🔬 mesoscale physics

Non-Hermiticity-induced chirality imbalance of Weyl Landau levels

This paper experimentally demonstrates that non-Hermiticity in a synthetic photonic Weyl semimetal can break the fundamental chirality constraint of Weyl nodes by using radiative boundary loss to selectively suppress surface states, thereby creating an observable imbalance between counter-propagating chiral Landau levels.

Original authors: Sachin Vaidya, Alaa Bayazeed, André Grossi Fonseca, Adolfo G. Grushin, Marin Soljačić, Christina Jörg

Published 2026-06-02

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CC BY 4.0

Original authors: Sachin Vaidya, Alaa Bayazeed, André Grossi Fonseca, Adolfo G. Grushin, Marin Soljačić, Christina Jörg

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

Imagine a perfectly balanced seesaw. In the world of physics, there is a fundamental rule (called the Nielsen–Ninomiya theorem) that says you cannot have a seesaw that tips permanently to one side. If you have a "left-handed" particle, you must also have a "right-handed" partner to cancel it out. This balance is so strict that in normal, closed systems, the total "handedness" (or chirality) of the universe must always add up to zero.

This paper explores what happens when you break the rules of a "closed" system by letting energy leak out. The researchers built a special optical device—a stack of thin layers of silicon and glass—to act like a playground for light particles (photons) that behave like these tricky "Weyl fermions."

Here is the story of their discovery, broken down into simple steps:

1. The Setup: A Synthetic World

The scientists didn't use a real 3D crystal. Instead, they built a 1D stack of layers (like a sandwich) but programmed the thickness of each layer to change in a specific pattern. By tweaking these patterns, they created a "synthetic world" where light behaves as if it is moving through a complex 3D landscape. In this landscape, light can get stuck in special "traffic lanes" called Landau levels when a magnetic field is applied.

2. The Normal Rule: The Balanced Seesaw

First, they applied a standard, uniform magnetic field.

What happened: Just like the physics rulebook predicts, the light split into two lanes. One lane carried "left-handed" light moving one way, and the other carried "right-handed" light moving the opposite way.
The result: The traffic was perfectly balanced. For every left-mover, there was a right-mover. The net flow was zero. This is the expected, boring (but correct) behavior.

3. The Twist: The Axial Field

Next, they changed the magnetic field to an "axial" field. Think of this as a field that pushes left-handed particles one way and right-handed particles the same way.

What happened: The researchers saw the "left-handed" and "right-handed" light lanes in the middle of their stack (the bulk) start to move in the same direction.
The problem: If you only looked at the middle of the stack, it looked like the balance was broken. It seemed like they had created a one-way street, violating the fundamental rule that says the total balance must be zero.

4. The Secret: The Hidden Escape Route

The paper reveals that the balance wasn't actually broken; it was just hidden.

In a perfect, closed system, the "missing" opposite traffic would be found on the very edges of the stack (the surface states). These edge lanes would carry the counter-flow to balance the middle lanes.
However, their device is not a closed box. It is an open window. Light can leak out of the edges into the air.
Because the "balancing" traffic was stuck on the edges, it leaked away (dissipated) very quickly. The "middle" traffic, being safe in the center, stayed around longer.

5. The Discovery: Non-Hermiticity Creates Imbalance

The term "Non-Hermiticity" is just a fancy physics word for "systems where energy leaks or is lost."

The researchers found that because the edge traffic leaked away so fast, it disappeared from their measurements.
The result: They could only see the long-lived traffic in the middle, which was all moving in the same direction.
The Conclusion: By letting the system "leak" (using non-Hermiticity), they effectively erased the balancing partner from the observable world. They created an apparent imbalance where the net flow looked one-sided, even though the total system still obeyed the laws of physics.

6. Proving the Theory

To prove this wasn't a mistake, they did one final experiment. They added a few extra layers of glass to the top and bottom of their stack to act like a shield, reducing the leakage at the edges.

What happened: When they stopped the light from leaking out so fast, the "hidden" edge traffic reappeared. Suddenly, the balancing partner was visible again, and the perfect seesaw balance was restored.

The Takeaway

This paper shows that in open systems (like light escaping into the air), you can manipulate the rules of the game. By controlling how much energy leaks out of the edges, you can hide the "balancing" particles and make a system look like it has a one-way flow, even when it's fundamentally balanced. It's like a magician making a balancing weight disappear so the scale looks like it's tipping, only to reveal the weight again when the trick is stopped.

