🔬 mesoscale physics

Theoretical investigation of two-dimensional semiconductor nanoribbons and nanoparticles for tailored light--matter interactions

This theoretical study investigates the optical response of 2D semiconductor nanostructures, revealing that while the localized nature of excitons in nanoribbon arrays limits geometric tunability, coating spherical nanoparticles with these materials offers a superior platform for achieving controllable light-matter interactions through hybridization.

Original authors: Christian Nicolaisen Hansen, Line Jelver, Christos Tserkezis

Published 2026-09-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Christian Nicolaisen Hansen, Line Jelver, Christos Tserkezis

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

In the world of modern materials science, researchers have long been fascinated by two-dimensional substances: sheets of matter so thin they are only a single layer of atoms thick. Since the discovery of graphene, a material made of carbon atoms arranged in a honeycomb pattern, scientists have realized that these ultra-thin layers behave differently than the bulk materials we encounter in everyday life. When light hits these sheets, it can interact with the electrons inside them in unique ways. If the material has a specific energy gap, the light can kick an electron up to a higher energy state, leaving behind a vacancy that acts like a positive charge. These two entities, the excited electron and the vacancy, stick together due to electrical attraction, forming a particle known as an exciton. These excitons are not just floating around; they can couple with light to create hybrid particles called polaritons, which are the focus of intense study for their potential to revolutionize how we control light and information. The question driving recent research is whether we can shape these materials into specific patterns to tune how they interact with light, much like how shaping a guitar string changes the note it plays.

A team of researchers at the University of Southern Denmark set out to investigate this question using two specific types of two-dimensional semiconductors: hexagonal boron nitride, which interacts with ultraviolet light, and tungsten disulfide, which interacts with visible light. They wanted to know if cutting these materials into tiny strips or wrapping them around tiny spheres would allow them to control the way the excitons respond to light. To test this, they built detailed computer models of two different shapes. First, they arranged the materials into long, parallel strips, creating a grid of nanoribbons. Second, they modeled the materials as thin coatings wrapped around spherical particles. By simulating how light hits these structures, they calculated how much light would be reflected, how much would pass through, and how much would be absorbed by the material.

The results for the flat strips were surprising and somewhat disappointing for those hoping for easy control. When the researchers varied the width of the strips or the distance between them, the way the material absorbed light barely changed. The absorption peaks remained stubbornly fixed at the specific energy levels where the excitons naturally exist. This behavior stands in sharp contrast to what happens with graphene, where similar patterns create plasmons—collective oscillations of electrons—that are highly sensitive to the shape of the material. In these semiconductor strips, the excitons are so tightly bound and localized that the geometry of the strip does little to alter their behavior. Even when the researchers changed the angle of the incoming light or the materials surrounding the strips, the response remained largely the same. The only minor change observed was a tiny shift in the color of the absorbed light when the strips were made extremely narrow, but this effect was too small to be useful for practical tuning.

However, the story changed completely when the researchers turned their attention to the spherical particles. When they modeled the two-dimensional materials as a thin shell coating a sphere, they found a much greater ability to tune the optical response. By simply changing the size of the sphere, they could shift the energy at which the material absorbed light. This effect was even more pronounced when the sphere was made of a standard dielectric material, like a type of glass, and then coated with the semiconductor. In this setup, the excitons in the coating interacted with the natural light-resonating modes of the sphere itself. This interaction caused the single absorption peak to split into two distinct peaks, a sign that the two systems were hybridizing and forming new, combined states of light and matter.

The researchers found that while the system showed signs of interaction, it did not always reach the regime of strong coupling for both materials. For the boron nitride coating, a sphere with a radius showing a splitting of its resonance, but this split did not satisfy the strict mathematical criterion required to confirm strong coupling due to the broad width of the underlying resonance. In contrast, the system with the tungsten disulfide coating did successfully demonstrate strong coupling. Specifically, a sphere coated in tungsten disulfide exhibited a splitting and linewidth values that met the condition for strong coupling. These findings suggest that while flat, patterned strips may not offer much control over excitons, wrapping these materials around spherical cores provides a powerful and flexible way to engineer light-matter interactions, though achieving the strongest coupling effects depends critically on the specific material and geometry. This approach opens a promising path for designing new, miniaturized devices that can manipulate light with precision, moving beyond the limitations of flat patterns to utilize the unique physics of curved, three-dimensional geometries.

