The charge-dependent nucleon-nucleon $\left(NN\right)$ interaction plays a crucial role in understanding the nuclear structure and reaction problems. In this work, we explore the charge-dependent $NN$ interaction in covariant chiral effective field theory. By incorporating the isospin-breaking contributions, we derive the charge-dependent covariant chiral $NN$ potential up to next-to-next-to-leading order. The calculated $np$ and $pp$ phase shifts are in satisfactory agreement with the PWA93 partial wave analysis. Our results contribute to a deeper understanding of isospin-breaking effects in nuclear forces and provide a solid foundation for future studies of nuclear structure and reactions within the covariant framework.

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• Effective field theory
• Nuclear forces
• Nucleon-nucleon interactions