Chiral induced Spin Polarized Electron Current: Origin of the Chiral Induced Spin Selectivity Effect

This paper theoretically demonstrates that the Chiral Induced Spin Selectivity effect arises from the coordinated necessity of molecular chirality to break spin degeneracy and the presence of dissipation to generate non-vanishing spin polarization.

The Gist

The Big Idea: The "Handed" Electron Filter

Imagine you are walking through a crowded hallway. Usually, people (electrons) walk through in all directions, and half of them are wearing red hats (spin up) while the other half wear blue hats (spin down). It's a balanced mix.

Now, imagine the hallway is shaped like a spiral staircase (a chiral structure). The paper argues that when electrons try to run through this spiral staircase, something magical happens: they start sorting themselves out. Suddenly, almost everyone wearing a red hat makes it to the other side, while the blue hats get stuck or turn around.

This phenomenon is called the Chiral Induced Spin Selectivity (CISS) effect. It's like a bouncer at a club who only lets in people with a specific hat color, but the bouncer is the shape of the building itself, not a person.

The Mystery: Why Does This Happen?

Scientists have known this happens for a while, but they didn't know why. Some thought it was just the shape of the molecule. Others thought it was magnetic fields.

This paper by Jonas Fransson solves the puzzle. He says you need two specific ingredients to make this "hat-sorting" happen. If you miss even one, the effect disappears.

Ingredient 1: The Spiral Shape (Chirality)

First, the molecule must be "chiral." In everyday terms, this means it has a "handedness," like your left and right hands. They look similar but are mirror images and cannot be stacked perfectly on top of each other.

• The Analogy: Think of a corkscrew. A straight wire (achiral) lets electrons pass through without caring about their hat color. But a corkscrew (chiral) twists the path. This twist interacts with the electron's "spin" (its internal magnetic direction) and breaks the balance between red and blue hats.
• The Catch: Just having a corkscrew shape isn't enough. If the corkscrew is perfectly still and isolated, the electrons still don't sort themselves out completely.

Ingredient 2: The "Leaky" System (Dissipation)

This is the most surprising part of the paper. To get the sorting effect, the system must be leaky. It must lose energy to its surroundings.

• The Analogy: Imagine a spinning top. If you spin a top on a perfectly frictionless, magical table, it spins forever. It never settles. But if you spin it on a real wooden table, friction (dissipation) slows it down, and it eventually wobbles and falls.
• The Science: The paper argues that electrons flowing through a chiral molecule need to "lose" some energy (dissipate) to the environment (like heat or vibrations) to lock into their sorted state. Without this energy loss, the electrons are too chaotic to organize themselves into a specific spin direction.

The Conclusion: You need the Spiral Shape to create the possibility of sorting, and you need Energy Loss (Friction) to actually make it happen.

How the Author Proved It

The author didn't just guess; he built a mathematical model (a simulation) to test this.

1. The Test: He created a virtual molecule made of 16 atoms.
   • Scenario A: A flat, zig-zag chain (no spiral).
   • Scenario B: A chain with one twist (a weak spiral).
   • Scenario C: A perfect helix (a strong spiral).
2. The Result:
   • In the flat chain, the electrons remained a 50/50 mix of red and blue hats. No sorting occurred.
   • In the spiral chains, the electrons sorted themselves. The stronger the spiral, the better the sorting.
3. The "Leak" Test: He also checked what happened if the molecule was perfectly isolated (no energy loss). The sorting vanished! This proved that dissipation is essential. The molecule needs to "talk" to its environment (vibrating, heating up) to create the spin filter.

Why Should We Care?

This isn't just about abstract physics; it explains how life works.

• Breathing: Our bodies use oxygen to make energy. Oxygen is a "triplet" (it has a specific spin). Our biological molecules are chiral (like DNA and proteins). This paper suggests that our cells might use this "spin filter" effect to make breathing more efficient, ensuring the right electrons get to the right place.
• New Technology: If we can build tiny electronic devices using chiral molecules, we could create "spintronic" computers. These would use the spin of electrons (like red/blue hats) instead of just their charge to store and process data. This could lead to faster, cooler, and more efficient electronics.

Summary in One Sentence

To turn a chiral molecule into a filter that sorts electrons by their spin, you need two things: the molecule must be twisted (chiral) to create the rules, and it must lose energy (dissipate) to the environment to actually enforce those rules.

Technical Summary

1. Problem Statement

The Chiral Induced Spin Selectivity (CISS) effect is a well-established phenomenon where electrons flowing through chiral materials become spin-polarized. Despite its experimental confirmation and implications for biological electrochemistry (e.g., respiration) and spintronics, the fundamental theoretical origin of the effect remains debated.

• The Gap: Previous theoretical approaches, including independent particle descriptions and standard Density Functional Theory (DFT), have failed to fully account for the effect. These models often neglect electron correlations and dissipative processes (losses), which are crucial for breaking symmetries required to generate spin polarization.
• The Question: What are the necessary physical conditions for a charge current flowing through a chiral molecule to become spin-polarized without external magnetic fields?

2. Methodology

The author employs a non-equilibrium Green's function (NEGF) formalism combined with a many-body approach to model electron transport through chiral and achiral molecular chains.

