Observation of dislocation bound states and skin effects in non-Hermitian Chern insulators

This paper presents the first experimental observation of non-Hermitian dislocation bound states and dislocation-induced skin effects in two-dimensional acoustic Chern lattices, demonstrating how precision-controlled gain and loss enable the probing of non-Hermitian topology through lattice defects.

The Gist

Imagine a vast, perfectly organized grid of tiny rooms, like a hotel where every room is connected to its neighbors by doors. In this "hotel," sound waves travel from room to room. Usually, if you knock on a door, the sound travels out equally in all directions. But in this experiment, the scientists built a special kind of hotel where the rules of physics are slightly "twisted."

Here is the story of what they did and found, explained simply:

1. The Twisted Hotel (Non-Hermitian Physics)

In the real world, sound usually fades away (loss) or gets louder if you have a microphone and speaker setup (gain). In physics, systems that have this mix of gain and loss are called Non-Hermitian.

Think of a normal room as a place where sound behaves predictably. In this twisted hotel, the scientists used "active meta-atoms" (smart speakers and microphones) to make the sound behave strangely:

• One-way doors: They made it so sound could travel easily from Room A to Room B, but not back from B to A.
• The "Skin" Effect: In these twisted systems, if you shout, the sound doesn't spread evenly. Instead, it tends to pile up at the edges of the building, like a crowd of people rushing to the exits. This is called the Non-Hermitian Skin Effect.

2. The Broken Floor (Dislocations)

Now, imagine taking this perfect grid of rooms and making a mistake in the construction. They removed two rows of rooms and stitched the remaining walls together. This created a "kink" or a dislocation in the floor.

In normal physics, these kinks are just defects. But in this twisted hotel, the scientists predicted that these kinks would act like traps. Just as a whirlpool traps water in the middle of a river, these kinks were supposed to trap sound waves right in the center of the defect, keeping them there even while the rest of the sound rushed to the edges.

3. The Experiment: Building the Trap

The team built a physical model using 56 acoustic cavities (tiny air chambers) arranged in a grid. They used a clever feedback loop:

• A microphone listens to the sound in a room.
• A speaker immediately plays it back, but with a specific "twist" (adding gain or loss).
• This allowed them to tune the "doors" between rooms with extreme precision, creating the one-way traffic and the twisted rules they needed.

They created a pair of these kinks (a dislocation and an anti-dislocation) in the middle of their grid.

4. What They Found

The Magic Traps (Dislocation Bound States):
When they sent sound into the grid, they found exactly what they predicted. In the "M phase" (a specific setting of their knobs), two distinct sound waves got stuck right at the center of the kinks. They were trapped, isolated from the rest of the sound rushing to the edges. It was like finding a secret room in the middle of the hotel where the sound never left.

The "Melting" of the Traps:
The scientists then turned up the "twist" (the gain and loss) to see how strong the traps could be.

• Moderate Twist: The traps still worked, but the sound waves started to lean slightly to one side, depending on which way the "one-way doors" were facing.
• Too Much Twist: When they turned the twist too high, something dramatic happened. The "traps" dissolved. The sound waves that were stuck in the middle suddenly let go, spread out, and joined the crowd rushing to the edges.

They called this "melting." The reason? At a certain point, the "energy gap" that held the traps open closed up. The special conditions that kept the sound trapped vanished, and the sound was forced to join the "skin effect" crowd at the boundaries.

The "Skin" Around the Kink:
They also noticed something interesting about the kinks themselves. If the kink was oriented in a specific direction relative to the "one-way" flow, the sound would pile up around the kink itself, not just at the edge of the whole building. It was like a mini-crowd forming right around the broken floor tiles.

5. Why It Matters (According to the Paper)

The paper doesn't claim this will build better speakers or medical devices right now. Instead, it says this is a proof of concept.

• New Way to See Topology: Usually, to see these strange topological effects, you have to look at the very edge of a material. This experiment shows that you can use defects (like a broken floor tile) as a tool to find and study these hidden physics.
• Testing the Limits: They showed exactly how much "twist" (gain/loss) a system can handle before the special trapped states disappear. They proved that when the system hits a critical point (called an "Exceptional Point"), the trapped states melt into the crowd.

In a nutshell: The scientists built a sound-based hotel with broken floors and one-way doors. They proved that broken floors can trap sound waves, but if you make the one-way doors too strong, the trap breaks, and the sound rushes to the exits. This helps us understand how to control waves in materials with defects.

