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Engineering Tunable Synthetic Su-Schrieffer-Heeger Chains in Liquid Crystal Microcavities

This paper demonstrates that liquid crystal microcavities hosting a dimerized uniform lying helix texture can serve as a versatile, voltage-tunable platform for engineering synthetic Su-Schrieffer-Heeger chains with orthogonal polarizations, thereby enabling precise control over photonic topological phases and interchain coupling at room temperature.

Original authors: Joanna Mędrzycka, Luciano S. Ricco, Piotr Kapuściński, Marcin Muszyński, Przemysław Morawiak, Rafał Mazur, Rafał Węgłowski, Eva Oton, Przemysław Kula, Wiktor Piecek, Jacek Szczytko

Published 2026-05-20

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Joanna Mędrzycka, Luciano S. Ricco, Piotr Kapuściński, Marcin Muszyński, Przemysław Morawiak, Rafał Mazur, Rafał Węgłowski, Eva Oton, Przemysław Kula, Wiktor Piecek, Jacek Szczytko

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 you have a tiny, transparent box filled with a special kind of "smart" liquid. This isn't just water or oil; it's a liquid crystal, the same kind of material found in your digital watch or laptop screen, but here it's trapped between two mirrors.

The scientists in this paper figured out how to turn this box into a playground for light, where they can make photons (particles of light) behave like they are walking on a very specific, tricky path. Here is how they did it, explained simply:

1. The Magic Liquid and the "Twist"

Inside the box, the liquid crystal molecules naturally want to line up in a spiral pattern, like a twisted staircase. The researchers call this a "Uniform Lying Helix" (ULH). Think of it like a long, flat ribbon of molecules that is twisted along its length.

Because of how these molecules are twisted, they treat light differently depending on which way the light is vibrating (its polarization).

The Analogy: Imagine a hallway with a floor that is bumpy for people walking on their left foot but smooth for people walking on their right foot. In this experiment, the "bumps" and "smooth spots" are created by the twisted liquid molecules.

2. The "Dimerized" Lattice (The Two-Step Dance)

When light travels through this twisted liquid, it sees a pattern of alternating strong and weak spots.

The Analogy: Imagine a dance floor with tiles arranged in pairs. Some pairs are close together (strong connection), and the gap between the pairs is wide (weak connection). This is called a "dimerized" lattice.
In physics, this specific pattern is famous because it's the simplest model for a Su-Schrieffer-Heeger (SSH) chain. Think of it as the "Hello World" of topological physics—a basic setup used to teach how particles can get stuck at the edges of a material.

3. The Two Parallel Dance Floors

Here is the clever part: The researchers didn't just make one dance floor; they made two that run side-by-side.

One floor is for light vibrating horizontally.
The other floor is for light vibrating vertically.
These two floors are linked. The light on one floor can "jump" to the other floor, and vice versa. It's like having two parallel train tracks where the trains can occasionally switch tracks.

4. The Remote Control (Voltage)

The most exciting feature of this experiment is that the researchers can change the rules of the game just by turning a knob (applying a voltage).

The Analogy: Imagine the two parallel train tracks are made of rubber. When you apply electricity, you stretch or squeeze the rubber. This changes how close the tracks are to each other and how easily a train can jump from one to the other.
By changing the voltage, they can tune how strongly the two "light chains" talk to each other. They can make the connection strong, weak, or even change the shape of the path the light takes.

5. What They Found (The "Trivial" Phase)

The scientists wanted to see if they could create a special "topological" state—a state where light is protected and can only move in one direction, like a one-way street that can't be blocked.

The Result: In the specific range of voltages they tested, the system ended up in a "trivial" state.
The Analogy: They tried to build a one-way street, but the traffic lights (the voltage) were set in a way that allowed cars to go both ways or get stuck. The special "protected" state didn't appear yet.
However: They proved mathematically that if they tweaked the settings just right (restoring a specific symmetry), they could create that special topological state. They showed the blueprint works, even if they didn't build the final house in this specific experiment.

Summary

The paper demonstrates a new way to build a reconfigurable physics lab using liquid crystals and light.

They created a system where light behaves like it's walking on a specific, alternating path (an SSH chain).
They made two of these paths that interact with each other.
They showed that by applying electricity, they can reshape the path and change how the two paths interact.

While they didn't find the "magic" topological state in this specific test, they proved that this liquid crystal box is a powerful, tunable tool. It's like showing that you have a Lego set that can be rearranged to build almost any machine, even if you haven't built the flying car yet. This opens the door for future experiments to simulate complex quantum behaviors using simple light and liquid.

