Coexistence of two order parameters and a pseudogaplike feature in the iron-based superconductor ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$

The nature and value of the order parameters (OPs) in the superconducting Fe-based oxypnictides ${\text{REFeAsO}}_{1-x}{\text{F}}_x$ ($\text{RE}=\text{rare}$ earth) are a matter of intense debate, also connected to the pairing mechanism which is probably unconventional. Point-contact Andreev-reflection experiments on ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$ gave us direct evidence of three energy scales in the superconducting state: a nodeless superconducting OP, ${\Delta }_1=2.8–4.6\text{meV}$, which scales with the local $T_c$ of the contact; a larger unconventional OP that gives conductance peaks at 9.8–12 meV, apparently closes below $T_c$ and decreases on increasing the $T_c$ of the contact; a pseudogaplike feature (i.e., a depression in the conductance around zero bias) that survives in the normal state up to $T^{\ast }\sim 140\text{K}$ (close to the Néel temperature of the undoped compound), which we associate to antiferromagnetic spin fluctuations coexisting with superconductivity. These findings point toward a complex, unconventional nature of superconductivity in ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$.

Figure 1

(Color online) The resistivity of a La-1111 polycrystalline sample used for the PCS measurements. The inset shows a magnification of the superconducting transition. Arrows indicate the deviation from the low-temperature linear behavior $\left(T=31\text{K}\right)$ and the onset of the superconducting transition defined as $T_c^{\text{on}}=\text{T}\left(90\%\right)=27\text{K}$.

Figure 2

(Color online) Three examples of raw conductance curves measured in different point contacts on the same polycrystalline ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$ sample. The contact resistance $R_N$ is indicated in the label. Arrows indicate the two peaks related to the smaller order parameter ${\Delta }_1$ and the (more or less pronounced) features related to a second, larger energy scale, ${\Delta }_2$. The thick black line in each panel represents the normal-state conductance measured at $T_c$.

Figure 3

(Color online) (a) Symbols: conductance curves of a point contact with $T_c=28.6\text{K}$ [the same as in Fig. 2a] after normalization. The normal state at $T<T_c$, experimentally inaccessible, was here estimated as explained in Appendix . Solid lines indicate the generalized two-band BTK fit. Inset: comparison between the two-gap (solid line) and single-gap (dashed line) BTK fit of the low-temperature conductance curve (symbols). (b) Temperature dependence of the amplitudes of the OPs, ${\Delta }_1$ and ${\Delta }_2$, extracted from the two-band BTK fit (solid symbols). Error bars indicate the uncertainty related to the fitting procedure. Dashed lines are guides to the eye. The inset reports the values of the broadening parameters ${\Gamma }_1$ and ${\Gamma }_2$; the values of the barrier parameters $Z_1$ and $Z_2$ and of the weight $w_1$ are temperature independent and are indicated in the label of the main panel. Open symbols indicate the values of ${\Delta }_1$ and ${\Delta }_2$ obtained with a different normalization (see Appendix for details). The uncertainty (not indicated) is of the same order of magnitude as in the case of solid symbols.

Figure 4

(Color online) (a) Temperature dependence of the conductance curves of a contact with $T_c=27.3\text{K}$ [the same as in Fig. 2c]. The experimental curves (symbols) were normalized as in Fig. 3; solid lines represent the generalized two-band BTK fit. Inset: comparison between the two-gap (solid line) and single-gap (dashed line) BTK fit of the low-temperature conductance curve (symbols). (b) Temperature dependence of ${\Delta }_1$ and ${\Delta }_2$ as obtained from the two-band BTK fit. The values of the other fitting parameters are also indicated in the label and in the inset. Lines are guides to the eye. The similarity with Fig. 3b is clear.

Figure 5

(Color online) (a) Magnetic-field dependence of the conductance curves of the same point contact as in Fig. 4. All the measurements were taken at 1.8 K. Symbols represent experimental data, lines are the best-fitting curves. (b) Magnetic-field dependence of ${\Delta }_1$ and ${\Delta }_2$ extracted from the fit of the curves shown in (a). Lines are only guides to the eye. The inset reports the magnetic-field dependence of the broadening parameters ${\Gamma }_1$ and ${\Gamma }_2$ while $Z_1$, $Z_2$, and $w_1$ are the same as in Fig. 4.

