boundaries. However, from our consideration of the vortex – antivortex problem one can expect that the effect of boundary scattering on the LDOS becomes important only when the distance from the vortex center to the sample edge is comparable with $\xi$. In this case the LDOS profiles in a vortex pair are affected by both the hybridization of the CdGM states and normal scattering. Considering the particular case of a doubly quantized vortex one can expect the boundary scattering to result in the spectrum oscillations (see Fig. 6) similar to the ones in a singly quantized vortex.

![\[FigSpectrumDisc2\] (Color online) Quasiparticle spectrum vs $\mu$ for a doubly quantized vortex in a disk of the small radius $R=2\xi$. The spectrum for a doubly quantized vortex in a disk of the large radius $R=7\xi$ is shown by the solid line. We choose here $k_F\xi=200$.](SpectrumD){width="1.0\linewidth"}

These oscillations should cause the broadening of the ring in the LDOS pattern with the typical broadening scale $r_0$. The same effect should result in the broadening of the anisotropic ring structure for a vortex pair of a finite size.

Conclusion {#sec:summary}
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To summarize, we have investigated the distinctive features of the LDOS profiles specific both for 