orbits near the degeneracy point $\theta_p=0$ are defined by the following equation: $$\label{orbit2}
  \varepsilon=\pm\sqrt{(\omega\mu)^2+(\delta \varepsilon)^2}
  -\omega(k_F a/2)\theta_p\,.$$ The classically forbidden angular domain at $\varepsilon=0$ has the width $\delta\theta_p=4\delta\varepsilon/(\omega k_F a)$. One can assume that the appearance of such classically forbidden domain explains the deep structure in the local DOS profile observed numerically in Ref.  for a vortex near the flat boundary of an $s$–wave superconductor. The classically forbidden angular domain results in the suppression of the overall DOS[@MelnikovPrb2008] and we show below that this mechanism is responsible for the anomalous spectrum branch disappearance when the vortex exits the sample.

To study the transformation of spectrum in the entire range of intervortex distances we solve numerically the quasiclassical Andreev equations (\[quasiclass\]) to find isoenergetic lines in $\mu -\theta_p$ plane. The resulting quasiclassical orbits for a vortex–vortex pair with the intervortex distances $a=2.5\xi$ and $a=1.5\xi$ are shown in Fig. \[Orbit\]a.

![\[Orbit\] Quasiclassical orbits in the $\mu-\theta_p$ plane corresponding to zero energy level. Upper panel (a): two vortices at distances $a=2.5\xi$ (solid line) and $a=1.5\xi$ (dashed line). Dotted lines correspond to the case of a doubly quantized vortex, i.e. to $a=0$. Lower panel (b): vortex-antivortex system with $a=2.5\xi$ (solid line), $a=1.7\xi$ (dashed line) 