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Nonequilibrium effect due to the imbalance in the number of the ? and ? spin electrons has been studied for the tunneling currents in the ferromagnet-insulator-superconductor (FIS) tunneling junctions within a phenomenological manner. It has been stated how the nonequilibrium effect should be observed in the spin-polarized quasiparticle tunneling currents, and pointed out that the detectable nonequilibrium effect could be found in the FIS tunneling junction at 77 K using HgBa2Ca2Cu3O8+? (Hg-1223) high-Tc superconductor rather than Bi2Sr2CaCu2O8+? (Bi-2212) one.

Transition from an equilibrium to non-equilibrium state due to an external perturbation makes an output. The well known case is the transport phenomena, which can be understood by solving the Boltzmann equation for classical treatment and the Liouville equation for quantum one. Even in superconductors, the departure from the equilibrium state of the distribution function is found when the superconductors are set in the time and/or spatial modulations as an external perturbation. Such a situation, the nonequilibrium superconductivity, can be understood as a change of superconducting parameters induced by modifications of the distribution function of quasiparticle excitations. Studies for the nonequilibrium superconductivity have focused on the effects of not only the simple quasiparticle injection and extraction but also the spin-polarized quasiparticle transport. The valuable considerations have already been done by Tinkham [^{*} and Q^{*} which represent the nonequilibrium temperature and quasiparticle charge density, respectively. In the case of the injection of spin-polarized quasiparticles, such as the quasiparticle tunneling in the ferromagnet-insulator-superconductor (FIS) tunneling junction, one can experimentally see the suppression of superconductivity whose origin is regarded as a pair-breaking mechanism of a Cooper-pair (CP).

CalTech group has extensively studied the nonequilibrium superconductivity under spin-polarized quasiparticle currents in the FIS tunneling junctions, and found that the phenomena manifesting nonequilibrium superconductivity in perovskite FIS heterostructure are observed and are attributed to the dynamic pair-breaking effect of spin-polarized quasiparticles in cuprate superconductors [_{c} of intrinsic Josephson junctions due to the spin injection and found that the observed modulation of I_{c} of Co/Au/Bi_{2}Sr_{2}CaCu_{2}O_{y} mesa is attributed to the injection of the spin-polarized current [

Spintronics including not only the ferromagnets but also superconductors is one of the most attractive subjects in solid state physics and technology. Therefore, it is surely expected that such a research will grow rapidly. For example, Kaiser and Parkin have measured the tunneling spin polarization using a superconducting tunneling spectroscopy for Al_{2}O_{3} tunnel barriers [_{2}CrAl, and pointed out that this effect is attributed to the appearance of a nonequilibrium state in the lead film as a result of spin injection into the superconductor [

Fundamental aspects of the proximity effect under nonequilibrium conditions even in normal metal-super- conductor bilayers are not clear [_{2} is selected because of its half metallic nature, i.e., a purely spin polarized, and HgBa_{2}Ca_{2}Cu_{3}O_{8+}_{d} (Hg-1223) and Bi_{2}Sr_{2}CaCu_{2}O_{8}_{ +}_{ }_{d} (Bi-2212) high-T_{c} superconductors are adopted as a S layer. Hg-based superconducting cuprates form a series with the general formula HgB_{2}C_{n}_{−1}CunO_{2n+2+}_{d} denoted as Hg-12mn _{2} layers, the transition temperature T_{c} progressively increases, reaching the maximum for Hg-1223 with a value of 135 K, and then decreases. The amplitude _{2}B_{2}C_{n}_{−1}CunO_{2n+4+}_{d} denoted as Bi-22mn _{c} increases with an increasing number n of CuO_{2} layers up to 110 K for Bi-2223. The T_{c} and _{2} layers showing a superconductive property. From the symmetry consideration for the CuO_{2} layer, these cuprate superconductors show the superconducting gap with

It is considered for the present study that 1) the electron states in the vicinity of the Fermi level E_{F} mainly come from 3d orbitals of Cu and Cr atoms; 2) the density of states (DOS) that originated from the 3d orbital shows a pointed structure meaning the localized nature, on the contrary to the DOS from s and p orbitals which show a broadened structure, i.e., the extended nature; therefore 3) the effective mass approximation, which is valid for the extended nature, may not be so good for the present system in which the electron states near the E_{F} are fairly well localized; and 4) the size of the insulating layer I is a realistic one, whose barrier strength is large enough, so it must be noted that 5) Blonder, Tinkham and Klapwijk (BTK) model [

Tunneling current

Here note that the S shown in Equation (1) is a symbol to identify the superconductor so that this symbol is used everywhere in the present paper. The charge and spin currents,

where C is a constant given by

quilibrium effect on the charge current

where

where

The

so that the value of

As a tunneling process, coherent, incoherent and WKB cases can be considered. In the present paper, the incoherent tunneling is mainly studied. The reason is described later. In the incoherent tunneling case, the

where f is a Fermi-Dirac distribution function and

function of energy

one electron energy relative to the Fermi level _{samp}.

