Comparative study of superconducting and normal-state anisotropy in Fe_1+yTe_0.6Se_0.4 superconductors with controlled amounts of interstitial excess Fe

Fe_1+yTe_1-xSe_x compounds are unique in iron-based superconductors (IBSs) because of their structural simplicity, consisting of only FeTe/Se layers. They have attracted much interest both in the fundamental physics and application research. In the fundamental physics, the SC transition temperature ($T_{\rm{c}}$) is found to be remarkably enhanced by applying pressure Medvedev et al. (2009); Gresty et al. (2009), intercalating spacer layers Burrard-Lucas et al. (2013); Lu et al. (2015), carrier doping by gating Shiogai et al. (2016); Lei et al. (2016), and reducing the thickness to monolayer He et al. (2013); Ge et al. (2015). A nematic state, which break the rotational symmetry, is observed in FeSe without long-range magnetic order Wang et al. (2016a); Wen et al. (2016); Wang et al. (2016b). The small Fermi energy, comparable to the superconducting gap size, indicates that superconductivity in Fe_1+yTe_1-xSe_x may be in the crossover regime from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) Kasahara et al. (2014); Lubashevsky et al. (2012). More interestingly, a topological surface superconductivity Zhang et al. (2018, 2019) and the possible Majorana bound state have been observed Wang et al. (2018); Machida et al. (2019), which make Fe_1+yTe_1-xSe_x the first high-temperature topological superconductor. In the view of application, the large upper critical field ($H_{\rm{c2}}$) and less toxic nature compared with iron pnictides make Fe_1+yTe_1-xSe_x an ideal candidate for fabricating SC wires and tapes. In practice, the SC tapes with a large critical current density, over 10⁶ A/cm² under self-field and over 10⁵ A/cm² under 30 T at 4.2 K, have already been fabricated Si et al. (2013).

Determination of the anisotropy ($\gamma$) is crucial for both fundamental physics and practical applications Gurevich (2011); Hosono et al. (2018). It provides information on the underlying electronic structure such as the Fermi-surface topology, and also shed light on the SC gap structure. In application, small $\gamma$ is advantageous for allowing high critical current density in the presence of magnetic field, due to the reduction of flux cutting effects and strong thermal fluctuations. Therefore, the anisotropy of Fe_1+yTe_1-xSe_x is pivotal for both understanding the intriguing physics and the future application.

In the SC state, $\gamma$ can be obtained by measuring $H_{\rm{c2}}$ or the penetration depth ($\lambda$). The former defines $\gamma_{H}$ = $H_{c2}^{ab}$/$H_{c2}^{c}$ = $\xi_{ab}$/$\xi_{c}$, where $\xi_{ab}$ and $\xi_{c}$ are the coherence lengths in the $ab$ plane and along $c$ axis, respectively. The later provides $\gamma_{\lambda}$ = $\lambda_{c}$/$\lambda_{ab}$, where $\lambda_{c}$ and $\lambda_{ab}$ are the penetration depths. Within the Ginzburg-Landau (GL) theory for a single-gap superconductor at the temperatures close to $T_{\rm{c}}$, $\gamma_{H}$ = $\sqrt{m_{c}^{*}/m_{ab}^{*}}$ = $\gamma_{\lambda}$, where $m_{c}^{*}$ and $m_{ab}^{*}$ are the effective masses along $c$ axis and in the $ab$ plane, respectively Tinkham (1996); Yuan et al. (2015). On the other hand, $\gamma$ in the normal state can be obtained by $\gamma_{\rho}$ = $\rho_{c}$/$\rho_{ab}$, where $\rho_{c}$ and $\rho_{ab}$ are the resistivity along the $c$ axis and in the $ab$ plane, respectively. In the approximation of isotropic scattering, $\rho_{c}$/$\rho_{ab}$ = $m_{c}^{*}/m_{ab}^{*}$. Therefore, $\gamma$ in the SC and normal state can be connected by the relation $\gamma_{H}$ ($\gamma_{\lambda}$) $\sim$ $\gamma_{\rho}^{1/2}$ Tanatar et al. (2009).

