  By using low-temperature scanning tunneling microscopy and spectroscopy
(STM/STS), we observe in-gap states induced by Andreev tunneling through a
single impurity state in a low carrier density superconductor (NaAlSi). The
energy-symmetric in-gap states appear when the impurity state is located within
the superconducting gap. In-gap states can cross the Fermi level, and they show
X-shaped spatial variation. We interpret the in-gap states as a consequence of
the Andreev tunneling through the impurity state, which involves the formation
or breakup of a Cooper pair. Due to the low carrier density in NaAlSi, the
in-gap state is tunable by controlling the STM tip-sample distance. Under
strong external magnetic fields, the impurity state shows Zeeman splitting when
it is located near the Fermi level. Our findings not only demonstrate the
Andreev tunneling involving single electronic state, but also provide new
insights for understanding the spatially-dependent in-gap states in low carrier
density superconductors.
