6.2 Results and Discussions
6.2.1 Seebeck Coefficient and Figure of Merit
Figure 6.1: The variation of the Seebeck coefficient, S as a function of temperature, T (scaled by superconducting order parameter, ∆0) (a) for pristine graphene, (b) for Au decorated graphene. The values of the spin-orbit coupling are shown in the figure.
Initially we show the results of Seebeck coefficient for a pristine graphene (λR =0, λI = 0). The variation of the Seebeck coefficient,S as function of the tem- perature (in units of superconducting gap, ∆0) for a pristine graphene is shown in Fig.(6.1a). This is included for comparison with that of Fig.(6.1b). The Seebeck coefficient, S is dimensionless (since e = 1 and kB = 1). It is understood that the Seebeck coefficient increases initially with temperature and after attaining a certain value it decreases very slowly. In this regard we should remind our- selves that the temperatures should be in a range such the superconductivity is not destroyed. From BCS theory it can be shown that the relationship be- tween superconducting temperature and the superconducting order parameter is Tc ∼ (0.5− 0.6)∆0. Now to get an idea about the role of spin-orbit couplings
Figure 6.2: The variation of the Seebeck coefficient, S as a function of temperature, T/∆0for a larger RSOC parameter by one order greater magnitude compared to that of the Au decorated graphene.
on value of the thermopower, in Fig.(6.1b) we present the variation of the spin resolved Seebeck coefficient, S as function of the temperature (in units of su- perconducting gap, ∆0) for an Au decorated graphene. From the first principal calculations, in the Au decorated graphene the values of the following parameters are, λI = 0.007t1 and λR = 0.0165t1  and one does not notice any significant change in the thermopower profile. Thus, by some means if we are able to en-
Figure 6.3: The variation of the spin resolved Seebeck coefficient, S as function of λR and λI for (a) up spin, (b) down spin. Reddish yellow regions indicate the parameters values needed for the achieving maximum, S.
hance the SOCs by one order of magnitude compared to the value present in the Au decorated graphene, there could be noticeable effects of SOC. Thus in Fig.(6.2) we have shown the thermopower profile with one order of greater magnitude of RSOC strengths where, indeed noticeable changes are obtained. For this reason in the later discussions we shall use these values of the SOCs strength. The in- teresting fact is that, in case of a normal junction (that is not graphene based) in the presence of RSOC, there is no spin resolved thermopower, which graphene
based junction devices, in presence of a bit high RSOC strengths show the spin resolved thermopower. The reason behind the spin resolved Seebeck coefficient is the same as that of the spin resolved conductance which has been explained in previous chapter. It is clearly understood that with the inclusion of the SOC parameters the Seebeck coefficient increases. Further the up spin shows larger values of thermopower compared to that of the down spin.
Figure 6.4: (a)The variation of the charge Seebeck coefficient as function of λRand λI,(b)The variation of the spin Seebeck coefficient as function of λR and λI.
To get an idea how the spin resolved Seebeck coefficient vary with both of the spin-orbit couplings, and also to get an operating regime in the parameter space, we have shown the spin resolved Seebeck coefficient as a function of λR and λI in Fig.(6.3a) and Fig.(6.3b) with temperature, T = 0.5∆0. The color plots yield the information of the Seebeck coefficient for different values of the RSOC and the ISOC parameters. For certain values of the RSOC parameter (>0.1t1), irrespective of the ISOC strength, both spins show higher values of thermopower, So we can infer that for both the spins RSOC enhances the thermopower.
Further we have shown results of the charge and spin Seebeck coefficients in Fig.(6.4a) and Fig.(6.4b). The charge Seebeck coefficient shows higher values for larger strengths of RSOC, and for certain values of the SOC parameters, the spin Seebeck coefficient vanishes. This map gives an idea of the magnitude of the Seebeck coefficient corresponding to a variety of choices of λR and λI. As the strengths of SOCs correspond to presence of different adatoms, a careful choice of the periodic table may provide useful information on tunable thermopower of these junction devices.
Now we show the results on the ’Figure of Merit’ (FM) which defines the effi- ciency of this system as a thermopower device. The variation of the Figure of Merit, ZT as function of the temperature (in units of superconducting gap,∆0) is shown in Fig.(6.5). It shows that, initially with temperature the efficiency of the system as a thermopower device increases and, after attaining a certain temperature it
decreases. The variations of the spin dependent FM, ZσT as the function of the
Figure 6.5: The variation of Figure of Merit, ZT as a function of temperature, T (scaled by superconducting order parameter, ∆0) for (a) λR = 0 and λI = 0, (b) λR =0.165t1and λI = 0.007t1.
spin-orbit couplings are presented in Fig.(6.6). This map gives an idea of the FM for different spins corresponding to different choices of λR and λI. Interestingly, the down spin shows more efficiency compared to that of the up spin. Further we
Figure 6.6: The variation of the ’Figure of Merit’, ZT as function of λRand λI for(a) up spin and(b)down spin.
have shown the results for charge and spin FM in Fig.(6.7a) and Fig.(6.7b) where it is observed that for higher values of ISOC the charge FM becomes larger. The spin FM becomes zero for the lower values of the RSOC parameters irrespective of the ISOC strengths. Such regions, along with others, are shown by black patches in Fig.(6.7b). Thus these maps aid in deciding on the values of the parameters that may be used for maximizing the gain of these KMNIS junction devices.
Figure 6.7: (a)The variation of the charge ’Figure of Merit’, ZchT as function of λR and λI,(b)The variation of the spin ’Figure of Merit’, ZspT as function of λRand λI,