So far, the relation $\gamma_{H}$ $\sim$ $\gamma_{\rho}^{1/2}$ has already been verified in most IBSs, as summarized in Table \Romannum1. However, the relation seems to be violated in Fe_1+yTe_1-xSe_x. A small SC-state anisotropy, $\gamma_{H}$($\gamma_{\lambda}$) $<$ 3, has already been confirmed by several previous reports Fang et al. (2010); Khim et al. (2010); Bendele et al. (2010). By contrast, an unexpectedly large normal-state anisotropy $\gamma_{\rho}$ $\sim$ 50-70 was reported Noji et al. (2010). Such a discrepancy between the SC and normal-state anisotropies still remains unresolved, which confuses both the study of fundamental physics and the application of Fe_1+yTe_1-xSe_x.

In this report, we successfully resolved the discrepancy by systematically probing the SC and normal-state anisotropies of Fe_1+yTe_0.6Se_0.4 single crystals with different amounts of excess Fe. Such discrepancy is demonstrated to originate from a large anisotropy in scattering times $\tau_{ab}$/$\tau_{c}$ $\sim$ 7.8 in the normal state.

Fe_1+yTe_0.6Se_0.4 single crystals were grown by the self-flux method as described in detail elsewhere Sun et al. (2013a). The as-grown crystals usually contain some amounts (represented by $y$) of excess Fe residing in the interstitial sites of the Te/Se layer. The excess Fe can be removed and its amount can be tuned by post annealing Sun et al. (2014a, 2013b, 2013c, 2019). After annealing, a series of single crystals with different amounts of excess Fe can be prepared. More details about the crystal preparation, excess Fe, and the basic properties can be found in our recent review paper Sun et al. (2019). The inductively-coupled plasma (ICP) atomic emission spectroscopy and the scanning tunneling microscopy (STM) were used for detecting the amount of excess Fe. STM images were obtained by a modified Omicron LT–UHV–STM system Sugimoto et al. (2008). The sample was cleaved in situ at 4 K in an ultra-high vacuum chamber of $\sim$ 10^-8 Pa to obtain fresh and unaffected crystal surface. Resistivity measurements were performed by the four-probe method. The electrical transport measurements under high magnetic field were performed at Wuhan High Magnetic Field Center, China. The bridges in the $ab$ plane and along the $c$ axis used for the measurements of normal state anisotropy, as shown schematically in the insets of Figs. 3(a) and 3(b), were fabricated by using the focused ion beam (FIB) technique Sun et al. (2020); Kakehi et al. (2016); Kakizaki et al. (2017).

In our as-grown single crystals, the amount of excess Fe is $\sim$ 14% as analyzed by ICP atomic emission spectroscopy. Although the excess Fe may be removed after annealing, it should still remain in the crystal, mainly on the surface, in some form of oxides Sun et al. (2019). Therefore, traditional compositional analysis methods such as the ICP, energy dispersive X-ray spectroscopy (EDX) and electron probe microanalyzer (EPMA) cannot precisely detect the amount change of excess Fe. To precisely determine the change in the number of excess Fe, we employ the STM measurement, which has atomic resolution. The excess Fe occupies the interstitial site in the Te/Se layer, and the previous report proved that the cleaved Fe_1+yTe_1-xSe_x single crystal possesses only the termination layer of Te/Se, which guarantee that the STM can directly observe the excess Fe in Te/Se layer without the influence of neighboring Fe layers Massee et al. (2009). Fig. 1(a) shows the STM image for the as-grown crystal. There are several randomly distributed bright spots in the image, which represent the excess Fe according to the previous STM analysis Massee et al. (2009); Hanaguri et al. (2010); Ukita et al. (2011). After annealing, the amount of bright spots, i.e. the excess Fe, is obviously reduced as shown in Fig. 1(b), and disappears in Fig. 1(c). By counting the number of the bright spots in the STM images together with the ICP result of 14% excess Fe for the as-grown crystal, the amount of excess Fe in Figs. 1(b) and 1(c) can be estimated as $\sim$ 7% and 0, respectively. Hence, the three crystals are labeled as Fe_1.14Te_0.6Se_0.4, Fe_1.07Te_0.6Se_0.4, and Fe_1.0Te_0.6Se_0.4 in the rest of this article.

