content_image/419098.jpg content_image/419110.jpg content_image/419112.jpg content_image/419113.jpg content_image/419101.jpg content_image/419102.jpg
<img src='content_image/419098.jpg'>

<img src='content_image/419110.jpg'>

following equation in terms of digamma functions: 40 

<img src='content_image/419112.jpg'>

where t = T/T$_{c}$ , γ ≡ [( α − h ) 2 − ( λ$_{so}$/ 2) $^{2}$]1 / 2 and 

Here, we assume that λ$_{so}$ =0 because the spin-orbit scattering is expected to be rather weak 41 and the equa- 

<img src='content_image/419113.jpg'>

tion can be simplified as: 

<img src='content_image/419101.jpg'>

When α =0, in the absence of the spin-paramagnetic effect and the spin-orbit interaction, orbital limited upper critical field H ∗ c 2 is described by: 

and µ$_{0}$H ∗ c $_{2}$(0)=-0.693( dµ$_{0}$H$_{c}$$_{2}$/dT )$_{T}$ c T$_{c}$ , i.e., eq. (1). 

As shown in the Fig. 6, the data points of µ$_{0}$H$_{c}$$_{2}$ ( T ) for H ‖ ab and H ‖ c in both samples cannot be explained well using the WHH model with α =0 and λ$_{so}$ =0 (Fig. 6(a,b) solid lines). We obtain excellent fits for the µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) and µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ) in Fig 6(a,b) using eq (4) with spin- paramagnetic effect. These results indicate that the spin- paramagnetic effect is the dominant pair-breaking mech- anism in Se-39 and Se-11 for both H ‖ ab and H ‖ c. The paramagnetically limited field µ$_{0}$H p c $_{2}$(0) 

is given by µ$_{0}$H p c $_{2}$(0)= µ$_{0}$H ∗ c $_{$_{2}$(0)/}$√$_{1 +}$ α 2 and α $_{=}$√$_{2}$$_{H}$ ∗ c $_{2}$(0)/ H$_{p}$ (0), where µ$_{0}$H$_{p}$ (0) is zero-temperature Pauli limited field. 42 The calculated µ$_{0}$H p c $_{2}$(0) and µ$_{0}$H$_{p}$ (0) using α obtained from H$_{c}$$_{2}$ ( T ) data fitting are listed in Table 2. From the µ$_{0}$H$_{c}$$_{2}$ (0) zero- temperature coherence length ξ (0) can be estimated with Ginzburg-Landau formula µ$_{0}$H$_{c}$$_{2}$ (0)=Φ$_{0}$/2 πξ $^{2}$(0), where Φ$_{0}$=2.07 × 10 − $^{15}$W b (Table 2). The µ$_{0}$H$_{c}$$_{2}$ (0) (de- termined by µ$_{0}$H p c $_{2}$(0)) of Se-39 in both field directions are close to previously reported. 43 Our results suggest that Fe(Te,Se) exhibits the spin-singlet pairing in the superconducting state. One the other hand, we also analyze our data using the two-band theory 17 , $^{44}$, and the fits are unsatisfactory the two-band model (not shown here). 

It is instructive to discuss the origin of enhance- ment of spin-paramagnetic effect, i.e., reduced values of µ$_{0}$H$_{p}$ (0). The Maki parameter α is enhanced for disor- dered systems. 41 , 45 For Se-39, more Se doping introduces more disorder than in Se-11. This effect could contribute to larger α$_{H}$$_{‖}$$_{ab}$ of Se-39 when compared to Se-11. How- ever, it cannot explain the inverse trend of α$_{H}$$_{‖}$$_{c}$ . There- 

<img src='content_image/419102.jpg'>

