Kerr Effect in Superconductor.

A magnetic field H is to make the time reversal symmetry of the system be broken. Using the formulation [1], neglecting H dependence of $\Delta $(T) and for the pair cyclotron frequency $\Omega $ = (2e/2m)H/c less than the photon frequency 2$\pi $ c/$\lambda $, the Kerr angle is obtained as $\theta _{{\rm K}}$(T) = $\theta _{K}$(0)[$\Delta $(T)/$\Delta $(0)]tanh [$\Delta $(T)/2k$_{B}$T], where $\theta _{{\rm K}}$(0) = A $\lambda ^{3} \quad \Omega $ / (8 $\pi ^{3}$ c N $\lambda _{L}^{2})$, A = (3$\lambda $/4, L)/$\xi _ {BCS}$ in the (non-local, local) limit, with mean free path length L and BCS coherence length $\xi _{BCS}=\hbar $v$_{F}$/$\pi \Delta $(0). N = (n-1) n (n+1) with index of refraction n. For Sr2RuO4 [2], $\lambda $ = 1550 nm, L = 1 $\mu $m, v$_{F}$ = 100Km/s, n=3 and the London penetration depth length $\lambda _{L}$ = 3 $\mu $m [3], T$_{C}$ = 1.5 K . In the strong coupling case [4], $\Delta $(0) = 2T$_{C}$. The effective H is sum of the external applied and internal (by pair current) magnetic fields, to maintain the fluxoid quantization. After cooling a sample in the external magnetic field, turning it off, before warming a sample, is not necessary to make H vanish, since the pair current was set in a sample during cooling it. Then, H$_{C2}$ = 750 Gauss [3], in the normal vortex core, is considered as H. With all values of parameters given above, we obtain $\theta _ {K}$(0) = (44, 38) nrad in the (non-local, local) limit in satisfactory agreement with data of 65nrad [2]. The fluxoid quantization makes the Kerr angle same within a range of the external applied magnetic fields. [1] Nam, PR. \textbf{156}, 470, 487 (67). [2] Xia et al., PRL. \textbf{97}, 167002 (06). [3] Mackenzie et al., RMP.\textbf{ 75}, 657 (2003). [4] Nam, PL. \textbf {A193}, 111 (94); (E) ibid\textbf{. A197}, 458 (95).