Problem Statement
Two-dimensional (2D) materials, particularly those with band gaps like hexagonal boron nitride (hBN) and transition-metal dichalcogenides (TMDs) such as WS $_2$ , exhibit strong excitonic responses. While the plasmonic response of patterned graphene is known to be highly sensitive to geometry, it remains unclear whether the optical response of 2D semiconductors can be similarly tuned by patterning them into nanoscale geometries. This paper investigates whether tailoring the excitonic response of 2D materials through nanopatterning is a viable strategy for controlling light–matter interactions, specifically comparing periodic nanoribbon arrays against spherical nanoparticles (nanospheres).

Methodology
The authors employ a theoretical framework based on electromagnetic (EM) boundary conditions modified to include a surface optical conductivity, $\sigma(\omega)$ , representing the 2D material.

Material Modeling:
- hBN: Modeled in the ultraviolet (UV) regime using an optical conductivity derived from first-principles calculations and the Elliott equation, incorporating two excitonic resonances ( $\hbar\omega_1 \approx 5.48$ eV and $\hbar\omega_2 \approx 6.41$ eV).
- WS $_2$ : Modeled in the visible regime using experimental reflectance data fitted to a sum of Lorentzian oscillators to determine the relative permittivity, which is then converted to sheet conductivity. This captures the A and B excitonic peaks.
Geometries and Solvers:
- Nanoribbons: An infinite array of ribbons on a dielectric substrate is analyzed using two analytical methods: the edge condition method (assuming current proportional to distance from the edge, valid for narrow ribbons) and the Fourier series method (expanding conductivity in Fourier modes, valid for arbitrary widths). Both utilize Fourier-Floquet decomposition to calculate reflectance, transmittance, and absorbance.
- Spherical Nanoparticles: Hollow shells and dielectric cores coated with 2D materials are analyzed using Mie theory. The standard Mie coefficients are modified to include the surface conductivity term, $g(\omega)$ , allowing for the calculation of extinction, scattering, and absorption cross-sections.

Key Contributions

Methodological Adaptation: The paper adapts established EM solvers (edge condition, Fourier series, and Mie theory) originally developed for graphene or bulk materials to specifically handle 2D semiconductors with localized excitonic resonances.
Comparative Analysis: It provides a direct theoretical comparison between the tunability of 2D semiconductor nanoribbons and coated nanoparticles, highlighting the distinct physics of exciton polaritons versus plasmons.
Hybridization Demonstration: The work demonstrates how coupling 2D excitons with the Mie modes of a dielectric core can lead to strong coupling regimes and resonance splitting.

Results

Nanoribbons (Weak Tunability):
- For both hBN and WS $_2$ nanoribbons, the absorbance peaks remain largely pinned to the intrinsic excitonic resonances of the planar material.
- While a slight blueshift is observed as ribbon width decreases (due to increased confinement), the overall tunability with geometric parameters (width and periodicity) is found to be weak.
- This contrasts sharply with graphene, where plasmonic resonances are highly geometry-dependent. The localized nature of excitons in 2D semiconductors limits their ability to hybridize with optical modes in a ribbon array to produce significant spectral shifts.
- The Fourier series method revealed secondary diffraction peaks in hBN ribbons at higher energies, which were absent in the edge condition approximation, though these did not significantly alter the main excitonic response.
Spherical Nanoparticles (Enhanced Tunability):
- Hollow shells of hBN and WS $_2$ exhibit extinction peaks near the intrinsic excitonic resonances. For hBN, a blueshift is observed as the shell radius decreases, attributed to increased screening from the surface current.
- Dielectric Core Hybridization: When a 2D semiconductor coats a dielectric core (e.g., $\epsilon = 11.7$ ), the excitons couple with the Mie modes of the core.
- This coupling leads to hybridization, resulting in the splitting of extinction resonances.
- The authors identify specific radii where the system enters the strong coupling regime (where the energy splitting exceeds the linewidths). For example, an hBN-coated particle at $R \approx 45.7$ nm and a WS $_2$ -coated particle at $R \approx 124.5$ nm satisfy the criteria for strong coupling between the exciton and the core's magnetic multipole modes.

Significance and Claims
The paper claims that while the localized nature of excitons in 2D semiconductors largely limits the tunability of optical responses via simple geometric patterning (as seen in nanoribbons), nanospheres with 2D semiconductor coatings offer a superior platform. Specifically, the hybridization of excitons with the optical modes of a dielectric core allows for controllable light–matter interactions, including resonance splitting and strong coupling.

The authors conclude that this approach provides a "fruitful path" for engineering hybrid optical responses. The demonstrated methods allow for the design and analysis of nanostructures using only the optical conductivity of the 2D material, offering a versatile framework for exploring polaritonic devices. The work suggests that while simple patterning may not yield high tunability, the combination of 2D materials with spherical geometries and dielectric cores holds promise for developing miniaturized polaritonic devices and controllable light–matter interaction systems.

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