Persistent Charge and Spin Currents in a Ferromagnetic Hatano-Nelson Ring

We investigate persistent charge and spin currents in a ferromagnetic Hatano-Nelson ring with anti-Hermitian intradimer hopping, where non-reciprocal hopping generates a synthetic magnetic flux and drives a non-Hermitian Aharonov-Bohm effect. The system supports both real and imaginary persistent currents, with ferromagnetic spin splitting enabling all three spin-current components, dictated by the orientation of magnetic moments. The currents are computed using the current operator method within a biorthogonal basis. In parallel, the complex band structure is analyzed to uncover the spectral characteristics. We emphasize how the currents evolve across different topological regimes, and how they are influenced by chemical potential, ferromagnetic ordering, finite size, and disorder. Strikingly, disorder can even amplify spin currents, opening powerful new routes for manipulating spin transport in non-Hermitian systems.

💡 Research Summary

In this work the authors investigate persistent charge and spin currents in a one‑dimensional Hatano‑Nelson (HN) ring that is both non‑Hermitian and ferromagnetically ordered. The lattice consists of N unit cells, each containing two sub‑lattice sites (A and B) with spin‑½ electrons. Non‑reciprocal intradimer hopping is introduced by taking the clockwise amplitude (t_c = t + i\gamma) and the counter‑clockwise amplitude (t_a = -t + i\gamma). Because (t_a \neq t_c^{*}), the hopping is anti‑Hermitian and generates a complex Peierls phase (\phi = \arctan(\gamma/t)). Over the whole ring the accumulated phase (\Phi = N\phi) acts as a synthetic magnetic flux, producing a non‑Hermitian Aharonov‑Bohm effect without any external field.

A uniform ferromagnetic exchange field (h,\boldsymbol{\sigma}) is added on every site, splitting the spin‑up and spin‑down sectors. The tight‑binding Hamiltonian therefore contains three key ingredients: (i) the non‑reciprocal intradimer hopping, (ii) a reciprocal inter‑dimer hopping (t_2) that preserves Hermiticity, and (iii) a Zeeman‑like term that lifts spin degeneracy. In momentum space the four bands read \