🔬 mesoscale physics

Tunneling amplifies chirality-induced spin selectivity and explains its current-direction invariance

This paper proposes a minimal quantum tunneling model incorporating current-induced magnetic fields to explain how chirality-induced spin selectivity achieves near-100% spin polarization and maintains current-direction invariance while respecting Onsager's reciprocity relations.

Original authors: Fedor Baranov, Virginia Gali, Gal Lemut, Maxim Breitkreiz

Published 2026-06-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Fedor Baranov, Virginia Gali, Gal Lemut, Maxim Breitkreiz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Spin-Selective Tunnel

Imagine you have a very long, narrow tunnel made of a spiral staircase (a chiral molecule). You want to send people (electrons) through it. These people come in two types: "Left-Handers" and "Right-Handers" (representing electron spin).

Usually, in physics, if you send a mix of Left-Handers and Right-Handers through a tunnel, they come out in the same mix. But in these specific spiral molecules, scientists have observed something strange: almost 100% of the people coming out are Left-Handers, even if you sent in a 50/50 mix. This is called Chirality-Induced Spin Selectivity (CISS).

The big mystery has been: How can such a tiny force, which usually does nothing, manage to sort the people so perfectly?

The Problem: The "Tiny Push"

The paper argues that the force causing this sorting is incredibly weak. It's like trying to push a heavy boulder with a gentle breeze. In a normal, open road (a conducting wire), that breeze wouldn't move the boulder at all.

The authors say the secret lies in the fact that these molecules are insulators. This means the tunnel is blocked. The people (electrons) can't walk through; they have to "tunnel" through a wall of energy. In quantum mechanics, tunneling is like a ghost slipping through a brick wall. The chance of slipping through drops off exponentially the thicker the wall is.

The Solution: The "Snowball Effect"

The authors propose a mechanism where this weak breeze becomes a hurricane because of the tunneling nature of the process.

The Current Creates a Magnetic Field: As the electrons flow through the spiral molecule, they create a tiny magnetic field (like a current in a wire).
The Magnetic Field Pushes the Spin: This magnetic field gives a tiny "nudge" to the electrons, slightly favoring one spin direction over the other.
The Tunnel Amplifies the Nudge: Because the electrons are tunneling through a barrier, the "nudge" changes how easily they can slip through.
- The Analogy: Imagine two runners trying to jump over a high fence. One runner gets a tiny, almost invisible push on their back. In a normal race, that push doesn't matter. But if the fence is so high that only the person with the perfect jump height can make it, that tiny push changes the jump height just enough to let one runner through while the other hits the fence.
- Because the tunneling probability changes so drastically with tiny energy shifts, that weak magnetic nudge gets amplified into a massive difference. One spin type flows easily; the other is blocked. This results in 100% spin polarization.

The Mystery of the "Direction"

There is another weird thing about this effect: If you reverse the direction of the current (send the people the other way through the tunnel), the spin preference stays the same. Usually, if you reverse a current, you expect the physics to flip.

The paper explains this with a clever switch:

Going Forward: When current flows one way, the electrons tunnel through the "top" of the energy barrier (near the LUMO). The magnetic field pushes the "Up" spin to go faster.
Going Backward: When you reverse the current, the electrons now tunnel through the "bottom" of the barrier (near the HOMO). The magnetic field flips direction because the current reversed, but because the electrons are now interacting with a different part of the energy landscape, the "Up" spin is still the one that gets the advantage.

It's like a turnstile that always lets people with red hats through, no matter which way they are walking. The mechanism changes to accommodate the direction, but the result (red hats only) remains the same. This solves a major puzzle in physics without breaking the fundamental rules of reciprocity (Onsager relations), because this only happens when the voltage is high enough to be in a "non-linear" state.

The Role of "Friction" (Dissipation)

The authors also explain why this effect is seen in experiments with films of molecules but not in single-molecule experiments.

They introduce the idea of dissipation (friction) at the point where the molecule touches the metal tip.

The Analogy: Imagine a water pipe with a leak. If you turn on the water, the pressure drops before it reaches the end.
In their model, this "leak" (resistance) at the contact point allows the voltage to stay high across the molecule for a wider range of settings. Without this "leak," the perfect spin sorting only happens at one very specific, tiny voltage setting. With the "leak," the perfect sorting happens over a wide range of voltages, making it easy to observe in the lab.

Summary

The paper claims that:

Tunneling is the amplifier: The fact that electrons must tunnel through an insulating barrier makes them extremely sensitive to tiny forces.
Current-induced magnetism is the trigger: The flow of electricity creates a magnetic field that nudges the spins.
The combination creates 100% sorting: The tiny nudge, when applied to a tunneling process, results in a massive separation of spins.
Friction helps: Contact resistance extends the range of voltages where this effect can be seen.
It explains the symmetry: The effect naturally keeps the same spin preference even when the current direction flips, because the electrons switch which part of the energy barrier they are tunneling through.

