Electronic band structure and momentum dependence of the superconducting gap in Ca${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ from angle-resolved photoemission spectroscopy

Electronic structure of newly synthesized single crystals of calcium iron arsenide doped with sodium with $T_{\mathrm{c}}$ ranging from 33 to 14 K has been determined by angle-resolved photoemission spectroscopy (ARPES). The measured band dispersion is in general agreement with theoretical calculations, nonetheless implies absence of Fermi-surface nesting at an antiferromagnetic vector. A clearly developing below $T_{\mathrm{c}}$ strongly band-dependant superconducting gap has been revealed for samples with various doping levels. The BCS ratio for optimal doping, $2\Delta /k_{\mathrm{B}}{T}_{\mathrm{c}}=5.5$, is substantially smaller than the numbers observed for related compounds.

Figure 1

(a) and (b) Fermi-surface maps of Ca${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ with $x=0.68\pm 0.04$ and $T_{\mathrm{c}}=33$ K, recorded at 40 and 80 eV excitation energy ($h\nu$) respectively. (c) Cuts through photoemission intensity distribution at different binding energies reveal holelike nature of the propellers blades, recorded at $h\nu =80$ eV. Energy-momentum cut passing close to $\Gamma X$ line recorded with 90 eV-horizontally (d) and-vertically (e) polarized light. (f) Theoretical band dispersion.

Figure 2

(a) Temperature dependence of the energy-momentum cut passing through the $\Gamma$ point for the sample with $T_{\mathrm{c}}=33$ K. (b) Temperature dependence of the partial density of states, i.e., integrated energy distribution curves (IEDCs). (c) Gap size, extracted from fit IEDC to Dynes function, equals 7.8 meV for the two $xz/yz$ inner $\Gamma$ barrels. (d) A similar analysis for the $xy$ outer $\Gamma$ barrel results in the gap magnitude of 2.3 meV. (e) Energy-momentum cuts along $\Gamma \Gamma$ and $\Gamma X$. (f) and (g) $k_{\mathrm{F}}$ EDC for the outer and inner $\Gamma$ barrels at $\Gamma \Gamma$ and $\Gamma X$. (h) Temperature dependence of the spectra recorded from $X$ pocket. (i) 61-K spectrum divided by Fermi function. (j) Temperature dependence of IEDC from $X$ pocket. (k) $k_{\mathrm{F}}$ EDC for inner $\Gamma$ barrel and propeller's blade. (l) Momentum dependence of the superconducting gap in Ca${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$.

Figure 3

(a) Temperature dependence of an energy-momentum cut passing through the $\Gamma$ point for Ca${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ sample with $T_{\mathrm{c}}=14$ K. (b) Temperature dependence of the partial density of states for the inner $\Gamma$ barrel. (c) The same for the outer $\Gamma$ barrel. (d) and (e) Data at 1 K and fits to Dynes function for inner and outer $\Gamma$ barrels respectively. The derived gap sizes are 3.5 for the inner and 1.9 meV for the outer $\Gamma$ barrels.

Figure 4

BCS ratio $2\Delta /k_{\mathrm{B}}{T}_{\mathrm{c}}$ for several hole-doped 122 iron arsenides: optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ with $T_{\mathrm{c}}=38$ K (Ref. 8), optimally doped ($T_{\mathrm{c}}=34$ K) and underdoped ($T_{\mathrm{c}}=10$ K) Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ (Ref. 23), optimally doped ($T_{\mathrm{c}}=33$ K) and underdoped ($T_{\mathrm{c}}=14$ K) Ca${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$. Red dots represent maximal gap for the inner $\Gamma$ barrel, blue dots represent outer $\Gamma$ barrel. All values were extracted from ARPES data by fitting partial density of states to Dynes function.