Figs. 1(d)-1(f) show the temperature dependence of resistivities for the three crystals, scaled by the values at 300 K. All the crystals manifest a similar onset of $T_{\rm{c}}$ $\sim$ 15 K. However, the temperature dependent behaviors for the resistivity are quite different. Fe_1.14Te_0.6Se_0.4 manifests a semiconducting behavior (d$\rho$/d$T$ $<$ 0) when the temperature approaches to $T_{\rm{c}}$. The residual resistivity ratio RRR, defined as $\rho$(300 K)/$\rho$($T_{\rm{c}}^{\rm{onset}}$), is estimated as $\sim$ 0.74. For Fe_1.07Te_0.6Se_0.4, the semiconducting behavior is suppressed, and replaced by a temperature-independent behavior with RRR = 0.92. On the other hand, resistivity for Fe_1.0Te_0.6Se_0.4 manifests a metallic behavior (d$\rho$/d$T$ $>$ 0) with RRR = 2. These observations suggest that the semiconducting behavior (d$\rho$/d$T$ $<$ 0) in Fe_1.14Te_0.6Se_0.4 originates from the localization effect of excess Fe, which can be suppressed by removing the excess Fe Liu et al. (2009); Sun et al. (2014b). More details about the transport properties such as the Hall effect and magnetoresistance have been reported in our previous publications Sun et al. (2014b, 2016).

To probe the anisotropy in the SC state, the SC transition was measured under a high magnetic field over 50 T for the three crystals. Figs. 2(a)-2(f) show the in-plane resisivity $\rho_{ab}$ of the three crystals as a function of the magnetic field along the $c$ axis ($H\parallel c$) and parallel to the $ab$ plane ($H\parallel ab$). $H_{c2}^{ab}$ (open symbols) and $H_{c2}^{c}$ (solid symbols) for the three crystals are determined by the 90% of the resistivity value just above the SC transition. (Due to the broad transition under $H\parallel c$ for Fe_1.14Te_0.6Se_0.4, the criteria of 50% and 10% of the resistivity value cannot be obtained at high temperatures.) Clearly, with such large field, we can reach the $H_{c2}$ down to very low temperatures $\sim$ 2 K, which is over 44 T for both $H\parallel ab$ and $H\parallel c$ in all the three crystals (see Figs. 2(i) - 2(k)). The obtained $H_{c2}$ is larger than the expected Pauli-limiting field estimated as $H_{p}$(0) = 1.86 $T_{\rm{c}}$ $\sim$ 27 T for a weak-coupling BCS superconductor, which indicates that the spin paramagnetic effect plays an important role in the determination of $H_{c2}$(0). On the other hand, $H_{c2}^{ab}$ shows a convex shape with similar curvatures for all the three crystals. The convex shape in $H_{c2}^{ab}$ is a common feature for IBSs Fang et al. (2010); Khim et al. (2010); Yuan et al. (2009); Zhang et al. (2011); Fuchs et al. (2009), which is usually explained by the strong spin paramagnetic effect with relative large Maki parameter $\alpha$ within the Werthamer-Helfand-Hohenberg (WHH) theory Helfand and Werthamer (1966). Therefore, almost the same behavior of $H_{c2}^{ab}$ for the three crystals indicates that the excess Fe has little effect on the spin paramagnetic effect for $H\parallel ab$.