The one electron energy

First of all, we must check how the current-voltage (I-V) characteristics are changed due to the change of tunneling mechanism such as coherent, incoherent and WKB ones. In order to do so, we have calculated the I-V characteristics _{2} with a half metal phase, the I is a nonmagnetic insulating layer with a real dimensional size, and the S is the Hg-1223 high-T_{c} superconductor. Here we wish to emphasize that the numerical calculations for the coherent and WKB cases need a very large CPU time as compared with the incoherent case [_{samp} = 4.2 K calculated for above three cases have told us that 1) the result calculated for the coherent case shows a unrealistic behavior so that there are some regions in which the differential conductance dI/dV is calculated as a negative value, 2) that for the incoherent case is reasonable, and 3) that for the WKB case is fairly similar to that for the incoherent one, but there are regions in which the dI/dV is calculated as a negative value. From above, we consider here only the incoherent tunneling case.

Next, we must consider the effect of the external magnetic field. In the present paper, the FIS tunneling junction, in which the F-layer shows a magnetization because of a half metallic CrO_{2} so that the spin-polarized quasiparticle injection has been well done for no applied field, is considered. Generally, the magnetic field has an obvious effect on the transition temperature T_{c} and superconducting gap Δ, however, the external magnetic field we consider here is a field made by the magnetization of the CrO_{2}-layer. Therefore, it seems that the effect of the external magnetic field may be small. In the present paper, thus, its effect has been taken into account by using the same method done by Tedrow and Meservey [_{k} has been replaced by _{ext} with the value of 1 T, and found that there is no detectable difference between the calculations for

Experimental current

This relation clearly shows that the logarithmic derivative LD calculated by using numerically calculated values is exactly equal to that by using the experimental one. In the following, therefore, we show only the LD values deduced from the full numerically calculated charge current

In the FIS tunneling junction, it is easily supposed that the imbalance in the number of the and ¯ spin electrons makes a decrease in the number of CPs. This is just a nonequilibrium effect that we consider here. The decrease in the number of CPs makes a decrease in the amplitude ^{*} which represents the nonequilibrium temperature. At low temperature region

where

The differences LD_{FIS} − LD_{NIS} of the logarithmic derivatives LD_{FIS} and LD_{NIS} deduced from the charge currents _{2} as F, an Al metal as N and a HgBa_{2}Ca_{2}Cu_{3}O_{8+}_{d} (Hg-1223) high-T_{c} superconductor as S, and (d), (e) and (f) are those by using the CrO_{2} as F, the Al as N and a Bi_{2}Sr_{2}CaCu_{2}O_{8}_{ +}_{ }_{d} (Bi-2212) high-T_{c} superconductor as S. As already stated, the T_{c} of Hg-1223 and Bi-2212 is 135 and 86 K, and the _{samp} even in the theoretical studies. In the present calculations, therefore, the reduced sample temperature _{samp} is 13.5, 67.5, 121.5, 8.6, 43.0 and 77.4 K, and the resultant _{N} defined by

of_{N} ≤ 5, so it must be noted that the real voltage _{samp} = 0.5 and 0.9, and (2) the remarkable change is found in Hg-1223 high-T_{c} superconductor rather than Bi-2212 one. This is caused to the fact that the

In order to make a comparison with the experimental study, we have chosen two temperatures 4.2 and 77 K as a T_{samp} and calculated the LD_{FIS} and LD_{NIS}. The results for the difference LD_{FIS} − LD_{NIS} are shown in Figures 2(a)-(d). _{2} as F, an Al metal as N and a HgBa_{2}Ca_{2}Cu_{3}O_{8+}_{d} (Hg-1223) high-T_{c} superconductor as S, and (c) and (d) are those with the CrO_{2} as F, the Al as N and a Bi_{2}Sr_{2}CaCu_{2}O_{8+}_{d} (Bi-2212) high-T_{c} superconductor as S. The T_{samp} is 4.2 K for (a) and (c) and 77 K for (b) and (d) and the

At the high voltage region, the I-V curve of FIS tunneling junction approaches to the ohmic line. Namely, the effect of the variation of superconducting gap decreases with an increasing the voltage applied to the junction.

This is a reason why the value of LD_{FIS} − LD_{NIS} at the high voltage region remains the same for the change of the

Our phenomenological approach for the nonequilibrium effect states that if the experiments for the difference LD_{FIS} − LD_{NIS} using the CrO_{2} as F, the Al as N and the Hg-1223 high-T_{c} superconductor as S are done at two temperatures such as 4.2 and 77 K and the detectable differences are found at these temperatures, then such a difference is directly correlated with the nonequilibrium effect due to the imbalance in the number of the and ¯ spin electrons.

For the c-axis tunneling currents observed in the ferromagnet-insulator-superconductor (FIS) tunneling junctions, we have phenomenologically studied the nonequilibrium effect due to the imbalance in the number of the and ¯ spin electrons, in order to see how the nonequilibrium effect due to spin injection should be observed in the spin-polarized quasiparticle tunneling. We have showed that 1) the nonequilibrium effect is found at 77 K rather than 4.2 K, and 2) its effect is clearly found in the FIS tunneling junction using the Hg-1223 high-T_{c} superconductor rather than Bi-2212 one as S.

Michihide Kitamura,Kazuhiro Yamaki,Akinobu Irie, (2016) Nonequilibrium Effect in Ferromagnet-Insulator-Superconductor Tunneling Junction Currents. World Journal of Condensed Matter Physics,06,169-176. doi: 10.4236/wjcmp.2016.63018