• Model System:
  • A molecular chain ($M$ sites) coupled to metallic leads (Left and Right) and a thermal reservoir.
  • The Hamiltonian includes free electrons in leads, a vibrating molecule, and a thermal bath of harmonic oscillators (phonons).
  • Spin-Orbit Coupling (SOC): Implemented via a curvature vector $\mathbf{v}^{(s)}_m$ derived from the non-coplanar arrangement of nuclei. The SOC term is written as $\mathbf{v} \cdot \boldsymbol{\sigma}$.
• Theoretical Framework:
  • The electronic structure is calculated using the single-electron Green's function $G$, expressed via the Dyson equation: $G = G_0 + G_0 \Sigma G$.
  • Self-Energy ($\Sigma$): Includes contributions from lead coupling (level broadening) and electron-phonon interactions (dissipation). The imaginary part of the self-energy represents dissipative processes.
  • Symmetry Analysis: The paper rigorously analyzes the breaking of two specific symmetries:
    1. Spin-degeneracy: Broken by chirality coupled with SOC.
    2. Time-reversal symmetry: Broken by dissipative processes (inelastic scattering/losses).
• Comparative Cases: The model is applied to:
  • Achiral structures: Planar zig-zag chains.
  • Minimally chiral structures: Chains with one non-coplanar site.
  • Helical structures: Fully helical chains.
  • Alternative Dissipation: A comparison is made between vibrational dissipation and on-site Coulomb repulsion (electron-electron correlations).

3. Key Contributions

The paper establishes two fundamental conditions required for the CISS effect to arise, arguing that both must be satisfied simultaneously:

1. Chirality is necessary to break Spin-Degeneracy:

   • In a centrally symmetric system, SOC vanishes.
   • For non-coplanar (chiral) nuclei distributions, the effective SOC vector acquires a longitudinal component ($v_z$). This introduces a "mass term" ($v_z \sigma_z$) in the spectrum, splitting the energy levels of spin-up and spin-down states (breaking spin-degeneracy).
   • Crucial distinction: Breaking spin-degeneracy alone (as seen in chiral molecules in isolation) does not result in a net spin-polarized current; it only creates a spin-texture.

2. Dissipation is necessary to break Time-Reversal Symmetry:

   • The paper demonstrates that a non-vanishing spin-polarization requires the breaking of time-reversal symmetry.
   • In the Green's function formalism, this breaking is linked to the imaginary part of the self-energy ($\Sigma^r - \Sigma^a$), which corresponds to dissipative processes (energy loss to the environment).
   • Without dissipation (e.g., in a closed, conservative system), the system remains time-reversal symmetric, and no net spin-polarization develops, even if the molecule is chiral.

Conclusion: The CISS effect emerges from the interplay between structural chirality (breaking spin-degeneracy) and environmental dissipation (breaking time-reversal symmetry).

4. Results

Numerical simulations based on the proposed model yield the following results:

• Equilibrium Spin Distributions:
  • Achiral Molecules: Show equal charge distributions for spin-up and spin-down ($n_\uparrow = n_\downarrow$), resulting in zero longitudinal spin polarization. However, they exhibit a non-trivial transverse spin texture due to SOC.
  • Chiral Molecules: Show broken spin-degeneracy. When coupled to a thermal reservoir (dissipation), they develop a non-vanishing longitudinal spin polarization ($n_\uparrow \neq n_\downarrow$).
  • Enantiomeric Specificity: The two enantiomers (L and D) exhibit opposite spin polarizations.
• Role of Dissipation:
  • The magnitude of the induced spin moment is inversely proportional to the vibrational lifetime ($\tau_{ph}$). As dissipation decreases (longer lifetime), the spin polarization vanishes. This confirms that losses are indispensable for the effect.
• Transport Properties:
  • Current Polarization: Under a voltage bias, chiral structures conduct a spin-polarized current, whereas achiral structures do not.
  • Enantiomeric Asymmetry: When an externally spin-polarized current is injected, the charge current differs between L and D enantiomers. This asymmetry is the hallmark of the CISS effect in transport measurements.
  • Helical vs. Minimally Chiral: Helical structures show stronger spin polarization and enantiomeric asymmetry due to phase accumulation from repeated curvature, but the effect exists even in minimally chiral structures.
• Robustness: The results hold true whether dissipation is modeled via phonons (vibrations) or electron-electron Coulomb repulsion, indicating the mechanism is general to any spin-dependent loss channel.

5. Significance

• Theoretical Resolution: The paper resolves the long-standing debate on the origin of CISS by identifying that previous models failed because they treated systems as conservative (closed) or ignored correlations. It proves that dissipation is not a nuisance but a fundamental requirement for the effect.
• Biological Implications: It provides a theoretical basis for understanding spin-selective electron transfer in biological systems (e.g., respiration), suggesting that the "lossy" nature of biological environments is essential for spin filtering.
• Device Applications: The findings suggest that chiral molecules can act as intrinsic spin-polarizers without external magnetic fields, provided they are coupled to a dissipative environment. This opens new avenues for designing spintronic devices and non-invasive methods to probe spin currents in living organisms.
• Experimental Validation: The theoretical predictions align with photo-emission and transport experiments, explaining why spin-polarized currents are observed in chiral systems only under specific non-equilibrium conditions.

In summary, Fransson demonstrates that the CISS effect is a non-equilibrium phenomenon driven by the synergy of chirality (structural symmetry breaking) and dissipation (time-reversal symmetry breaking).