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Quasi-one-dimensional (Q1D) Cr-based pnictide K$_2$Cr$_3$As$_3$ has arousedgreat research interest due to its possible triplet superconducting pairingsymmetry. Recent experiments have shown that incorporating hydrogen atoms intoK$_2$Cr$_3$As$_3$ would significantly change its electronic and magneticproperties. Hence, it's necessary to investigate the impact of hydrogen dopingin superconducting pairing symmetry of this material. Employing the hydrogen asan non-trivial electron-doping, our calculates show that, different from the$p_z$-wave obtained without hydrogen, the system exhibits $p_x\pm ip_y$ pairingsuperconductivity under specific hydrogen doping. Specifically, we adopt therandom-phase-approximation approach based on a six-band tight-binding modelequipped with multi-orbital Hubbard interactions to study the hydrogen-dopingdependence of the pairing symmetry and superconducting $T_c$. Under therigid-band approximation, our pairing phase diagram shows the spin-tripletpairing states is dominated through out the hydrogen-doping regime $x\in(0,0.7)$. Particularly, the $T_c\sim x$ curve shows a peak at the 3D-quasi-1DLifshitz transition point, and the pairing symmetry around this doping level is$p_x\pm ip_y$. The physical origin of this pairing symmetry is that the densityof states is mainly concentrated at $k_x(k_y)$ with large momentum. Due to thethree-dimensional character of the real material, this $p_x\pm ip_y$-wavesuperconducting state possesses point gap nodes. We further provide experimentprediction to identify this triplet $p_x\pm ip_y$-wave superconductivity.

Hydrogen Doping Induced $p_x\pm ip_y$ Triplet Superconductivity in Quasi-One-Dimensional K$_2$Cr$_3$As$_3$