content_image/390766.jpg content_image/390769.jpg content_image/390765.jpg content_image/390772.jpg
<img src='content_image/390766.jpg'>

has the meaning of ”phase” 

which is dependent on the vector potential field ⃗ A = (0 , A$_{y}$ ( x ) , 0). The spectrum of Eq. (1) is similar to Kulik’s spectrum [17] for the current state of the SNS contact. However, Eq. (1) includes an angle-dependent magnetic flux instead of the phase difference of the con- tacting superconductors. 

The length of the quasiparticle trajectory ( 2 AB ) is readily found from Fig.1 using the sine and cosine theo- rems: 

<img src='content_image/390769.jpg'>

where sin( − ≤ ≤ trum in Eq. (1) was derived assuming that the mean free path of the quasiparticles was much longer than the cross-section perimeter of the cylinder and the require- ment d ≪ R was obeyed. In this limit L 0 = 2 AB ∼ = 2 d/ cos ( α ) ( lim α$_{c}$ → π/ $_{2}$AB = d/ cos ( α ) , i.e., the radius R drops out from the expression for the spectrum. Al- though the boundary curvature of the sample is disre- garded, the information about its cylindrical geometry is retained through a correct choice of the limits of in- tegration for the angle α : − α$_{c}$ ≤ α ≤ α$_{c}$ . Putting L 0 = 2 d/ cos ( α ), we obtain the following expression for the spectrum ( as in [9] ): 

<img src='content_image/390765.jpg'>

<img src='content_image/390772.jpg'>

The spectrum in Eq. (4) has an important feature [8], [9]. As the ”phase” Φ Eq. (2) changes, the density of states exhibits resonance spikes. Every time when the Andreev level coincides with the chemical potential of the metal, the state of the NS structure suffers strong degen- eracy showing up spikes. The dependence of the density of states upon the magnetic flux calculated numerically for the NS system is illustrated in Fig.2 . 

Note that in [1], [18] the diamagnetic current of NS structure was calculated using α$_{c}$ = π/ 2 instead of the 

upper limit of integration for the angle ( α$_{c}$ < π/ 2 ) and assuming implicitly an infinitely large number of Andreev levels. Therefore, these results cannot be conformed with the experimental findings. The reason is not only that the calculation was made for a flat geometry rather than for a curved NS boundary. Numerical analysis shows that an adequate interpretation of the experimental magnetic moment-field dependence is possible only with a proper choice of the upper limit of integration with respect to α . If α > α$_{c}$ or α$_{c}$ = π/ 2, the consideration includes 

