$\varepsilon\ll\Delta_0$ the quasiclassical expression for the LDOS near the vortex center reads: $$\label{LDOSDisc0}
  N(r,\varepsilon)=\frac{k_F}{2\pi\xi}\sum_{j=1,2}\int_0^{2\pi}\delta
  (\varepsilon-\varepsilon_{j})d\theta_p\,.$$ The Eq.(\[LDOSDisc0\]) can be derived from the general expression for LDOS (\[DOS\]) by setting the amplitude of the wave function $|\tilde
U_n|^2={\rm const}$ which is a good approximation at the small distances $r\ll\xi$ from the vortex center. Evaluating this expression for the LDOS we obtain: $$\begin{aligned}
\label{LDOSDisc}
  N(r,\varepsilon=0)=N_0\frac{\xi}{\sqrt{r^2-r_0^2}}\,,
  \quad {\rm for}\ \ r>r_0\,,
  \nonumber\\
  N(r,\varepsilon=0)=0\,, \quad {\rm for}\ \  r<r_0\,,\end{aligned}$$ where $$r_0=\frac{\delta|\cos(2k_F R)|}{\omega k_F}
  \sim\xi|\cos(2k_F R)|e^{-2R/\xi}\,.$$ Thus, the zero-bias peak of the LDOS at the vortex center which exists in an isolated vortex transforms into a ring structure which is similar to the LDOS pattern for a doubly quantized vortex. The only difference is that the radius of this ring is exponentially small comparing to the one in a doubly quantized vortex: $r_0/\xi\propto\exp(-R/\xi)\ll1$. Therefore, this splitting of the LDOS peak in tunneling spectroscopy experiments should be strongly affected by different smearing effects like disorder scattering or finite temperature. In particular, for the observation of the above effect we should assume the elastic mean free path to exceed the characteristic size of the LDOS ring: $l\geq\xi\exp(-R/\xi)$. Note that this condition is not very restrictive because it 