in a vortex-antivortex pair follows a different scenario (see Fig. \[LDOSvav\]). When the distance between vortices is large enough there appear deep structures at the LDOS peaks (see Fig. \[LDOSvav\]a). The peaks themselves are slightly shifted towards the middle point at the line connecting the vortex and antivortex centers. Below the critical intervortex distance $a_c/\xi\sim 1.7$ the two peaks merge into one peak at the middle point (see Fig. \[LDOSvav\]b). As we discussed above this phenomenon is explained by the shrinkage of the quasiclassical orbits in the $\mu - \theta_p$ plane. When the vortex and antivortex come closer the amplitude of the LDOS peak is reduced and finally it disappears completely when the vortex and antivortex merge and annihilate. Mapping the solution of the vortex–antivortex problem on the one for a vortex near the flat surface we conclude that the zero bias LDOS peak appears to be positioned exactly at the surface provided the distance from the vortex to the surface becomes less than $0.85\xi$.

Vortex in mesoscopic cylinder {#subsec:cylinder}
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In this subsection we study another generic example illustrating the effect of the normal quasiparticle reflection at the sample boundary on the LDOS profiles in the vortex state. We 