Inhomogeneous superconductivity in thin crystals of FeSe_1−xTe_x (x = 1.0, 0.95, and 0.9)

Figure 1(a)–(c) show the optical microscope images of typical four-point terminal devices in FeSe_1−xTe_x. The thickness of the thin crystals of FeSe_1−xTe_x (x = 1.0, 0.95, and 0.9) used in the resistivity and microbeam x-ray diffraction measurements was estimated using an AFM as shown in figures 1(d) and (e). The bulk crystals (#10–0, #095–0, and #09–0) refer to small pieces of 30- to 70-μm-thick as-grown single crystals, while details of thin crystals are fully shown in table 1. Figure 2(a)–(c) show the temperature-dependence of the resistivity in the range of 2–300 K for different thicknesses of FeSe_1−xTe_x with x = 1.0, 0.95 and 0.9. Note that the absolute values of resistivity showed no logical order for each concentration. A possible reason for this is that the correction factor for the four-point probe resistivity measurement was not considered in our results. The resistivity value should be precisely evaluated when considering the correction factor value that is related to the size of crystals (length, width, and thickness) and the probe tip spacing with the four-point probe technique [23]. Although the bulk and thin crystals had various shapes and sizes in this study, we evaluated the resistivity as an ideal case without including the correction factor. Therefore, the absolute resistivity values might slightly vary, resulting in no logical order for each concentration. The bulk (#10–0) and thin crystals (#10–1 and #10–2) of FeTe (x = 1.0) exhibit an anomaly in resistivity related to the structural and magnetic transition at around 50–60 K, and no superconducting transition (see figures 2(a) and (d)). Here we define T_t as the temperature of an anomaly in resistivity related to the structural and magnetic transition. The T_t of thin crystals decreases in comparison with that of bulk crystal, and the resistivity anomaly is broadened. However, the anomaly does not completely disappear even at a thickness of 70 nm, and no superconducting transition is observed. The study of 60- to 150-nm-thick FeTe thin films on oxide substrates, which was reported by Han et al, showed that the resistivity anomaly due to the first-order magnetic and structural transition was broadened, and superconductivity with an onset superconducting transition temperature T_c^onset of 13 K suddenly emerged [17]. This result suggested that out-of-plane contraction (uniaxial pressure) was important to induce superconductivity in the FeTe system, which is accompanied by in-plane extension of FeTe film on oxide substrates. However, the application of hydrostatic pressures up to 19 GPa could not induce superconductivity in polycrystalline FeTe_0.92 [24]. Therefore, the application of greater pressure along the c-axis (out-of-plane) may be indispensable for inducing superconductivity in FeTe thin crystals.