Figure 6

(Color online) (a) Conductance curves of a $15\Omega$ point contact with $T_c=31.0\text{K}$ after normalization (symbols) together with the generalized single-band BTK fit (lines). At $T=1.8\text{K}$ the best-fitting parameters are $\Delta =4.59\text{meV}$, $\Gamma =3.27\text{meV}$, and $Z=0.40$. Inset: comparison between the two-gap (solid line) and the single-gap (dashed line) BTK fit of the low-temperature conductance curve (symbols). The use of the two-band model does not sensibly improve the fit. (b) Magnetic-field dependence of the conductance curves of the same contact. All the measurements were taken at 1.8 K. (c) Temperature dependence of the OP extracted from the single-band BTK fit of the curves shown in (a). The trend is definitely non-BCS and very similar to that shown in Figs. 3b, 4b for ${\Delta }_1$. The dashed line is only a guide to the eye. (d) Magnetic-field dependence of the OP extracted from the fit of the curves shown in panel (b). This behavior is compatible with that predicted for type-II superconductors and with a critical field on the order of 55 T.

Figure 7

(Color online) Values of ${\Delta }_1$ and ${\Delta }_2$ (solid and open circles) from the two-gap fit of the low-temperature conductance curves of different point contacts, reported as a function of the critical temperature of the contact. Gap values obtained from the single-gap fit of some of these curves are reported as well (open squares). Error bars also take into account the different normalizations. The spread in $T_c$ values is due to the fact that the sample presents homogeneous, large crystallites with various F concentrations embedded in a disordered matrix. The measurements show that ${\Delta }_1$ is always close or below the BCS value (solid line) and increases with $T_c$ while ${\Delta }_2$ is well above the BCS line and decreases on increasing $T_c$, until a single (or two, very close to each other) BCS OP is observed.

Figure 8

Two examples of temperature dependence of the conductance curves measured up to temperatures well above $T_c$. The first nonsuperconducting conductance curve (upper thick line) clearly shows a pseudogaplike feature which is progressively filled on increasing the temperature and disappears at about 140 K (bottom thick line). The temperatures corresponding to the thick lines are highlighted in the labels.

Figure 9

Explanation of the two alternative choices for the normalization of the conductance curves. (a) Dark gray circles represent the raw conductance curve at 4.3 K. The normal state at $T=4.3\text{K}$ is simulated by a “guess” curve (line) obtained by connecting the black points with a $B$-spline function. In this way, the calculated normal state at 4.3 K is deeper than the measured normal state at $T_c$ (open circles) respecting the progressive filling of the pseudogaplike feature suggested, for example, by the conductance curve at $T=21.8\text{K}$ (light gray circles). (b) All the curves are divided by the measured normal state at $T_c$ (solid line), translated if necessary (e.g., at $T=21.8\text{K}$, dashed line).

Figure 10

The two contributions $G_1^{\text{BTK}}$ (line) and $G_2^{\text{tunn}}$ (symbols) to the total point-contact conductance shown in Fig. 3a. The sum of these contributions, divided by 2, gives the original conductance curve. $G_1^{\text{BTK}}$ is obtained by fitting the central part of the original conductance curve, disregarding the additional features at higher energy. $G_2^{\text{tunn}}$ is then obtained by subtraction as explained in the text.

Figure 11

(Color online) (a) Temperature dependence of $G_2^{\text{tunn}}$ obtained from the conductance curves of Fig. 3a. (b) Temperature dependence of the peak position ${\Delta }_{\text{peak}}$ in $G_2^{\text{tunn}}$ (open circles) and of the values of ${\Delta }_1$ from $G_1^{\text{BTK}}$ (open squares) compared to the result of the two-band BTK fit of the same curves (solid symbols).

Figure 12

(Color online) (a) Magnetic-field dependence of ${\Delta }_{\text{peak}}$ from $G_2^{\text{tunn}}$ (open circles) and of the values of ${\Delta }_1$ from $G_1^{\text{BTK}}$ (open squares) obtained from the conductance curves of Fig. 5a compared to the results of the two-band BTK fit (solid symbols). (b) Values of ${\Delta }_1$ and ${\Delta }_{\text{peak}}$ (open squares and open circles) from the superconducting and tunneling contributions to the low-temperature conductance curves of different point contacts, reported as a function of the local $T_c$ of the contact. The result of the two-band BTK fit is also shown (solid symbols) for comparison.