocity and Fe-As bond length in iron arsenide superconductor systems

Abstract

Two-dimensional (2D) massless Dirac fermions (MDF), which represent a type of quasi-particles 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 magneto-infrared spectroscopy studies of the iron-arsenide-superconductor systems NaFeAs and $A\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2(A=\mathrm{Ca},\mathrm{Ba})$ 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 $A\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2(A=\mathrm{Ca},\mathrm{Ba})$, 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 new avenues for exploring and tuning novel quantum phenomena based on 2D MDF in the superconducting bulk states of 3D materials.

Accepted in Physical Review B (Letter)

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