Resonant Edelstein and inverse-Edelstein effects, charge-to-spin conversion, and spin pumping from chiral-spin modes

This paper investigates how electron correlations induce resonant enhancements in the Edelstein and inverse-Edelstein effects via in-plane chiral-spin modes in two-dimensional electron systems, demonstrating their potential for resonant charge-to-spin conversion and directional spin control in spintronics applications.

The Gist

Imagine you have a crowded dance floor (the electrons in a material). Usually, if you want to make the dancers spin, you need to push them with a giant magnet (a magnetic field). But in certain special materials, there's a hidden rule: if you push the dancers with an electric wind (an electric current), they naturally start spinning. This is called the Edelstein effect. Conversely, if you make the dancers spin in a coordinated way, they can generate an electric wind (the Inverse Edelstein effect).

This paper is like a detailed manual on how to make these effects work perfectly and loudly by finding the "sweet spot" frequency, much like pushing a child on a swing at just the right moment to make them go higher.

Here is the breakdown of the paper's discoveries using simple analogies:

1. The Hidden Dance: Chiral-Spin Modes

In these special materials, the electrons don't just spin randomly; they form a synchronized wave, like a stadium "wave" or a ripple in a pond. The authors call these Chiral-Spin Modes (CSMs).

• The Analogy: Imagine a line of people holding hands. If you push the first person, a ripple travels down the line. In these materials, the "ripple" is a wave of spinning electrons.
• The Discovery: The paper shows that if you hit the material with an electric or magnetic field at the exact frequency of this ripple, the effect goes into overdrive. It's like pushing a swing at its natural rhythm; the swing goes huge. This is called resonance.

2. The Two Types of Pushes (Electric vs. Magnetic)

The researchers tested two ways to drive this dance:

• The Electric Push (Edelstein Effect): You send an electric current. The electrons spin up.
• The Magnetic Push (Inverse Edelstein Effect): You wiggle a magnetic field. The electrons spin, and this spinning creates an electric current.

The Big Surprise:
Usually, it's much harder to make electrons move using a magnetic field than an electric field. It's like trying to push a car with a feather (magnetic) versus a strong wind (electric).

• The Paper's Finding: Even though the magnetic push is weak, when you hit the "resonance frequency" (the swing's sweet spot), the magnetic push becomes surprisingly effective. However, the electric push is still the "heavy lifter." The electric push creates a massive background noise (like a loud engine rumble) that hides the special resonance. The magnetic push, however, is quiet and clean, making the resonance very easy to spot and measure.

3. The "Split Personality" of the Dance (Electron Interactions)

The paper also looked at what happens when the electrons start talking to each other (electron-electron interaction).

• The Analogy: Imagine the dancers are on a trampoline. If they are alone, they bounce in one rhythm. But if they are all bouncing together and pushing against each other, the trampoline gets complicated.
• The Finding: In materials with two types of electron "valleys" (like a double-layered trampoline), the interaction splits the single dance rhythm into two distinct rhythms.
  • One rhythm is low-energy (slow and heavy).
  • One rhythm is high-energy (fast and light).
  • Crucial Detail: The "heavy" low-energy rhythm carries most of the energy (spectral weight). It's the main star of the show.

4. Why This Matters for Future Tech (Spintronics)

Spintronics is the next generation of electronics that uses the spin of electrons instead of just their charge to store and process data. It's faster and uses less energy.

• Super Efficient Conversion: The paper shows that by using these resonant ripples, we can convert electricity into spin (and vice versa) with 100 to 1,000 times more efficiency than usual. It's like turning a small key into a massive engine power.
• Steering the Spin: They propose a new way to "pump" spins.
  • Analogy: Imagine you want to send a package (spin) to a specific house. Usually, you just throw it and hope it lands there.
  • The New Method: By using a specific type of light (circularly polarized) or a magnetic field, you can aim the package perfectly. You can control exactly which way the spin points (up, down, left, right). This gives engineers a "remote control" for electron spins.