Technical Summary: Engineering Tunable Synthetic Su-Schrieffer-Heeger Chains in Liquid Crystal Microcavities

Problem Statement
Topological phases of matter, particularly those described by minimal models like the Su-Schrieffer-Heeger (SSH) chain, are central to modern condensed matter physics and photonics. While the SSH model serves as a fundamental textbook example of a topological insulator, most experimental realizations (e.g., in atomic chains, quantum dots, or fixed microcavity arrays) suffer from static lattice geometries and coupling strengths. These platforms offer limited in-situ tunability, restricting the ability to explore on-demand internal degrees of freedom, inter-chain couplings, or selective symmetry breaking. There is a need for a versatile platform capable of realizing synthetic topological Hamiltonians with high electrical reconfigurability to study extended 1D topological regimes beyond minimal models.

Methodology
The authors utilize Liquid Crystal Microcavities (LCMCs) as a tunable photonic platform. The experimental setup consists of a microcavity formed by two Distributed Bragg Reflectors (DBRs) coated with a homeotropically orienting polyimide layer. The cavity is filled with a chiral liquid crystal mixture that self-assembles into a Uniform Lying Helix (ULH) texture. This texture is controlled by an external voltage applied via transparent Indium Tin Oxide (ITO) electrodes, operating within a range of 4.00 V to 7.25 V.

The study employs white light transmission measurements to characterize the system. The birefringence of the liquid crystal creates a spatially modulated photonic potential that acts as a 1D dimerized lattice for photons. The authors analyze the transmission spectra in reciprocal space ( $k$ -space) and measure Stokes parameters ( $S_0, S_1, S_2, S_3$ ) to determine the polarization characteristics of the photonic bands. Theoretical analysis involves constructing an effective Hamiltonian for two coupled SSH chains with orthogonal linear polarizations (acting as a pseudospin degree of freedom). The model includes staggered onsite potentials, intracell and intercell hopping amplitudes, and interchain coupling terms modulated by the applied voltage.

Key Results

Realization of Coupled SSH Chains: The ULH texture generates a photonic potential that mimics two coupled SSH chains. One chain corresponds to horizontal ( $H$ ) polarization and the other to vertical ( $V$ ) polarization. The dimerization manifests as an alternating intensity pattern in the transmission signal, which is more pronounced for $H$ polarization.
Voltage-Dependent Tunability: Applying an external electric field reorients the liquid crystal molecules, modifying the effective refractive index anisotropy. This results in a tunable photonic potential landscape. Specifically, increasing the voltage from 4.00 V to 7.25 V causes a spatial shift in the transmitted intensity for $H$ polarization while leaving $V$ polarization largely unchanged. This allows for the dynamic control of interchain coupling.
Photonic Band Structure: The system exhibits three distinct photonic bands within the cavity's parabolic dispersion.
- The lowest band ( $s_V$ ) is predominantly vertically polarized and exhibits a sinusoidal dispersion with bonding-antibonding characteristics typical of an SSH lattice.
- The higher bands ( $p_V$ and $s_H$ ) show complex, non-trivial dispersions due to strong mixing between $s$ -like and $p$ -like states of opposite polarizations. This mixing is driven by the birefringence-induced degeneracy of the bands.
- The energy splitting and dispersion shapes of these bands are highly sensitive to the applied voltage. For instance, the $s_H$ band evolves from a non-trivial shape at 4.0 V to a near-flat band at 7.25 V, indicating an increase in effective photonic mass.
Symmetry Analysis: Theoretical fitting of the experimental data using the coupled SSH Hamiltonian reveals that for the explored voltage range, both chiral symmetry and inversion symmetry are broken. Consequently, the system resides in a topologically trivial phase. The absence of a quantized Zak phase in the current configuration is attributed to the staggered onsite potentials and the specific interchain coupling parameters.
Restoration of Symmetry: The analysis indicates that inversion symmetry can be restored in principle by tuning the system parameters (specifically setting the staggered potential $\epsilon_\sigma = 0$ and equalizing interchain couplings $\alpha_+ = \alpha_-$ ). This suggests a pathway to a topological regime characterized by a quantized Zak phase, even in the absence of chiral symmetry.

Significance and Claims
The paper establishes LCMCs as a versatile platform for engineering synthetic topological Hamiltonians. The primary contribution is the demonstration of a voltage-controlled, coupled double SSH chain where the interchain coupling and polarization-dependent interactions can be tuned in-situ.

The authors claim that while the current experimental parameters place the system in a trivial phase, the platform's inherent tunability allows for the exploration of extended 1D topological regimes. Specifically, the system can be engineered to restore inversion symmetry, potentially enabling the realization of crystalline topological phases protected by inversion symmetry rather than chiral symmetry. Furthermore, the platform offers the potential to engineer next-nearest-neighbor hoppings and more complex interactions (e.g., via nematic or cholesteric structures combined with focused ion beam patterning). This work opens avenues for the on-demand simulation of synthetic lattices and the study of exotic topological phenomena, including those supporting fractionally charged fermionic quasiparticles, within a reconfigurable optical environment.