On the other hand, $H_{c2}^{c}$ for most IBSs manifests a nearly linear behavior (or less convex than $H_{c2}^{ab}$), suggesting that the spin paramagnetic effect for $H\parallel c$ is negligible (or much smaller than $H\parallel ab$) Fang et al. (2010); Khim et al. (2010); Yuan et al. (2009); Zhang et al. (2011). For Fe_1+yTe_1-xSe_x, both the convex and linear $H_{c2}^{c}$ have been reported previously Fang et al. (2010); Khim et al. (2010). In our case, $H_{c2}^{c}$ for Fe_1.14Te_0.6Se_0.4 shows a linear behavior, while a slightly convex behavior (with smaller curvature than $H_{c2}^{ab}$) is observed in Fe_1.07Te_0.6Se_0.4 and Fe_1.0Te_0.6Se_0.4. Our results reveal that the previous controversy in the $H_{c2}^{c}$ of Fe_1+yTe_1-xSe_x is due to the sample dependence of excess Fe. For the crystals free from or with small amount of excess Fe, the spin paramagnetic effect is finite for $H\parallel c$, although smaller than that for $H\parallel ab$. However, the spin paramagnetic effect for $H\parallel c$ is is more easily suppressed by excess Fe, and becomes almost negligible in crystal with too much excess Fe. We also note that $H_{c2}^{c}$ for Fe_1.14Te_0.6Se_0.4 shows a weaker rise close to $T_{\rm{c}}$ than those for Fe_1.0Te_0.6Se_0.4 and Fe_1.07Te_0.6Se_0.4, suggesting a more strongly-divergent behavior of $\xi_{ab}$ close to $T_{\rm{c}}$. This leads to the finite difference of the SC state anisotropy dependent on the excess Fe, as will be discussed below.

Due to the convex shape, $H_{c2}^{ab}$ finally meets $H_{c2}^{c}$ at low temperatures for all the three crystals, which means that the $H_{c2}$ becomes isotropic. With further decreasing temperature, $H_{c2}^{ab}$ becomes even smaller than $H_{c2}^{c}$. Such a crossover behavior is a unique feature of Fe_1+yTe_1-xSe_x, which is not observed in other IBSs Gurevich (2011). In a similar compound FeSe, a high-filed phase was observed at low temperatures, and suggested to originate from the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state Kasahara et al. (2020). The large value of Maki parameter $\alpha$ and the possibility of FFLO state in FeTe_1-xSe_x have also been discussed previously Khim et al. (2010). However, the realization of the FFLO state usually needs the crystal to be in the clean limit, i.e. the mean free path ($\ell$) should be much larger that the coherence length ($\xi$). According to the expressions $\ell$ = $\frac{\pi{c}\hbar}{{N}{e^{2}}{k_{F}}{\rho_{0}}}$ Kasahara et al. (2020), where c is the lattice parameter, N is the number of formula units per unit cell, $k$_F $\sim$ 1.0 nm^-1 Lubashevsky et al. (2012) is the Fermi wave vector, and $\rho$₀ $\sim$ 200 $\mu\Omega$ Sun et al. (2013d) is the residual resistivity, $\ell$ for Fe_1.0Te_0.6Se_0.4 is estimated as $\sim$ 1.8 nm. $\ell$ is smaller than $\xi$ $\sim$ 2.8 nm Lei et al. (2010), implying that the crystal is in the dirty limit rather than the clean limit. On the other hand, considering the fact that the transition from BCS state to the FFLO state is of first order, the FFLO state should be readily destroyed by disorders. It is obviously in stark contrast to our observations that the crossover of $H_{c2}^{ab}$ and $H_{c2}^{c}$ is almost identical in the three crystals containing different amounts of excess Fe. Therefore, the above discussion has ruled out the possibility of the FFLO state in Fe_1+yTe_0.6Se_0.4. A possible origin of the crossover behavior in the $H_{c2}$ is the multi-band effect. The upturn in $H_{c2}^{c}$ may be due to the contribution from another band. Similar upturn behavior has also been observed in S-doped FeSe Abdel-Hafiez et al. (2015) and Ba₂Ti₂Fe₂As₄O Abdel-Hafiez et al. (2018). We want to point out that such upturn behavior only occurs at low temperatures, which will not affect the value of anisotropy at high temperatures close to $T_{\rm{c}}$.

