Energy-Selective Complete Spin Polarization in an Extended Su-Schrieffer-Heeger Ferromagnetic Chain

TL;DR

Addresses field-free, robust spin filtering in a one-dimensional chain by adopting an extended SSH model with Fibonacci quasiperiodicity and cosine-modulated NN and NNN hopping. Using nonequilibrium Green's function formalism at $T=0$, the authors compute spin-resolved transmissions and the polarization $P_{ ilde{\sigma}}$ as functions of energy and model parameters. They show that suitable tuning yields complete separation of spin channels with $P_{ ilde{\sigma}}=\pm1$ over broad energy windows, and including NNN hopping enhances tunability and robustness. Phase diagrams reveal quantized polarization across extended regions of parameter space, not just fine-tuned points, and the effect persists with increasing system size. These results establish the extended SSH chain as a scalable platform for controllable spin-polarized transport in low-dimensional systems.

Abstract

We study spin-dependent transport in an extended Su-Schrieffer-Heeger chain with cosine modulated nearest- and next-nearest-neighbor hopping using the nonequilibrium Green's function formalism. Suitable tuning of the hopping parameters yields a complete separation of spin channels and perfect spin polarization over broad energy windows. The inclusion of next-nearest-neighbor hopping enhances both tunability and robustness, while systematic phase-diagram analyses reveal quantized polarization across extended regions of parameter space rather than at isolated fine-tuned points. These characteristics persist for larger system sizes, establishing the extended SSH model as a versatile platform for controllable spin-polarized transport.

Figures (6)

• Figure 1: (Color online). The schematic illustrates a long-range Su-Schrieffer-Heeger (SSH) chain symmetrically coupled to source and drain electrodes, with onsite energies modulated according to a Fibonacci sequence. The interplay between quasiperiodicity and long-range hopping provides a versatile platform for spin-polarized transport.
• Figure 2: (Color online). Energy-dependent transmission and spin polarization for two representative NN-hopping configurations. (a) Spin-resolved transmission showing partial overlap of up- and down-spin channels. (b) Complete separation of spin-resolved transmission within the NN-hopping framework. (c) Corresponding spin polarization for (a), exhibiting energy-dependent fluctuations due to channel overlap. (d) Corresponding spin polarization for (b), yielding quantized values $P=\pm1$ due to complete spin-channel separation.
• Figure 3: (Color online). Phase diagrams of the spin polarization $P_\sigma$. (a) Energy–$\delta$ dependence, showing predominantly quantized values $P_\sigma=\pm1$ over most of the parameter space, with only small regions of intermediate polarization. (b) Energy–$\beta$ dependence, again exhibiting near-complete spin polarization over a broad parameter range, with a clear periodic modulation along the $\beta$ axis arising from the cosine-modulated hopping amplitudes.
• Figure 4: (Color online). Energy-dependent transmission and spin polarization for two representative NNN-hopping configurations. (a) Spin-resolved transmission with partial overlap of up- and down-spin channels. (b) Complete separation of spin-resolved transmission within the NNN-hopping framework. (c) Corresponding spin polarization for (a), showing energy-dependent fluctuations due to channel overlap. (d) Corresponding spin polarization for (b), yielding quantized values $P_{\sigma}=\pm1$ as a result of complete spin-channel separation.
• Figure 5: (Color online). Phase diagrams of the spin polarization $P$ in the presence of both NN and NNN hopping. (a),(b) Energy–$\delta$ and energy–$\eta$ dependence, showing predominantly quantized values $P=\pm1$ over most of the parameter space, with only small regions of intermediate polarization. (c),(d) Energy–$g_a$ and energy–$g_b$ dependence, again revealing near-complete spin polarization across broad parameter ranges. (e),(f) Energy–$\beta$ and energy–$\alpha$ dependence of the polarization a clear periodic modulation along the $\beta$ axis is observed due to cosine-modulated hopping, while no such periodicity appears in the $\alpha$ dependence.