Hidden symmetry and enhanced Rudermann-Kittel-Kasuya-Yosida interaction in P-N junctions of two-dimensional materials*

Correlation between magnetic atoms (spins) in non-magnetic two-dimensional (2D) systems and materials is one of the central issues in condensed matter physics. Engineering this correlation relies heavily on the carrier-mediated Rudermann-Kittel- Kasuya-Yosida (RKKY) interaction. However, tailoring and direct detection of spin-spin correlation has been limited to spins separated by a few nanometers due to the rapid $1/R^2$ decay of RKKY interaction with inter-spin distance R. Here we reveal a hidden symmetry -- absent from the Hamiltonian -- in planar P-N junctions, which could qualitatively change the spatial scaling of various response functions in a wide range of 2D systems and materials. In particular, it allows RKKY interaction to attain $1/R$ decay, the slowest decay in extended systems. This dramatically enhances RKKY interaction and enables long-range correlation between distant spins, with applications in nanoscale magnetism, spintronics, and solid-state quantum computation.