Technical Summary: Non-Hermiticity-induced chirality imbalance of Weyl Landau levels

Problem Statement
In Hermitian lattice systems with periodic momentum space, the Nielsen–Ninomiya theorem imposes a strict global constraint: the net chiral topological charge must vanish. In Weyl semimetals, this necessitates that Weyl nodes of opposite chirality occur in pairs. Under a magnetic field, this constraint manifests in the Landau-level spectrum: while higher Landau levels are non-chiral, the zeroth Landau levels (0LLs) associated with opposite Weyl nodes disperse in opposite directions, ensuring a balanced net chiral spectral flow. Even in axial magnetic fields (e.g., induced by strain), where bulk 0LLs may share the same chirality, the global constraint is satisfied by counter-propagating topological surface states.

The central question addressed is how this fundamental chirality balance is affected in open, non-Hermitian systems. In such systems, coupling to external degrees of freedom (e.g., radiation or loss) grants modes finite lifetimes. The authors investigate whether non-Hermiticity can selectively suppress specific spectral channels, thereby producing an observable chirality imbalance that would be forbidden in a closed Hermitian system.

Methodology
The authors experimentally realize a synthetic photonic Weyl semimetal using one-dimensional multilayer Bragg stacks composed of alternating silicon (Si) and silicon dioxide (SiO $_2$ ) layers.

Synthetic Dimensions: While the physical structure is 1D, the layer thicknesses are modulated by two periodic parameters, $p$ and $q$ . Together with the physical Bloch momentum $k_y$ , these parameters form a synthetic three-dimensional toroidal space $(p, k_y, q)$ , mapping to the momentum space $(k_x, k_y, k_z)$ of a 3D Weyl system.
Weyl Nodes: The specific modulation of layer thicknesses creates isolated linear degeneracies (Weyl nodes) between photonic bands, carrying quantized Chern numbers of $\pm 1$ .
Magnetic Field Engineering: The authors introduce synthetic magnetic fields by spatially varying the parameter $q$ $q$ along the propagation direction ( $y$ $y$ , indexed by unit cell $n$ $n$ ):
- Homogeneous Field ( $B$ ): $q$ varies linearly with $n$ ( $q_{hom} \propto n$ ). This mimics a standard Landau gauge vector potential, coupling identically to all Weyl nodes.
- Axial Field ( $B_5$ ): $q$ varies as $q_{inhom}(n, p) = q_{hom}(n) \cos(\pi p)$ . This modulation causes the effective field to change sign across the synthetic parameter $p$ , coupling with opposite signs to Weyl nodes of opposite chirality.
Non-Hermiticity: The system is inherently non-Hermitian due to radiative boundary losses at the interfaces with free space and the substrate. The authors further manipulate this by adding cladding layers to reduce boundary loss.
Measurement: Transmission spectra are measured using broadband light and a spectrometer for stacks with varying $p$ values, effectively probing the synthetic band structure.

Key Results

Homogeneous Field Regime: Under a synthetic homogeneous magnetic field, the experiment reproduces the expected chirality-balanced spectrum. The zeroth Landau levels associated with opposite Weyl nodes disperse in opposite directions (counter-propagating), maintaining the global chirality constraint.
Axial Field Regime: Under a synthetic axial magnetic field, the bulk zeroth pseudo-Landau levels acquire the same group velocity (co-propagating), suggesting a local chirality imbalance.
Non-Hermitian Chirality Imbalance: In the open photonic structure, the compensating chiral channels required by the Nielsen–Ninomiya theorem are realized as surface states localized at the boundaries. Because these surface states are exposed to the open boundaries, they experience significant radiative loss. This loss broadens their spectral signatures and suppresses them from the long-lived observable spectrum. Consequently, the measured transmission spectrum exhibits a net chirality imbalance, dominated solely by the long-lived bulk co-propagating modes.
Recovery of Balance: By adding cladding layers to reduce boundary loss, the authors recover the hidden surface-state contribution. These states reappear as sharp resonances, demonstrating that the global chirality balance is restored when the non-Hermitian suppression is mitigated.

Significance
The paper demonstrates that non-Hermiticity, a natural feature of photonic systems, can be used to control and relax fundamental chirality constraints in topological systems. Specifically, it shows that radiative boundary loss can selectively suppress the spectral channels (surface states) that enforce global topological conservation laws. This allows for the experimental access to "forbidden" spectral responses, such as a net chiral spectral flow, which are not observable in closed Hermitian lattices. The work establishes a route for manipulating chiral spectral flow and accessing topological responses beyond the limitations of closed systems, without altering the underlying topological charge of the lattice itself.