We investigated quantum spin pumping in a non-Hermitian triple-quantum-dot (TQD) system governed by a parity-time ($\mathcal{PT}$)-symmetric Hamiltonian. Using the nonequilibrium Green's function (NEGF) formalism, we derived spin current expressions for both adiabatic and nonadiabatic regimes, and performed numerical simulations to study the impact of the non-Hermitian component on the spin current. Our results show that $\mathcal{PT}$-symmetric complex potentials significantly affect spin current behavior. Notably, even weak non-Hermitian strength generates a substantial pure spin current at the Fermi level in the adiabatic regime, where none would occur in a Hermitian system. This arises from the breakdown of wavefunction antisymmetry in the $\mathcal{PT}$-symmetric non-Hermitian system. We also found that the distribution and magnitude of the spin current depend on the parity of $(L+1)/2$, where $L$ is the number of TQD units. Odd values of $(L+1)/2$ show a pronounced spin current peak at the Fermi level, while even values display a dip, revealing an even-odd oscillation. This effect is linked to the wavefunction symmetry in the $\mathcal{PT}$-symmetric Hamiltonian. In the nonadiabatic regime, the spin current shows nonlinear dependence on the magnetic field oscillation frequency, with its magnitude influenced by the non-Hermitian strength. These findings offer valuable insights into spin transport in non-Hermitian systems, with potential applications in nanoelectronics and spintronics.

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• PT-symmetric quantum mechanics
• Quantum transport
• Spin pumping
• Non-Hermitian systems
• Quantum dots
• Nonequilibrium Green's function
• Tight-binding model