content_image/408249.jpg content_image/408251.jpg content_image/408254.jpg content_image/408250.jpg content_image/408255.jpg content_image/408256.jpg content_image/408270.jpg content_image/408248.jpg content_image/408271.jpg content_image/408272.jpg content_image/408245.jpg content_image/408246.jpg content_image/408247.jpg content_image/408252.jpg content_image/408253.jpg content_image/408269.jpg
that is 

At the same time from the difference of the Maxwell equa- tions (51) inside and outside of material we obtain 

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The difference of the magnetic inductions at the bound- ary is given by the jump of magnetzation 

In the stationary magnetic field parallel to the surface of the metal H out = H$_{x}$ ˆ x this equation yields 

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In the normal state where ν = 0 the boundary condi- tions add nothing special to the centrosymmetric case. In the superconducting state the solution of the London equations supplied by these boundary conditions results in quite unusual helical field distribution found in the paper. 14 

For the light incident to the metallic surface using (70), (71), and (65) we obtain 

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Substituting here eqns. (67), (68) we come to 

For the combinations E ± = E$_{x}$ ± iE$_{y}$ of the electric field component this relation can be rewritten as 

## D. Reflection coefficient and the Kerr effect 

The equations (69) and (75) allow express the ampli- tudes of reflected wave through the amplitude of the in- cident wave. We have for reflection coefficient 

where the refraction index is 

Now one can rewrite eqn. (76) in more habitual form 

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where an effective refraction index is 

and the effective differences in the real and imaginary parts of the refraction indices of circularly polarized lights with the opposite polarization are 

Making use these definitions we can apply the standard procedure 22 to calculate the Kerr rotation for linearly po- larized light normally incident from vacuum to the flat boundary of a medium. The light is reflected as ellip- tically polarized with the major axis rotated relative to the incident polarization by an amount 

To find the Kerr rotation in the normal state let us sub- stitute the eqn. (28) in eqns. (80), (81). We find Δ˜ κ = 0 and Δ˜ n expresses through ratio of the light frequency to the band splitting 2 γ$_{0}$k$_{F}$ as 

Here, α = e $^{2}$/ ¯ hc is the fine structure constant. 

We limit ourselves by the frequencies not exceeding the band splitting γ$_{0}$k$_{F}$ . Although the latter is not known for many noncentrosymmetric materials, one can expect it is about hundred Kelvin or in the frequency units ∼ 10 $^{13}$rad/sec . 23 As an example we consider the sit- uation when the frequency of light is of the order of this value and larger than the quasiparticles scattering rate (clean limit): 1 << ωτ < ω$_{p}$τ , where ω$_{p}$ = √ 4 πne $^{2}$/m ∗ is the plasma frequency. In this frequency region the real and imaginary part of conductivity are σ ′ ≈ ω 2 $_{p}$/ 4 πω $^{2}$τ and σ ′′ ≈ ω 2 $_{p}$/ 4 πω . Then, one can find 2 nκ ≈ ω 2 $_{p}$/ω $^{3}$τ and κ 2 − n 2 ≈ ω 2 $_{p}$/ω $^{2}$. Thus, for the Kerr angle we ob- tain 

So, the Kerr angle in noncentrosymmetric metals can have measurable magnitude, in particular if we compare it with the Kerr angle of the order of 6 × 10 − 8 rad mea- sured in the superconducting Sr$_{2}$RuO$_{4}$ by the Stanford group. 24 

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## VI. THE KERR ROTATION 

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