Emergence of charge and spin current in non-Hermitian quantum ring

We investigate the charge and spin transport in a non-Hermitian ring of electrons subject to an external Zeeman field. By introducing non-Hermiticity through anti-Hermitian hopping in the nearest neighbour bonds, we demonstrate that anti-Hermiticity, along with the applied Zeeman field significantly modify the energy spectrum and strongly influence transport properties. As a result, we obtain that when antiferromagnetic Zeeman field is considered, a finite charge current emerges in both the real and imaginary parts of the current, which are in contrast to the ferromagnetic case where only the imaginary current exist. On the other hand, in both cases, the spin current vanishes. Interestingly, we reveal an emergence and strong enhancement of spin currents under balanced spin population upon introducing quasiperiodicity in the presence of antiferromagnetic ordering. At the same time, the charge current also exhibits substantial enhancement due to quasiperiodic modulation. These results highlight non-Hermitian quantum rings as versatile platforms for unconventional spin-charge transport.

💡 Research Summary

In this work the authors investigate charge and spin transport in a one‑dimensional ring of spin‑½ fermions whose nearest‑neighbour hopping is made anti‑Hermitian (tL = −tR*). This choice renders the Hamiltonian non‑Hermitian but introduces a complex phase ϕ = tan⁻¹(η/t0) that acts as an effective magnetic flux threading the ring without any external gauge field. The system is subjected to a Zeeman field h_z that can be configured either uniformly (ferromagnetic, FM) or staggered alternately on even and odd sites (antiferromagnetic, AF). The authors compute the ground‑state energy as a function of the synthetic flux and define spin‑resolved currents Iσ = −c ∂E0,σ/∂ϕ; the total charge current is Ic = I↑ + I↓ and the spin current Is = I↑ − I↓. Because the spectrum is complex, the real and imaginary parts of the energy give rise to distinct “real” and “imaginary” components of the currents, which are evaluated separately.

In the clean limit (no on‑site potential) the spectrum is purely imaginary when h_z = 0, so the real part of the current vanishes while a saw‑tooth‑like imaginary current appears for both spin species. Adding a uniform FM Zeeman field merely shifts the two spin bands by ±h_z; this shift does not depend on the flux and therefore does not generate a real current. Consequently, for FM ordering the current remains purely imaginary and the spin current is zero.

The situation changes dramatically for the staggered AF Zeeman field. The AF field couples the two sublattices and modifies the Bloch Hamiltonian such that the eigenvalues can be either real or imaginary depending on momentum, flux, and the relative strength of h_z and the anti‑Hermitian hopping t. When |h_z| ≥ 2|t| the spectrum contains real bands, leading to a finite real charge current while the imaginary component is suppressed. When |h_z| < 2|t| the spectrum is purely imaginary and the current is again imaginary but with a much larger amplitude than in the FM case. In both regimes the spin‑up and spin‑down contributions are equal in magnitude, so the net spin current vanishes, but a finite charge current exists only for the AF configuration.

To explore the effect of disorder the authors introduce a quasiperiodic on‑site modulation ε_j = λ cos(2πβj) with β = (√5 − 1)/2. This quasiperiodicity breaks the symmetry between the two spin channels in the AF case. As a result, the spin‑resolved currents become unequal, giving rise to a non‑zero spin current while the charge current is simultaneously enhanced. Both currents show strong dependence on the synthetic flux and increase markedly with the modulation amplitude λ, indicating that the quasiperiodic potential amplifies the transport response induced by the non‑Hermitian hopping.

The paper thus demonstrates three key findings: (i) anti‑Hermitian hopping creates an effective flux that can drive currents even in the absence of a real magnetic field; (ii) a staggered Zeeman field enables real charge currents and, depending on its strength, can switch the system between purely real and purely imaginary transport regimes, while the spin current remains zero; (iii) adding quasiperiodic modulation lifts the spin‑symmetry in the AF case, generating a finite spin current and strongly enhancing both charge and spin currents. These results position non‑Hermitian quantum rings as versatile platforms for engineering unconventional spin‑charge transport, with potential applications in spintronics, non‑reciprocal devices, and topological current control.