Unconventional Bulk Superconductivity in ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ Single Crystals

Sharp superconducting transition anomalies observed in a new generation of single crystals establish that bulk superconductivity is intrinsic to high purity ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$. Low temperature heat capacity measurements suggest a disorder and field dependent residual Sommerfeld coefficient, consistent with disorder-induced in-gap states as expected for a sign-changing order parameter. The sevenfold reduction in disorder scattering in these new crystals to residual resistivities $\simeq 0.45\mu \mathrm{\Omega }\mathrm{cm}$ was achieved using a new liquid transport growth technique, paving the way for multiprobe experiments investigating the normal and superconducting states of ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$.

Figure 1

Sommerfeld ratio of the heat capacity $C/T$ (upper panel) and electrical resistivity (lower panel) of ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ single crystals from different growth batches. $\mathrm{SF}=\text{standard flux}\text{growth}$, $\mathrm{MF}=\text{modified}$ flux growth, $\mathrm{LT}=\text{liquid}$ transport growth. These samples show a wide variation in their heat capacity superconducting anomaly, resistive transition, and residual resistivity. Lower residual resistivities correlate with sharper superconducting heat capacity anomalies.

Figure 2

Superconducting transition signatures for two high-quality batches of ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ samples. [(a),(b)] Electrical resistivity $\rho$, [(c),(d)] Sommerfeld coefficient of the heat capacity $C/T$, [(e),(f)] magnetization ($\mathrm{FC}=\text{field cooled}$, $\mathrm{ZFC}=\mathrm{zero}-\mathrm{field}\mathrm{cooled}$). The vertical dash-dotted lines denote the temperatures at which resistivity drops to zero in (a) and (b). The vertical dashed lines indicate the peaks of $C/T$ in (c) and (d).

Figure 3

Electronic contribution to the specific heat capacity versus temperature, $C_{\mathrm{el}}/T$, of a ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ single crystal from batch LT-A. Applied fields are 0 T (labeled), 0.1 T (red), 0.2 T (green), 0.35 T (black), 0.5 T (pink), 0.7 T (labeled), and 1 T (dark green). $C_{\mathrm{el}}$ is obtained by subtracting from the total specific heat capacity the fitted nuclear contribution $C_n(H,T)=\alpha (H)/T^2$ [20]. Inset: extrapolated zero-temperature residual $C_{\mathrm{el}}/T$ versus applied field.

Figure 4

${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ single crystals produced using (a) SF, (b) MF, and (c) LT methods on millimeter-scale paper. Dendrite formation is observed in the SF-grown crystals, which usually contain only one well defined facet along the [100] $a$ axis in each crystal. Crystals from the MF batches display less obvious dendritic patterns, smoother surfaces, and more rectangular shapes. Both the SF- and MF-grown crystals form thin plates, whereas those from the LT batch are bulkier in the [001] c direction with thickness reaching up to 2 mm. (d) Schematic illustration of the LT technique.

Figure 5

Lattice constants $c$ (upper panel) and $a$ (lower panel) of polycrystalline (open symbols) [18] and single-crystal (solid symbols) ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ samples, as obtained by powder XRD refinement, versus the corresponding RRR values. Green circles (red triangles) indicate that superconducting heat capacity anomalies have (have not) been observed. Error bars are estimated from repeated measurements on selected batches of polycrystals. The pink and blue shades are guides to the eyes.

Figure 6

Schematic phase diagram illustrating ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ growth from Sn flux. SF growth proceeds from fully molten charge (red trajectory) and leads to Fe-poor crystals if the apex of the ${\mathrm{YFe}}_{2-x}{\mathrm{Ge}}_{2+x}$ homogeneity range lies at an off-stoichiometric composition. MF growth proceeds from a saturated solution of ${\mathrm{YFe}}_2{\mathrm{Ge}}_2$ (orange trajectory), enabling a higher flux-to-charge ratio in the melt and consequently lower precipitation temperatures. It produces crystals with closer to the ideal stoichiometry but with considerable inhomogeneity. LT growth precipitates at a well-defined low temperature and produces the highest quality crystals. At temperatures above $\sim 1000°\mathrm{C}$ (purple zone), alien phases such as ${\mathrm{YFe}}_6{\mathrm{Ge}}_6$ may form, which affects the composition of the melt.