5. The "Detective Work"

The paper also acts as a guide for scientists to identify what kind of "glue" (Spin-Orbit Coupling) is holding the material together.

• The Analogy: Different types of glue (Rashba vs. Dresselhaus) leave different fingerprints on the dance floor.
• The Finding: By looking at how the electrons respond to electric vs. magnetic fields, scientists can tell exactly which type of glue is present in the material. This helps in designing better materials for future computers.

Summary

This paper is a blueprint for tuning the natural vibrations of electrons in special materials. By hitting the right frequency, we can:

1. Make weak magnetic signals do heavy lifting.
2. Split electron rhythms to control them better.
3. Create super-efficient switches for the next generation of ultra-fast, low-power computers.

It turns a subtle quantum effect into a loud, controllable, and useful tool for the future of technology.

Technical Summary

1. Problem Statement

The paper addresses the dynamical response of systems with broken inversion symmetry and spin-orbit coupling (SOC) to oscillatory electric ($E$) and magnetic ($B$) fields. While the static Edelstein effect (current-induced spin polarization) and inverse-Edelstein effect (spin-polarization-induced current) are well-established, their behavior in the dynamical regime (specifically at terahertz frequencies) involving electron-electron interactions (eei) remains less explored.

Key questions include:

• How do collective excitations known as Chiral-Spin Modes (CSMs) affect the resonant behavior of these effects?
• How do electron correlations modify the resonance frequencies and spectral weights in single-valley (2DEG) versus multi-valley (Dirac) systems?
• Can these resonances be exploited to enhance charge-to-spin conversion efficiency and control spin injection directions for spintronic applications?

2. Methodology

The authors employ a Landau kinetic equation formalism for a Fermi liquid with SOC.

• Systems Studied:
  1. Single-valley 2DEG: Modeled with Rashba or Dresselhaus SOC (typical of semiconductor heterostructures).
  2. Multi-valley Dirac System: Modeled as gated monolayer graphene on a Transition Metal Dichalcogenide (TMD) substrate, featuring both Rashba and Valley-Zeeman (VZ) SOC.
• Theoretical Framework:
  • The non-equilibrium distribution function $\hat{n}(k,t)$ is expanded in terms of Pauli matrices (spin) and valley matrices.
  • The kinetic equation is linearized with respect to weak oscillatory $E$ and $B$ fields and weak SOC.
  • Electron-Electron Interactions: Included via the Landau functional $\hat{F}(k, k')$, which renormalizes resonance frequencies and splits modes in multi-valley systems.
  • Relaxation: Treated phenomenologically in the ballistic regime ($\lambda_{SOC}\tau \gg 1$) to model resonance broadening without introducing complex scattering mechanisms.
• Observables: The authors calculate the induced electric current density ($J$) and magnetization ($M$) to derive:
  • Direct responses: Conductivity ($\sigma$) and Spin Susceptibility ($\chi^s$).
  • Cross-responses: Edelstein conductivity ($\sigma_{ME}$) and Inverse-Edelstein susceptibility ($\chi_{JB}$).

3. Key Contributions and Results

A. Resonant Edelstein and Inverse-Edelstein Effects

• Resonance Mechanism: Both effects exhibit sharp resonances at the frequencies of Chiral-Spin Modes (CSMs). These are collective oscillations of spin polarization occurring even in the absence of a static magnetic field.
• In-Plane vs. Out-of-Plane: The authors demonstrate that only in-plane spin oscillations contribute to the resonant cross-responses. Out-of-plane modes do not couple to the cross-response tensors in the same way.
• Driving Fields:
  • Electric-Field Driving: Induces the resonant Edelstein effect (magnetization $M \propto E$). The response is orders of magnitude stronger than magnetic driving due to the larger coupling of $E$-fields to charge.
  • Magnetic-Field Driving: Induces the resonant inverse-Edelstein effect (current $J \propto B$).
• Tensor Structure: The cross-response tensors ($\sigma_{ME}$ and $\chi_{JB}$) have distinct anisotropic structures for Rashba vs. Dresselhaus SOC. This allows for the unambiguous identification of the dominant SOC type in a material, unlike direct responses (conductivity/susceptibility) which are often isotropic or diagonal.

