Superconductivity-induced phonon renormalization on ${\text{NaFe}}_{1-x}$${\text{Co}}_x$As

We report a study of the lattice dynamics in superconducting NaFeAs ($T_c$ = 8 K) and doped ${\text{NaFe}}_{0.97}$${\text{Co}}_{0.03}$As ($T_c$ = 20 K) using Raman light scattering. Five of the six phonon modes expected from group theory are observed. In contrast with results obtained on isostructural and isoelectronic LiFeAs, anomalous broadening of $E_g$(As) and $A_{1g}$(Na) modes upon cooling is observed in both samples. In addition, in the Co-doped sample, a superconductivity-induced renormalization of the frequency and linewidth of the $B_{1g}$(Fe) vibration is observed. This renormalization cannot be understood within a single band and simple multiband approaches. A theoretical model that includes the effects of spin-density wave correlations along with sign-changing $s$-wave pairing state and interband scattering has been developed to explain the observed behavior of the $B_{1g}$(Fe) mode.

Figure 1

Room-temperature Raman spectra on NaFeAs in $z\left(xy\right)z$, $z\left(x^{\prime }{y}^{\prime }\right)z$, $z\left(x^{\prime }{x}^{\prime }\right)z$, $z\left(xx\right)z$, $y\left(xz\right)y$, and $y\left(zz\right)y$ configurations. Spectra have been shifted vertically for clarity. Starting from the left, the peaks are assigned to the $E_g$(As), $A_{1g}$(As), $A_{1g}$(Na), $B_{1g}$(Fe), and $E_g$(Fe) modes.

Figure 2

Temperature dependence of the (a)—(e) phonon frequencies and (f)—(j) linewidths in NaFeAs. Dashed lines correspond to $T_{\text{SDW}}$ and $T_S$.

Figure 3

Temperature dependence of the (a)—(e) phonon frequencies and (f)—(j) linewidths in ${\text{NaFe}}_{0.97}$${\text{Co}}_{0.03}$As. Dashed lines correspond to $T_c$.

Figure 4

(a) Normalized Raman spectra of the $B_{1g}$(Fe) for 5 and 20 K for NaFeAs. Black squares are the raw data; the red line is the fit. The spectra have been shifted vertically for clarity. (b) Same plot for ${\text{NaFe}}_{0.97}$${\text{Co}}_{0.03}$As. (c) and (d) Low-temperature frequencies and linewidths of the $B_{1g}$(Fe) mode for NaFeAs. (e) and (f) Same plot for ${\text{NaFe}}_{0.97}$${\text{Co}}_{0.03}$As. The pink dashed line marks $T_c$, and the red line is the result of a conventional phonon anharmonic model (see text).

Figure 5

(a) Pattern of the $B_{1g}$(Fe) phonon mode. (b) Planar projection of the Fe plane as well as the SDW order (red arrows). The dashed line of the smaller square is the one-Fe unit cell. The corresponding Brillouin zones of the (c) one- and (d) two-Fe unit cells and the SDW wave vector $\mathbf{Q}$ connecting the hole band (circular shapes) and the electron band (ellipsoidal). The color code indicates the orbital character (plain green for $d_{zx}$ and dashed red for $d_{zy}$) of the bands in a minimal two bands model [55]. The vector $\tilde{\mathbf{Q}}=(\pi ,\pi )$ in panel (c) corresponds to the unit-cell doubling that must be taken into account when considering the $B_{1g}$ vibration, while $\mathbf{Q}$ represents the SDW wave vector that connects nested portions of the electron and hole pockets.

Figure 6

Real and imaginary parts of polarizability $\Pi (\mathbf{q}=\mathbf{0},\omega )$ in the normal and superconducting state. (a) and (b) Standard intraband polarizability ${\Pi }_{\left(hh\right)}$. (c) and (d) Interband polarizability ${\Pi }_{\left(he\right)}$.