  The charge loop current (cLC) state has attracted increasing attention in
kagome metals. Here, we calculate the spontaneous currents along the nearest
sites $i$ and $j$, $J_{i,j}$, induced by the cLC order that is the imaginary
and odd-parity hopping integral modulation $\delta t_{i,j}$. We reveal that the
magnitude of $J_{i,j}$ strongly depends on the nearest sites $i$ and $j$ in the
$2\times2$ cLC state, where $\eta\equiv |\delta t_{i,j}|$ is equivalent for all
nearest sites. The obtained $J_{i,j}$ becomes large near the van-Hove
singularity (vHS) filling ($n\sim n_{vHS}$) even when $\eta$ is fixed.
Interestingly, the obtained $J_{i,j}$ exhibits the logarithmic divergence
behavior at low temperatures for $n\sim n_{vHS}$ with a fixed $\eta$, by
reflecting the vHS points that are the characteristic of kagome metals. The
present study provides useful information for local electronic state
measurements, such as the site-selective NMR and STM experiments.