B. Impact of Electron-Electron Interactions (eei)

• Single-Valley Systems: eei renormalizes the resonance frequency (shifting it) and reduces the amplitude but does not split the mode.
• Multi-Valley Systems (Dirac): eei couples the spin-chiral and spin-valley degrees of freedom. This causes the in-plane CSMs to split into two distinct modes ($\Omega_+$ and $\Omega_-$).
  • Spectral Weight Distribution: The spectral weight is distributed unevenly between the two split modes. The lower-energy mode carries the majority of the spectral weight in cross-responses ($\sigma_{ME}, \chi_{JB}$), whereas the direct conductivity ($\sigma$) shows a more balanced distribution depending on interaction parameters.
• Line Shapes: The paper analyzes how damping affects the line shapes, noting that while direct response peaks broaden and lower with damping, the amplitude of the resonant Edelstein conductivity ($\sigma_{ME}$) can actually increase with damping in certain regimes due to normalization effects.

C. Charge-to-Spin Conversion (C2S)

• The authors define a dynamic figure-of-merit for C2S conversion: $\eta_{C2S}(\Omega) \propto |\sigma_{ME}(\Omega) / \sigma(\Omega)|$.
• Resonant Enhancement: Near the CSM resonance, $\eta_{C2S}$ is enhanced by 2 to 3 orders of magnitude compared to the DC limit.
• Significance: This enhancement occurs even at high carrier densities (large chemical potential $\mu$), a regime where DC conversion efficiency is typically suppressed. This suggests a pathway for efficient spintronic devices operating at THz frequencies.

D. Spin Pumping Protocols

The paper proposes a protocol for ultrafast spin pumping using CSMs in graphene/TMD heterostructures:

1. Circularly Polarized Light: Induces out-of-plane spin precession, pumping spins into an adjacent SOC-free region.
2. Linearly Polarized Light + Static $B$-field: Allows for directional control of the injected spins. The static field determines the precession axis, enabling the injection of spins with specific in-plane polarization.

4. Experimental Implications

• Detection: The resonant inverse-Edelstein effect (current induced by $B$-field) is best observed using grazing incidence of an electromagnetic wave. This geometry eliminates the Drude background current (induced by the $E$-field), allowing the much weaker magnetic-driven resonance to be resolved.
• Material Systems: The effects are predicted to be observable in:
  • Semiconductor 2DEGs (GaAs, InGaAs).
  • Graphene on TMD substrates (e.g., WS$_2$, WSe$_2$), where proximity-induced SOC creates the necessary conditions.
• Frequency Range: Resonances occur in the Terahertz (THz) range, making them relevant for THz spectroscopy and ultrafast spintronics.

5. Significance

This work bridges the gap between collective mode theory and practical spintronic applications.

1. Fundamental Physics: It clarifies the role of electron correlations in splitting and weighting chiral-spin modes in multi-valley systems.
2. Diagnostic Tool: The unique tensor structure of the cross-response provides a robust method to distinguish between Rashba and Dresselhaus SOC types experimentally.
3. Technological Impact: It proposes a mechanism to drastically enhance charge-to-spin conversion efficiency at THz frequencies, overcoming the limitations of DC devices. Furthermore, it offers a method for all-electric, ultrafast spin pumping with tunable polarization direction, a critical capability for next-generation spin-based logic and memory devices.

In summary, the paper establishes that chiral-spin modes act as a resonant amplifier for spin-charge conversion, and that electron-electron interactions are crucial for tailoring these resonances in multi-valley materials, opening new avenues for THz spintronics.