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As shown in figures 2(b) and (c), the resistivity anomaly is also observed in the temperature dependence of resistivity for bulk single crystals of FeSe_1−xTe_x with x = 0.95 (#095–0) and 0.9 (#09–0), in which the superconducting transition is not clearly found for x = 0.95 (#095–0). However, we found the superconducting transition in their mechanically exfoliated thin crystals. A clear drop in resistivity is observed at T_c of 10.4 K and 11.5 K in 170- and 90-nm-thick FeSe_0.05Te_0.95 (#095–1 and #095–3), respectively, although the resistivity anomaly is still observed (see figures 2(b) and (e)). Finally, the resistivity of the 90-nm-thick FeSe_0.05Te_0.95 (#095-3) reaches zero at a T_c^zero of 3.0 K, but the superconducting transition temperature width ΔT_c (= T_c–T_c^zero) is large (ΔT_c = 8.5 K), as seen in figure 2(e). Here we define T_c as the intersection of the tangent at the inflection point of the resistive transition and a straight-line fit of the normal state just above the transition, and T_c^zero as the temperature reaching zero resistivity. In thin crystals of FeSe_0.1Te_0.9, as shown in figures 2(c) and (f), the anomaly completely disappears and a sharp superconducting transition is observed at a T_c of 13.2 K (#09–1, 155 nm), 13.3 K (#09–2, 100 nm), and 12.9 K (#09–3, 55 nm). With decreasing thickness, the transition width becomes smaller, with ΔT_c = 2.8 K to 1.6 K, as seen from figure 2(f). Interestingly, the temperature dependence of resistivity in the normal state of FeSe_0.1Te_0.9 shows a gradual change from semiconducting to metallic behavior with decreasing thickness (figure 2(f)). Such behavior has also been observed in the substitution of Se for Te [15] and in the enhancement of annealing temperature of single crystal Fe_1+ySe_0.4Te_0.6 [25]. The inhomogeneity of Se/Te distribution and the presence of 'excess Fe', which are strongly related to the physical properties of FeSe_1−xTe_x, have been discussed in references [25–27] as one of the origins of such semiconductor-metal transition; 'excess Fe' refers to Fe atoms not forming part of the structure of FeSe_1−xTe_x. To summarize the transition temperatures for FeSe_1−xTe_x crystals with various thickness, the T_t, T_c, T_c^zero, and ΔT_c are plotted as a function of thickness as shown in figure 3(a) (x = 1.0), (b) (x = 0.95), and (c) (x = 0.9). The superconductivity tends to be clearly observed in the thinner crystals in x = 0.95 and 0.9 as discussed above. One possibility is that heating in the lithography process makes thin crystals homogeneous and improves superconductivity. Our photolithography method includes heating at 110 ^oC for 6.5 min and at 180 ^oC for 3 min in air for the prebaking of photoresist. These temperatures and times are much lower and shorter than those in previous reports, e.g., 200 °C–300 ^oC for 2 h in air [25] ^and 400 ^oC for more than 10 days in vacuum [28], for changing the transport property. For ∼100-nm-thick crystals, however, such a process may not only reduce the amount of excess Fe, but also effectively enhance a homogeneity of Se/Te distribution.

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To explore the origin of the difference in the temperature dependence of resistivity between bulk and thin crystals of FeSe_1−xTe_x, we investigated the variation in the c value corresponding to the FeSe_1−xTe_x interlayer distance. The value of c was determined from the 004 Bragg peak of FeSe_1−xTe_x by microbeam x-ray diffraction measurements. The diffraction patterns were measured at several different positions in the same crystal. The average c values with the estimated standard deviations are listed in table 1. Figure 4(a) shows the 004 Bragg peaks of the thin crystals of FeSe_0.1Te_0.9. The width of the diffraction peak becomes broader with decreasing thickness. The broadening of a diffraction peak is related to the size of the sub-micrometer particles (crystallites) in a solid. The crystalline size, i.e., the average thickness along the c-axis, of thin crystals is roughly estimated in terms of the Scherrer equation, with the shape factor K = 0.94, to be 140(1) nm (#09–1), 108(9) nm (#09–2), and 39(3) nm (#09–3). These values correlate with the thickness determined by AFM and an approximate trend of thickness of thin crystals can be obtained, as listed in table 1.