The SC state anisotropies for the three crystals estimated as $\gamma_{H}$ = $H_{c2}^{ab}$/$H_{c2}^{c}$ are shown in Fig. 2(l). At low temperatures, $\gamma_{H}$ becomes isotropic for all the three crystals. Then, $\gamma_{H}$ gradually increases with increasing temperature, and manifests a stronger increase with excess Fe. The temperature dependence of $\gamma_{H}$ has been discussed by using $\Delta(k_{z})$=$\Delta_{0}$(1+$\eta$cos$k_{z}\alpha$), including the coefficient $\eta$ for the $k_{z}$ dispersion of the gap Kogan and Prozorov (2012). $\gamma_{H}$ reaches a value $\sim$ 1.5 close to $T_{\rm{c}}$ for Fe_1.0Te_0.6Se_0.4. On the other hand, $\gamma_{H}$ close to $T_{\rm{c}}$ slightly increases with increasing the amount of excess Fe, and reaches a value $\sim$ 2.5 for Fe_1.14Te_0.6Se_0.4. Within the anisotropic three-dimensional GL-theory for a single-gap superconductor, $\gamma_{H}$ = $H_{c2}^{ab}$/$H_{c2}^{c}$ = $\sqrt{m_{c}^{*}/m_{ab}^{*}}$, through the anisotropy of the GL coherence lengths. The anisotropy of effective mass $m_{c}^{*}/m_{ab}^{*}$ is estimated as 2.25, 3.24, and 6.25 for Fe_1.0Te_0.6Se_0.4, Fe_1.07Te_0.6Se_0.4, and Fe_1.14Te_0.6Se_0.4, respectively. The influence of excess Fe on the $m_{ab}^{*}$ of the heavy band has been reported in the previous ARPES measurements Rinott et al. (2017). Here, our results reveal that the anisotropy of $m_{c}^{*}/m_{ab}^{*}$ is also strongly affected by the excess Fe.

In order to estimate the normal-state anisotropy, we need to measure the resistivity both in the $ab$ plane ($\rho_{ab}$) and along the $c$ axis ($\rho_{c}$). To measure $\rho_{c}$ for bulk sample, the specific configuration of contact electrodes is required for layered superconductors such as IBSs. This leads to a problem that $\rho_{c}$ and $\rho_{ab}$ are obtained from different samples. Here, we report a method to obtain the $\rho_{c}$ measured in a part of the region where $\rho_{ab}$ was measured, by using a $c$-axis neck structure fabricated additionally in the in-plane bridge. To fabricate the $c$-axis bridge, the crystal was first cleaved into a slice with $\sim$10 $\mu$m in thickness, by using scotch tape. The slice was glued on a sapphire substrate, and sputtered by four Au contacts to improve the electric contact. Then the sliced crystal was etched by using FIB and a narrow in-plane bridge with a width of $\sim$1 $\mu$m was fabricated between voltage terminals, as shown schematically in the inset of Fig. 3(a). The resistance $R_{1}$ for the in-plane bridge is measured by four probe method, which can be treated as a sum of three resistances in series, and expressed as

where $t_{0}$ is the thickness, $w$ and $W_{0}$ are the width, $l_{L1}$, $l_{center}$, and $l_{R1}$ are the length of the three parts, as shown in the inset of Fig. 3(a). Temperature dependence of $R_{1}$ is shown in the main panel of Fig. 3(a).

