Superconductivity and electronic fluctuations in ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ studied by Raman scattering

Using polarization-resolved electronic Raman scattering we study underdoped, optimally doped, and overdoped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ samples in the normal and superconducting states. We show that low-energy nematic fluctuations are universal for all studied doping ranges. In the superconducting state, we observe two distinct superconducting pair-breaking peaks corresponding to one large and one small superconducting gap. In addition, we detect a collective mode below the superconducting transition in the $B_{2g}$ channel and determine the evolution of its binding energy with doping. Possible scenarios are proposed to explain the origin of the in-gap collective mode. In the superconducting state of the underdoped regime, we detect a reentrance transition below which the spectral background changes and the collective mode vanishes.

Figure 1

(a) Crystal structure of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. (b) Definition of the $X, Y, X^{\prime }$, and $Y^{\prime }$ directions. The green and black lines represent the 4-Fe and 2-Fe unit cells, respectively. (c) Schematic representation of the Fermi surface of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the 2-Fe Brillouin zone.

Figure 2

Doping and temperature evolution of the Raman susceptibility of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in different symmetry channels. Left column: UD ($x=0.25$); central column: OPD#1 ($x=0.4$); right column: OD ($x=0.6$). (a)–(c) Temperature dependence of the Raman response in the $A_{1g}$ channel. The asterisk in (a) marks a small peak due to laser plasma, whereas the arrow indicates a $A_{1g}$ phonon. (d)–(f) Temperature dependence of the Raman response in the $B_{2g}$ channel. (g)–(i) Same as (d)–(f) but for the $B_{1g}$ channel. (j)–(l) $T$ dependence of the static Raman susceptibilities ${\chi }_{B_{2g}}(0,T)$ (red solid circles) and ${\chi }_{B_{1g}}(0,T)$ (blue solid squares). The inset of (j) shows the inverse nematic susceptibility $1/{\chi }_{\mathrm{nem}}^{\mathrm{el}}$ (black line) of ${\mathrm{Ba}}_{0.86}{\mathrm{K}}_{0.24}{\mathrm{Fe}}_2{\mathrm{As}}_2$ extracted from Young's modulus measurements in Ref. [37]. The cyan dots in the inset of (j) are values of $1/{\chi }_{B_{2g}}(0,T)$ derived from Raman.

Figure 3

(a)–(c) Raman response of ${\mathrm{Ba}}_{0.4}{\mathrm{K}}_{0.6}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (OPD#2) at 45 K (red) and 6 K (blue) in the (a) $A_{1g}$, (b) $B_{1g}$, and (c) $B_{2g}$ channels. The dashed lines in (c) mark a broad feature at 70 ${\mathrm{cm}}^{-1}$ ($2{\mathrm{\Delta }}_{\beta }$), a collective mode ($E_{\text{CM}}$) around 140 ${\mathrm{cm}}^{-1}$, and a pair-breaking peak at 172 ${\mathrm{cm}}^{-1}$ ($2{\mathrm{\Delta }}_{\alpha }$). (d)–(f) Same as (a)–(c) but for sample OPD#1. For the OPD#1 sample we find $2{\mathrm{\Delta }}_{\beta }=50$ ${\mathrm{cm}}^{-1}, E_{\text{CM}}=120$ ${\mathrm{cm}}^{-1}$, and $2{\mathrm{\Delta }}_{\alpha }=168$ ${\mathrm{cm}}^{-1}$.

Figure 4

Raman response of ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (OD) at 40 K (red) and 6 K (blue) in the $B_{2g}$ channel. The dashed lines mark a broad peak at 50 ${\mathrm{cm}}^{-1}$ ($2{\mathrm{\Delta }}_{\beta }$), a collective mode $E_{\text{CM}}$ at 115 ${\mathrm{cm}}^{-1}$, and a pair-breaking peak at 162 ${\mathrm{cm}}^{-1}$ ($2{\mathrm{\Delta }}_{\alpha }$).

Figure 5

Raman response of ${\mathrm{Ba}}_{0.75}{\mathrm{K}}_{0.25}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (UD 30 K) at 40 K (red) and 6 K (blue) for the (a) $A_{1g}$, (b) $B_{1g}$, and (c) $B_{2g}$ symmetries. The star in (a) represents a laser plasma line. The inset in (c) shows the Raman responses recorded with a 752-nm laser excitation. (d) ${\chi }_{B_{2g}}^{\prime \prime }\left(\omega \right)$ at various temperatures. The dashed lines in (d) indicate $2{\mathrm{\Delta }}_{\beta }$ and $E_{\text{CM}}$. The red curves in (d) are fits of the $E_{\text{CM}}$ peaks. The yellow and green shadings emphasize different spectral backgrounds associated to different phases.

Figure 6

(a) Raman response of ${\mathrm{Ba}}_{0.75}{\mathrm{K}}_{0.25}{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the $B_{2g}$ channel at 13 K. (b) Difference between the Raman spectra at 6 K in the SC state and in the normal state, recorded in the $B_{2g}$ channel for different dopings. (c) Summary of the SC pair-breaking peaks and in-gap mode in ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ obtained in the $B_{2g}$ channel. The full and open symbols correspond to results from this work and from ARPES [47, 50, 51], respectively.