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

TL;DR

Non-Hermitian rings with anti-Hermitian hopping are studied to understand charge and spin transport under Zeeman fields and quasiperiodic onsite modulation. The approach introduces a synthetic flux $\phi' = \frac{2\pi}{L}\tan^{-1}(\eta/t_0)$ from NH hopping, analyzes the real and imaginary energy sectors, and computes spin-resolved currents via $I_{\sigma}^{r/i}=-c\frac{\partial E_{0,\sigma}^{r/i}}{\partial \phi}$; in the clean limit, AFM yields finite real charge current while spin current vanishes, whereas NM/FM yield only imaginary currents. Introducing Aubry-André-Harper quasiperiodicity with strength $\lambda$ strongly enhances both charge and spin currents and produces nonmonotonic, re-entrant transport behavior as a function of $h_z$ and $\lambda$, with currents reaching large magnitudes. The work demonstrates that non-Hermitian topology and controlled symmetry breaking provide a versatile platform for tunable spin-charge transport via synthetic flux and quasiperiodic engineering.

Abstract

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.

Figures (10)

• Figure 1: Schematic illustration of an anti-Hermitian spinful quantum ring. The arrows attached to individual lattice sites represent the local spins. $t_R$ and $t_L$ denotes the directional hopping processes between the nearest neighbour sites.
• Figure 2: Real $(I_{\mathrm{real}})$ and imaginary $(I_{\mathrm{imag}})$ components of the current as functions of the flux $\phi$. Panels (a) and (d) correspond to the case without a Zeeman field. Panels (b) and (e) show the results in the presence of a Zeeman field $h_z = 1.0$ for a ferromagnetic configuration, while panels (c) and (f) correspond to $h_z = 1.0$ with an antiferromagnetic configuration. The solid blue and red curves represent the spin-up ($I_\uparrow$) and spin-down ($I_\downarrow$) currents, respectively.
• Figure 3: Flux dependence of the real $(I_{\mathrm{real}})$ and imaginary $(I_{\mathrm{imag}})$ components of the current for different Zeeman-field configurations. Panels (a) and (d) show the response in the absence of a Zeeman field. Panels (b) and (e) correspond to a uniform (ferromagnetic) Zeeman field with strength $h_z = 1.0$, while panels (c) and (f) display the results for a staggered (antiferromagnetic) Zeeman field of the same strength. The charge ($I_c$) and spin ($I_s$) currents are indicated by the blue and red solid lines, respectively.
• Figure 4: (a) Real and (b) imaginary parts of the current as a function of the field strength $h_z$ for $\lambda=1$. The red and blue curves correspond to the charge and spin currents, $I_c$ and $I_s$, respectively.
• Figure 5: (a) Real and (b) imaginary components of the current versus disorder strength $\lambda$ for $h_z = 0.37$. The red and blue curves correspond to the charge ($I_c$) and spin current ($I_s$), respectively.