Technical Summary

Technical Summary: Observation of Dislocation Bound States and Skin Effects in Non-Hermitian Chern Insulators

Problem Statement
The intersection of non-Hermitian (NH) topology and crystal defects represents a significant frontier in condensed matter physics, yet its experimental exploration has been hindered by the dual challenges of precise defect engineering and the measurement of complex energy spectra. While theoretical models suggest that crystalline defects (such as dislocations) can host robust bound states in NH systems, and that these defects can induce a "dislocation-induced non-Hermitian skin effect" (D-NHSE), these phenomena have remained largely unobserved. The difficulty lies in the requirement for delicate defect manipulation combined with precision-controlled NH perturbations (gain/loss and nonreciprocity) within a system capable of supporting complex-valued eigenenergies. Furthermore, the interplay between defect-bound states and bulk exceptional points (EPs)—which can cause the "melting" or delocalization of these states—lacks experimental validation.

Methodology
To address these challenges, the authors constructed a two-dimensional (2D) acoustic lattice using a coupled acoustic cavity system (CACS). The experimental platform consists of 56 acoustic cavities, where each cavity functions as a lattice site supporting a dipole resonant mode.

• Active Control and Tuning: To overcome fabrication imperfections and inherent disorder, the authors employed an active self-feedback mechanism. Microphones and loudspeakers within each cavity were used to lock the resonance of all cavities to a uniform reference frequency, allowing for the precise engineering of onsite potentials and hopping parameters.
• Realization of NH Chern Insulator: The system implements a NH Chern Hamiltonian by introducing nonreciprocal hopping terms and imaginary hopping components via active meta-atoms. This breaks time-reversal symmetry, a prerequisite for realizing a Chern insulator. The design includes an embedded edge dislocation-antidislocation pair created by removing specific unit cells and reconnecting sites, thereby introducing a Burgers vector.
• Measurement Technique: Recognizing that conventional excitation methods cannot selectively target complex poles in the Green's function, the authors utilized a Green's function-based measurement approach. By sequentially activating a source at every site and capturing the full frequency response via an array of microphones, they reconstructed the full Green's function matrix. This allowed for the accurate extraction of complex-valued eigenenergies and both left and right eigenstates.

Key Contributions and Results
The study provides the first experimental observation of NH dislocation bound states (NHDS) and the D-NHSE in a line-gap NH Chern lattice.

1. Validation of Bulk Exceptional Points (EPs): The authors first characterized a pristine lattice to identify bulk EPs. They demonstrated that as NH perturbations ($h_j$) approach a critical value relative to the hopping strength ($t_0$), the complex energy spectra coalesce. This was quantitatively verified by measuring the "phase rigidity" of eigenstates, which collapses near the EP, signaling a bulk spectral phase transition and the closure of the real-energy line gap.
2. Observation of NH Dislocation Bound States (NHDS): In the Hermitian limit and under moderate NH perturbations, the experiments confirmed the existence of robust defect-bound states localized at the dislocation cores within the line gap of the complex spectrum. These states were observed specifically in the "M phase" (where the Chern number $C = -1$ and the momentum $K \cdot b = \pm \pi$), while the "Γ phase" ($C = 1$, $K \cdot b = 0$) remained devoid of such mid-gap states, consistent with theoretical predictions.
3. Dislocation-Induced NH Skin Effect (D-NHSE): Under periodic boundary conditions (PBCs), the authors observed a weak D-NHSE where eigenstate weight accumulated around the dislocation core. This effect was found to be anisotropic and dependent on the direction of the Burgers vector relative to the NH perturbation. For instance, a nonzero $h_y$ (breaking reflection symmetry about the x-axis) induced a D-NHSE, whereas $h_x$ did not, due to the specific coordination geometry of the defect.
4. Melting of NHDS via EPs: The study elucidated the fate of NHDS as NH perturbations increase. As the system approaches the EP threshold where the line gap closes, the localized NHDS gradually delocalize and merge with the bulk (or skin) states. Under open boundary conditions (OBCs), these states ultimately merge into the conventional skin states at the system's exterior boundaries.

Significance
The paper claims to bridge the gap between NH band topology and defect physics, establishing crystal defects as universal tools for probing NH topological phases. By experimentally demonstrating the coexistence of D-NHSE and topological defect-bound states in a line-gap system, the work distinguishes these phenomena from the D-NHSE characteristic of point-gap systems. The findings pave an experimental pathway for probing NH topology via lattice defects and suggest new avenues for defect-engineered topological devices. The authors emphasize that their platform, which realizes the Hamiltonian governing actual physical wave propagation, offers insights transferable to other wave-based platforms such as photonics and mechanics.