After measuring of $R_{1}$, two separated slits were further fabricated in the sidewalls of the in-plane bridge to make a small neck along the $c$ axis, as shown in the upper inset of Fig. 3(b). The length of $c$ axis neck was adjusted by a vertical overlap between the two slits (typically $\sim$1 $\mu$m). Such a crank structure enforces the current to flow along the $c$ axis in the bridge region as marked by the rectangular frame in the lower inset of Fig. 3(b). The whole resistance $R_{2}$ for this device can be treated as a sum of seven resistances in series as shown schematically in the lower inset of Fig. 3(b). The current flows along the $ab$ plane in the left and right three parts, while it flows along the $c$ axis in the center one with dimension of $l\times w\times t$. Therefore, $R_{2}$ can be expressed as

$\rho_{ab}$ and $\rho_{c}$ can be simply estimated by solving Eqs. (1) and (2). By this method, $\rho_{ab}$ and $\rho_{c}$ are obtained from almost the same region in an identical crystal, therefore they are not affected by the sample-dependent variations.

$\rho_{ab}$ and $\rho_{c}$ for the Fe_1.0Te_0.6Se_0.4 obtained by the above method are shown in the main panel of Fig. 4(a). Temperature dependence of $\rho_{ab}$ shows similar behavior as the bulk one [see Fig. 1(f)], which confirms that FIB fabrication will not introduce visible damage in the bridge part. In contrast to the $\rho_{ab}$, $\rho_{c}$ increases slightly with decreasing temperature down to 60 K, then it shows a metallic behavior down to $T_{\rm{c}}$. Similar temperature dependent behavior of $\rho_{c}$ was also reported previously by using the conventional method for bulk samples Liu et al. (2009). Normal state anisotropy $\gamma_{\rho}$ calculated as $\rho_{c}$/$\rho_{ab}$ for Fe_1.0Te_0.6Se_0.4 is shown in the inset of Fig. 4(a). $\gamma_{\rho}$ is $\sim$ 7 at 250 K, and gradually increases with decreasing temperature. Below $\sim$ 30 K, the increment accelerates, and $\gamma_{\rho}$ finally reaches a value of $\sim$ 17 just above $T_{\rm{c}}$. On the other hand, $\rho_{c}$ for Fe_1.14Te_0.6Se_0.4 with abundant excess Fe continues to increase with cooling down in the whole temperature range [see Fig. 4(b)]. Besides, the SC transition is not observed in $\rho_{c}$, which is due to the fact that superconductivity in Fe_1.14Te_0.6Se_0.4 is filamentary as proved by the absent of SC transition in bulk measurements such as specific heat and magnetization Sun et al. (2014a). Our observation indicates that the filamentary superconductivity in crystals with abundant excess Fe is localized, andmay not show up in a small region where we probe $\rho_{c}$. The $\gamma_{\rho}$ for Fe_1.14Te_0.6Se_0.4 increases with decreasing temperature, while it decreases slightly below $\sim$ 50 K [see the inset of Fig. 4(b)]. In contrast to Fe_1.0Te_0.6Se_0.4, $\gamma_{\rho}$ for Fe_1.14Te_0.6Se_0.4 manifests a much larger value ranging from 32 - 50. Such larger normal-state anisotropy is close to that reported previously Noji et al. (2010). Our results reveal that the normal-state anisotropy is strongly affected by the amount of excess Fe.

To directly observe the temperature evolution of anisotropy in the whole temperature range from the SC to normal state, we summarized the results of $\gamma_{H}$ and $\gamma_{\rho}$ in Fig. 5. For comparison, the anisotropy $\gamma_{\lambda}$ estimated from penetration depth measurements (the amount of excess Fe was claimed to be $\sim$ 0) Bendele et al. (2010), and the $\gamma_{\rho}$ calculated from crystal with more excess Fe ($y$ = 0.18) Liu et al. (2009) are also included. The normal-state anisotropy is compared with $\gamma_{H}$ by using a square root of $\gamma_{\rho}$, since $\gamma_{H}$ $\sim$ $\gamma_{\rho}^{1/2}$ is expected in the isotropic scattering case. In the SC state, both $\gamma_{H}$ and $\gamma_{\lambda}$ show relatively small values $<$3. On the other hand, $\gamma_{\lambda}$ increases with decreasing temperature, while $\gamma_{H}$ decreases with decreasing temperature. The different temperature dependence of $\gamma_{\lambda}$ and $\gamma_{H}$ in FeTe_1-xSe_x has already been discussed in the previous report Bendele et al. (2010), and was also observed in other IBSs Prozorov and Kogan (2011) and MgB₂ Fletcher et al. (2005). It may originate from the multiband effect, where the contributions of electronic bands with different $k$-dependent Fermi velocities and gap values lead to different ratios of $\gamma_{\lambda}$ and $\gamma_{H}$ Kończykowski et al. (2011).

