  We analyze superconducting correlations in the one-dimensional Kondo lattice
models with Ising anisotropy under transverse magnetic fields, using the
density matrix renormalization group. For the spin-1/2 local spin model, the
Ising anisotropy is introduced by the ferromagnetic Ising interaction between
the local spins, while for the spin-1 model, it is taken by the single-ion
anisotropy. The magnetic properties under the transverse fields for the
spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K.
Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting
correlations, we analyze various Cooper pairs within nearest-neighbor pairs
including composite ones between the local spins and the electrons. We find
that, for the spin-1/2 model, the superconducting correlations are highly
enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase,
where the conduction electrons and the local spins are strongly coupled with a
finite spin gap for the Ising axis. This is a clear contrast to the model under
the longitudinal magnetic fields, where there are no noticeable superconducting
correlations. Competitions between the transverse magnetic field and the Kondo
singlet formation lead to this enhanced superconducting correlations. For the
spin-1 model, the single-ion anisotropy suppresses the superconducting
correlation and there is no noticeable enhancement. We also examine the large
Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction
between the local spins, we find that another type of superconducting
correlation is enhanced inside the ferromagnetic phase. We discuss a possible
relation between our results and reentrant superconductivity in U-based
ferromagnetic superconductors under transverse magnetic fields.
