Trembling motion of electrons driven by Larmor spin precession

We show that the initialization of an ensemble of electrons in the same spin state in strained n-InGaAs subject to a perpendicular magnetic field triggers an AC electric current at GHz frequencies. The AC current emerges in the absence of any driving force and survives until the coherent precession of the electron spins is lost. The current amplitude increases linearly with both the spin-orbit coupling strength and the external magnetic field. The generation mechanism of the observed oscillatory charge motion can be fruitfully described in terms of the periodic trembling motion of spin-polarized electrons, which is a solid-state analog to the Zitterbewegung of free Dirac electrons. Our results demonstrate that the hidden consequence of relativistic quantum mechanics is realized and can be studied in a rather simple solid-state system at moderate temperatures. Furthermore, the large amplitude of the AC current at high magnetic fields enables ultra-fast spin sensitive electric read-out in solids.

💡 Research Summary

The authors investigate a striking phenomenon in strained n‑InGaAs where an ensemble of electrons, all prepared in the same spin orientation, generates a self‑sustained alternating electric current when subjected to an in‑plane magnetic field, even though no external driving electric field is applied. Using picosecond circularly polarized laser pulses, the electron spins are initialized along the +z or –z direction (σ⁺/σ⁻ excitation). The sample is placed in a static magnetic field B‖x, which induces Larmor precession of the spin ensemble at a frequency ωL = |g|μB B/ħ (|g|≈0.62). The resulting current is detected via high‑frequency contacts and a sampling oscilloscope with nanosecond time resolution.

Key experimental observations include: (i) a clear AC current component that persists for several nanoseconds after the photo‑generated electron‑hole plasma has recombined, indicating that the spin angular momentum of the resident electrons is transferred to charge motion; (ii) the current oscillates at the Larmor frequency, matching the spin precession measured simultaneously by time‑resolved Faraday rotation (TRFR); (iii) the amplitude I0 of the AC current grows linearly with the magnitude of B and reverses sign when the magnetic field direction is inverted; (iv) the phase of the current is in phase (φ≈0°) with the out‑of‑plane spin component Sz, whereas a spin‑galvanic effect (SGE) contribution, observed along certain crystal axes, is phase‑shifted by ≈π/2 and does not depend on B.

The authors separate the total current into two contributions: (a) the conventional SGE, proportional to the in‑plane spin component Sy and independent of B, and (b) a newly identified precession‑driven trembling motion (PDTM), proportional to the product ωL × Sz and thus linear in B. The total amplitude follows I0(B)=√