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The c value of bulk crystal decreases with increasing Se quantity (decreasing x), which is consistent with previous studies [29–31]. The standard deviations of the c values for bulk crystals are larger than that of thin crystals, reflecting the large inhomogeneity of the presence of excess Fe and Se/Te distribution by Se doping. On the other hand, the variation in the c value of thin crystals with different thicknesses for each x does not show a unified trend, as seen in figure 4(b). A tendency for swelling along the c-axis with thinning of the crystal was reported in nano-thick crystals (thickness, 14–31 nm) of 1T-TaS₂ [32], in which the charge-density-wave (CDW) transitions were systematically controlled by changing thickness. In the case of FeSe_1−xTe_x, however, the value of c does not simply depend on the thickness of thin crystals, probably because of various factors such as inhomogeneity of Se/Te distribution and inhomogeneous distribution of excess Fe. This may cause the different behavior of temperature-dependent resistivity of thin crystals. Indeed, inhomogeneous superconductivity was observed in the temperature dependence of resistivity in the 15- to 100-nm-thick crystals of FeSe_0.35Te_0.65 [26] and in the 12- to 90-nm-thick crystals of FeSe_0.5Te_0.5 [27]. These results suggested that the different superconducting behavior in these thin crystals with different thickness might be related to the inhomogeneous distribution of excess Fe [26, 27] and/or the inhomogeneity of Se/Te distribution [27], and the temperature dependence of resistivity in the thin crystal that was taken from the low concentration region of excess Fe in the bulk crystal showed a sharp superconducting transition and homogeneous superconductivity [26]. A narrowing of superconducting transition width ΔT_c was observed in the case of thinner single crystals of x = 0.95 and 0.9, as seen in table 1, which can be explained by a scenario proposed in reference [26] as mentioned above, but there is no direct evidence to determine whether the thin crystal contains a low concentration of excess Fe or not. The c value may be one of the parameters to confirm a variation in the amount of excess Fe and the homogeneity of Se/Te in FeSe_1−xTe_x.

In order to clearly indicate a relationship between the superconductivity and the c values of thin crystals, the characteristic temperatures, T_t, T_c, T_c^zero, and ΔT_c are plotted as a function of c in figure 4(c). The color bars (blue, green, and orange) indicate the variation width of the c values for x = 1.0, 0.95, and 0.9, respectively. With decreasing c, T_t becomes lower, and then a superconducting transition (plot of T_c) appears. Furthermore, zero resistivity (plot of T_c^zero) is observed and the T_c^zero increases with the narrowing of ΔT_c. In the study of Fe_1+δTe reported by T. Machida et al, the different T_t was caused by an inhomogeneous distribution of excess Fe. However, the T_t did not show any monotonic change with a decrease in the amount of excess Fe, while the c value monotonically increased with a decreasing amount of excess Fe [33]. Therefore we can't conclude that the amount of excess Fe decreases with decreasing thickness for x = 1.0, but the lower T_t was realized in FeTe thin crystals with a smaller c value. Furthermore, in Fe_ySe_0.5Te_0.5 (y = 0.95–1.10), more metallic behavior in the normal state, a clearer superconducting transition, and an increase in the c value were observed with decreasing amount of excess Fe [34]. This trend is not consistent with our result showing more metallic behavior and clearer superconducting transition with a decrease in the c value.

On the other hand, from the viewpoint of the Se/Te distribution, the c value tends to decrease monotonically with increasing Se content. The increase in the Se content is more suitable for stabilizing the metallic and superconducting states, as suggested from the comparison with non-superconducting FeTe. In our study, the metallic and superconducting states are stabilized as the c value decreases, indicating that the stabilization cannot be associated with a decrease in the amount of excess Fe, which results in an increase in c. Thus, a change of the amount of excess Fe that influences the c value may not occur in exfoliated thin crystals of FeSe_1−xTe_x. Therefore, the result indicates that the inhomogeneity of the Se/Te distribution of bulk crystals may sensitively affect the metallic and superconducting states in thin crystals of FeSe_1−xTe_x with low Se content (high Te content; x $\geqslant$ 0.9), and exfoliation and/or heating in the photolithography process make thinner crystals more homogeneous Se/Te distribution. The phase diagram was well drawn by plotting the characteristic temperatures against the c value of the thin crystals with different Te content (x) and thickness. Yue et al reported that fluctuation in the Se/Te distribution and/or the presence of a trace amount of excess Fe led to nanoscale phase separation [27]. The superconductivity was suppressed below a critical thickness of ∼12 nm in FeSe_0.5Te_0.5 due to the lack of a continuous superconducting path, while the superconducting islands were well connected and formed robust superconducting paths in thick crystals (thickness >40 nm). In our study, the crystal thickness of 35–170 nm is enough to form three-dimensional (3D) superconducting paths, and a low dimensional effect (size effect) such as the two-dimensional (2D) quantum confinement effect may be eliminated.