This model successfully explains how a weak force can create a massive, 100% spin-polarized current in insulating chiral molecules.

Technical Summary: Tunneling Amplifies Chirality-Induced Spin Selectivity

Problem Statement
The paper addresses two fundamental challenges in understanding Chirality-Induced Spin Selectivity (CISS) in dc transport through insulating chiral molecules. First, quantitatively, it is difficult to explain how the weak intrinsic spin-orbit coupling (SOC) in these systems can generate the experimentally observed spin polarizations (SP) reaching ~100%. Second, qualitatively, existing theories struggle to explain the characteristic symmetry of CISS: the invariance of the SP sign upon reversal of the current direction, without violating Onsager's reciprocity relations. Furthermore, many theoretical models assume conducting molecules, whereas experimental setups often involve insulating molecules where transport occurs via quantum tunneling.

Methodology
The authors propose a minimal model based on quantum tunneling through an insulating chiral molecule, treated as a one-dimensional potential barrier. The core mechanism relies on interaction-induced spin splitting rather than intrinsic SOC alone. Specifically, the model incorporates a weak Zeeman interaction arising from a current-induced magnetic field within the helical molecule. This field, which scales with the total current $I$ and the molecular chirality $\chi$ , creates a spin-dependent energy shift (Zeeman splitting) of the molecular orbitals.

The transport is modeled using the Landauer-Büttiker formalism. The transmission probability $T_\sigma(E)$ for a spin $\sigma$ is calculated for a barrier of length $L$ with a spin-dependent height $V_\sigma = V_0 - \sigma \chi \alpha(I)$ . The authors analyze the system in two regimes:

Zero Temperature: Where transport is strictly limited to the energy window defined by the bias voltage.
Finite Temperature: Where thermal broadening allows for over-barrier transport.

Crucially, the model includes a phenomenological, spin-independent resistance $R$ at the tip-molecule interface to account for dissipation. This resistance modifies the effective voltage drop across the molecule ( $V_{mol} = V_b - IR$ ), allowing the authors to explore how dissipation affects the voltage range over which high spin polarization occurs. The authors also demonstrate that a single-particle description is insufficient due to Kramers' degeneracy, necessitating the inclusion of current-induced symmetry breaking.

Key Contributions and Results

Amplification via Tunneling: The paper demonstrates that quantum tunneling acts as a powerful amplifier for weak spin-dependent perturbations. While a Zeeman splitting of $\sim 10^{-4}$ eV (induced by a $\sim 1$ T magnetic field) is too weak to produce significant SP in a conducting regime, it drastically alters the decay length of the wavefunction in the tunneling regime. The transmission probability depends exponentially on the barrier width and height; thus, a small spin-dependent shift in the barrier height leads to a massive difference in transmission probabilities for opposite spins.
Current-Direction Invariance: The model naturally reproduces the observed CISS symmetry where the sign of the SP remains invariant under current reversal. This occurs because the tunneling path switches between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) depending on the bias polarity. Simultaneously, the current-induced magnetic field (and thus the Zeeman splitting) flips sign with the current. These two effects compensate for each other, ensuring that the same spin projection always encounters the lower tunneling barrier, regardless of the voltage polarity.
Role of Dissipation: The authors show that while high SP is theoretically possible only in a very narrow energy range near the barrier edge (where tunneling dominates), the inclusion of a spin-independent resistance at the interface extends this range significantly. The resistor causes a voltage drop that keeps the potential across the molecule close to the barrier height over a wider range of applied bias voltages, allowing for large SP (order of 100%) across a finite voltage window.
Onsager Reciprocity: The paper clarifies that the observed symmetry does not violate Onsager's reciprocity relations. These relations apply strictly to the linear response regime (zero bias). In this model, the large SP arises in the non-linear response regime at finite bias, where the current-induced magnetic field is non-zero. At zero bias, the induced field vanishes, and the conductance remains spin-independent, satisfying reciprocity.
Scaling Laws: Numerical results confirm that the spin polarization scales with the product of the molecular length $L$ and the square root of the Zeeman splitting strength. This explains why SP increases with molecular length, as observed in experiments.

Significance and Claims
The paper claims to provide a minimal, self-consistent explanation for the large spin polarizations observed in insulating chiral molecules without invoking exotic mechanisms or strong intrinsic spin-orbit coupling. By combining quantum tunneling with a current-induced magnetic field and interface dissipation, the model resolves the quantitative gap between weak microscopic interactions and macroscopic 100% polarization.

Furthermore, the work offers a theoretical explanation for the discrepancy between experimental setups: large SP is observed in molecular films (where dissipation and loose ends are likely present) but not in single-molecule break junctions (which are rigidly coupled and lack the specific dissipative environment modeled here). The authors conclude that their tunneling scenario, driven by current-induced symmetry breaking, provides a robust framework for understanding CISS in the non-linear transport regime, consistent with both the magnitude of the effect and its specific symmetry properties.