Obviously, the anisotropy in the normal state is much larger than that in the SC state. For Fe_1.0Te_0.6Se_0.4, $\gamma_{\rho}^{0.5}$ resides in the region of 2.5 - 4. However, it increases up to $\sim$ 5.7 - 7 in Fe_1.14Te_0.6Se_0.4, and $\sim$ 7.7 - 8.8 in Fe_1.18Te_0.6Se_0.4 Liu et al. (2009). The values of $\gamma_{H}$ and $\gamma_{\rho}$ are also summarized in Table \Romannum1. In order to resolve the observed discrepancy between the SC and normal-state anisotropies, we need to reconsider the empirical relation of $\gamma_{H}$ $\sim$ $\gamma_{\rho}^{0.5}$. According to the Drude Model, $\gamma_{\rho}$ can be expressed as

where $n$ is the charge carrier density, and $\tau_{ab}$ and $\tau_{c}$ are the carrier scattering times in the $ab$-plane and along the $c$ axis, respectively. The empirical relation of $\gamma_{H}$ $\sim$ $\gamma_{\rho}^{0.5}$ is approximately obtained by assuming the isotropic scattering. Therefore, the different anisotropy between the SC and normal state, observed universally for samples with different amounts of excess Fe, clearly shows the contribution of the anisotropic scattering time $\tau$. By assuming that the ratio of $m^{*}_{c}$/$m^{*}_{ab}$ is continuously connected at $T_{\rm{c}}$, we roughly estimate the ratio of $\tau_{ab}$/$\tau_{c}$ (=$\gamma_{\rho}$/$\gamma_{H}^{2}$) as $\sim$ 7.77 for Fe_1.0Te_0.6Se_0.4 and $\sim$ 7.80 for Fe_1.14Te_0.6Se_0.4. Therefore, the large discrepancy between the SC and normal-state anisotropies is due to the anisotropy of the scattering.

Besides, the anisotropy of $\tau_{ab}$/$\tau_{c}$ is almost identical for crystals with different amounts of excess Fe, which indicates that the scattering from excess Fe should be isotropic. The excess Fe in the interstitial position is reported to be strongly magnetic, which provides local moments that interact with the Fe in the FeTe/Se plane Zhang et al. (2009). Neutron scattering measurements find out that the excess Fe in Fe_1+yTe_1-xSe_x will cause spin clusters involving more than 50 Fe in the nearest two neighboring Fe-layers Thampy et al. (2012). Considering the amount of excess Fe is as large as 14% in Fe_1.14Te_0.6Se_0.4, the influence of such magnetic clusters to the scattering should be more extensive, compared to the case of isolated impurities. Our observation of the isotropic scattering from excess Fe suggests that the magnetic moment should be randomly orientated without order.

We investigated the reported discrepancy between the SC and normal state anisotropies of Fe_1+yTe_1-xSe_x superconductors by probing the anisotropies of crystals with controlled amounts of excess Fe. The SC-state anisotropy $\gamma_{H}$ is found to be in the range of 1 $\sim$ 2.5 in the crystals with excess Fe ranging from 0 to 14%, while the normal-state anisotropy $\gamma_{\rho}$ shows a much larger value of 17 $\sim$ 50 at the temperature above $T_{\rm{c}}$. Combining the results of $\gamma_{H}$ and $\gamma_{\rho}$, we found out that such discrepancy originates from a large anisotropic scattering time $\tau_{ab}$/$\tau_{c}$ $\sim$ 7.8 in the normal state. Besides, the $\tau_{ab}$/$\tau_{c}$ is found to be independent of the excess Fe.