Onsager relations in a two-dimensional electron gas with spin-orbit coupling.

Area of Science:

• Condensed Matter Physics
• Spintronics
• Quantum Mechanics

Background:

• Theoretical predictions for a two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction suggest a vanishing spin Hall conductivity (SHC) alongside a finite inverse spin Hall effect (ISHE).
• This apparent contradiction challenges conventional understanding of spin transport phenomena.

Purpose of the Study:

• To reconcile the seemingly contradictory theoretical predictions of vanishing SHC and finite ISHE in a 2DEG with Rashba spin-orbit interaction.
• To demonstrate the compatibility of these results with the Onsager relations.
• To clarify the conditions under which a vanishing bulk SHC does not imply a vanishing spin Hall effect.

Main Methods:

• Theoretical analysis based on the Onsager relations.
• Examination of spin and particle (charge) currents in a 2DEG.
• Consideration of experimental setup dependencies.
• Inclusion of extrinsic spin-orbit interaction from impurities.

Main Results:

• The Onsager relations are shown to hold for spin and charge currents in the 2DEG, even with a vanishing bulk SHC.
• The form of the Onsager relations is dependent on the specific experimental setup.
• A vanishing bulk SHC does not necessarily preclude a finite spin Hall effect.
• Extrinsic spin-orbit interaction from impurities can lead to a non-zero bulk SHC.

Conclusions:

• The apparent contradiction between vanishing SHC and finite ISHE is resolved through a nuanced application of the Onsager relations.
• The findings highlight the importance of experimental configurations in interpreting spin transport phenomena.
• The study provides a theoretical framework for understanding spin Hall effects in systems with varying spin-orbit interactions.