Orbital ac spin-Hall effect in the hopping regime.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Spin-orbit interactions, specifically Rashba and Dresselhaus effects, are crucial in spintronics.
• Understanding electron behavior in localized systems coupled to phonons is key for novel electronic devices.

Purpose of the Study:

• To investigate the low-temperature spin-Hall effect arising from Rashba and Dresselhaus spin-orbit interactions.
• To analyze the influence of frequency-dependent electric fields and phonon coupling on spin currents.
• To explore the generation of persistent spin currents at thermal equilibrium.

Main Methods:

• Theoretical analysis of electron hopping paths in the presence of spin-orbit interactions.
• Modeling the effects of frequency-dependent electric fields (E(omega)).
• Incorporating electron-phonon coupling to study temperature-dependent phenomena.

Main Results:

• Both Rashba and Dresselhaus interactions induce a spin-Hall effect for localized electrons coupled to phonons.
• A frequency-dependent electric field generates a spin-polarization current due to hopping path interference.
• At zero temperature, spin-Hall conductivity is real and proportional to omega^2; at nonzero temperatures, an imaginary term proportional to omega appears due to phonon coupling.
• Persistent spin currents are generated at thermal equilibrium (E=0).
• Contributions from Dresselhaus and Rashba interactions to the interference oppose each other.

Conclusions:

• The interplay of spin-orbit interactions, electric fields, and phonons provides a mechanism for generating spin currents.
• The study highlights the potential for controlling spin polarization and currents in materials.
• Opposing contributions from Rashba and Dresselhaus interactions offer tunable spintronic properties.