Fermi velocity, and $\mu$ is half an odd integer. Note that hereafter we assume the Fermi surface to be a cylinder and neglect the dependence of the quasiparticle energy on the momentum component along the vortex axis $z$ considering a motion of quasiparticles only in $xy$ plane. Introducing a cylindrical coordinate system $(r,\theta,z)$ and defining an impact parameter as $b=-\mu/k_F=[{\bf r},{\bf k}_F]\cdot{\bf z}_0/k_F$ the quasiclassical LDOS inside the isolated vortex core ($r\ll\xi$) can be found as follows: $N=(k_F/2\pi\xi)\int_0^{2\pi}\delta(\varepsilon-\omega
k_Fr\sin(\theta-\theta_p))d\theta_p$. Here we evaluate the LDOS summing up over the quasiparticle states at the trajectories characterized by the orientation angle $\theta_p$. This expression yields a singularity of zero energy LDOS at the vortex center[@Ullah; @Maki; @IchiokaStar]: $N=1/(2\pi\omega r\xi)\approx N_0 \xi/r$, where $N_0=(1/2\pi)m/\hbar^2$ is a normal metal LDOS. Smearing of energy levels due to scattering effects leads to a reduction of LDOS peak amplitude at the vortex center. However, the peak in the LDOS distribution survives even in “dirty” limit when a mean free path is smaller than a coherence length $l<\xi$ (see Refs. ).

The increase in the external magnetic field results in the decrease in the intervortex distance which should be accompanied by the overlapping of wave functions describing the quasiparticle 