Ubiquitous V-shape density of states in mixed state of clean limit type II superconductors; STM experiment and theory

It is demonstrated theoretically and experimentally that the low energy density of states $N(E)$ is described by a singular V-shape form $N(E)=N_0(H)+\alpha |E|+O(E^2)$ for all clean superconductors in a vortex state, irrespective of the underlying gap structure. The linear term $\alpha |E|$ which has been not recognized so far is obtained by exactly evaluating the vortex contribution. Based on microscopic Eilenberger theory $N(E)$ is evaluated for isotropic gap, line and point node gaps to yield a V-shape $N(E)$. STS-STM experiments on NbSe$_2$ and YNi$_2$B$_2$C give direct evidence for this. We provide arguments on significance of this finding and on relevance to other experiments.