Possible nodal superconducting gap in Fe${}_{1+y}$(Te${}_{1-x}$Se${}_x$) single crystals from ultralow temperature penetration depth measurements

Using a radio-frequency tunnel diode oscillator technique, we measured the temperature dependence of the in-plane London penetration depth $\Delta {\lambda }_{ab}\left(T\right)$ in Fe${}_{1+y}$(Te${}_{1-x}$Se${}_x)$ single crystals, down to temperatures as low as 50 mK. A significant number of samples, with nominal Se concentrations $x=0.36$, 0.40, 0.43, and 0.45, respectively, were studied and in many cases we found that $\Delta {\lambda }_{ab}\left(T\right)$ shows an upturn below 0.7 K, indicative of a paramagnetic-type contribution. After subtracting the magnetic background, the low-temperature behavior of penetration depth is best described by a power law with exponent $n\approx 2$ and with no systematic dependence on the Se concentration. Most importantly, in the limit of $T\to 0$, in some samples we observed a narrow region of linear temperature dependence of penetration depth, suggestive of nodes in the superconducting gap of Fe${}_{1+y}$(Te${}_{1-x}$Se${}_x)$.

Figure 1

Left: Picture of one of the $8\times 8$ mm${}^2$ flat coils with 3 turns/mm milled on a copper-clad laminate 1-oz. PCB board. Right: Spatial arrangement of the coils and sample. The setup is symmetric with respect to reflection across the $z=0$ plane.

Figure 2

The simulated magnetic field distribution of our setup for the normal state of the sample. (a) Magnetic field lines and flux density distribution over the $y=0$ cross section of the setup (side view). (b) Flux density distribution over the $z=0$ cross section of the setup (top view). (c) Expanded view on the $y=0$ plane. (d) Expanded view on the $z=0$ plane. The white rectangles symbolize the domain of a $2\times 2\times 0.1$ mm${}^3$ sample. The color scale corresponds to the $B$ field magnitude relative to its value in the center of the sample (0,0,0).

Figure 3

$\Delta {\lambda }_{ab}\left(T\right)$ (continuous lines) in Fe${}_{1+y}$(Te${}_{1-x}$Se${}_x)$ for the low-temperature range in two different specimens for each nominal Se concentration, namely, (a) $x=0.36$, (b) $x=0.40$, (c) $x=0.43$, and (d) $x=0.45$. The dashed black lines are the representative allometric fits for each sample in the 0.5 K–$T_c/3$ temperature range with the fitting parameters $A$ and $n$ shown. The curves have been offset by 10 nm for clarity. Inset: Relative frequency variations from TDO measurements for each sample.

Figure 4

The relative variation of the in-plane penetration depth $\Delta {\lambda }_{ab}\left(T\right)$ data (points) at ultralow temperatures for all eight samples after subtracting the $C/T$ paramagnetic contribution as a function of $T^{2.15}$. The continuous lines are linear fits for the $T_{\min }–$2 K temperature range with the slope values of $A$ from Table . The data for each sample have been shifted by 10 nm. Inset: the raw $\Delta {\lambda }_{ab}\left(T\right)$ data (filled spheres) and the data with the subtracted paramagnetic dependence (open circles) for two samples, namely, 40#2 and 45#2 (the data have been shifted by 20 nm). The continuous lines represent the $A{T}^n+C/T$ fit of the raw data.

Figure 5

Superfluid density ${\rho }_s\left(T\right)$ in Fe${}_{1.02}$Te${}_{1-x}$Se${}_x$ for the lowest Se doping $x=36$ (sample 36#1, top) and highest Se doping $x=45$ (sample 45#1, bottom) calculated from experimental data assuming two extreme values for $\lambda \left(0\right)$ reported in literature, i.e., 430 nm (Ref. 18) and 560 nm (Ref. 16). The dashed (black) lines illustrate the two-gap fit over the entire temperature range up to $T_C$. Inset: the low-temperature region.

Figure 6

The relative variation of the in-plane penetration depth $\Delta {\lambda }_{ab}\left(T\right)$ raw experimental data (red points) for two samples with $x=0.36$ (36#1) and $x=0.43$ (43#1) at low temperatures revealing a linear region.