Probing Dielectric Screening in van der Waals Heterostructures via Pressure-Tuned Exciton Rydberg Series

This paper proposes a methodology to directly measure the pressure-dependent dielectric constant of hexagonal boron nitride by analyzing the pressure-induced shifts in the exciton Rydberg series of encapsulated monolayer WSe$_2$ within a van der Waals heterostructure.

The Gist

Imagine a tiny, flat sheet of a special material called WSe2 (a type of semiconductor) sandwiched between two layers of a hard, insulating material called hBN (hexagonal boron nitride). Think of this like a delicate, single-layer sandwich where the filling is the star of the show.

Inside this sandwich, electrons and "holes" (missing electrons) can pair up to form little particles called excitons. These excitons are like tiny solar systems: the electron orbits the hole, just like a planet orbits a star.

The "Fingerprint" of the Exciton

Usually, these excitons have a specific set of energy levels, similar to the rungs on a ladder. The lowest rung is the ground state, and the higher rungs are excited states. Scientists call this the Rydberg series.

In this paper, the researchers discovered that the spacing between these rungs acts like a fingerprint of the environment. If the air around the sandwich changes, the spacing between the rungs changes too.

Squeezing the Sandwich

The researchers put this atomic sandwich inside a Diamond Anvil Cell, which is a machine that can squeeze things with immense pressure (like a very strong, microscopic vice).

As they squeezed the sandwich:

1. The layers got closer together.
2. The "air" (or vacuum gap) between the layers got thinner.
3. The insulating material (hBN) itself changed its properties slightly, becoming better at "screening" or blocking electric forces.

What They Saw

When they squeezed the sandwich, they watched the exciton's "ladder" of energy levels. They saw the rungs get closer together.

Think of it like a spring: if you squeeze a spring, the coils get tighter. In this case, the "spring" is the electric force holding the exciton together. Because the surrounding material changed under pressure, the electric force became stronger and more effective at screening, causing the energy levels to compress.

The Detective Work

The scientists had to figure out why the rungs got closer. Was it because the WSe2 sheet itself changed its internal structure? Or was it because the surrounding hBN layers changed?

They used computer models (like a digital simulation of the atoms) to test this. They found that:

• The WSe2 sheet itself barely changed at all under this pressure.
• The real change came from the hBN layers. The pressure made the hBN layers squeeze closer to the WSe2 and also made the hBN material itself better at conducting electric fields (changing its dielectric constant).

The Big Takeaway

The paper concludes that these excitons are incredibly sensitive sensors. By simply looking at how the "ladder" of energy levels shifts, scientists can measure exactly how the dielectric properties (the ability to screen electricity) of the surrounding material are changing under extreme pressure.

In short: They used the "vibrations" of tiny atomic particles to measure how the "air" around them was being squished and changed, proving that these particles can act as precise rulers for the invisible forces in the microscopic world.

Technical Summary

Technical Summary: Probing Dielectric Screening in van der Waals Heterostructures via Pressure-Tuned Exciton Rydberg Series

Problem Statement
Excitons in two-dimensional (2D) semiconductors, such as monolayer transition metal dichalcogenides (TMDs), exhibit unusually large binding energies and form complex many-body states due to reduced dielectric screening and quantum confinement. The energy spacing of their excited states, known as the Rydberg series, serves as a sensitive fingerprint of the exciton's dimensionality and its surrounding dielectric environment. While high-quality van der Waals (vdW) heterostructures have enabled the observation of these series, the dielectric environment in such samples is typically fixed by the sample architecture (e.g., encapsulation layers) and cannot be tuned in situ. Although hydrostatic pressure has been successfully used to modify interlayer distances and coupling strengths in vdW materials, its specific influence on dielectric screening within these heterostructures remains largely unexplored.

Methodology
The authors investigated a high-quality heterostructure consisting of a monolayer (ML) WSe$_2$ encapsulated between hexagonal boron nitride (hBN) layers (specifically a 38 nm bottom hBN layer and a 10 nm top hBN layer). The sample was assembled using a PDMS-based dry transfer technique onto the culet of a diamond anvil cell (DAC).

Experiments were conducted using low-temperature photoluminescence (PL) spectroscopy under hydrostatic pressure, utilizing an ethanol-methanol (4:1) mixture as the pressure-transmitting medium. Pressure values were calibrated via ruby luminescence. The study tracked the evolution of the exciton Rydberg series (specifically the 1s, 2s, and higher excited states) as pressure increased up to 3 GPa.

To interpret the experimental data, the authors developed a microscopic dielectric model based on density functional theory (DFT) calculations. This model treats the WSe$_2$ ML as a slab of finite thickness ($h$) separated from the surrounding bulk hBN by an effective vacuum-like vdW gap ($d$). The electron-hole interaction was described using a quasi-2D potential incorporating the Rytova–Keldysh formalism. The model accounted for pressure-induced changes in two key parameters:

1. The interlayer distance ($d$), derived from the pressure dependence of the Se–BN separation calculated via DFT.
2. The bulk dielectric constant of hBN ($\epsilon_{hBN}$), also obtained from DFT calculations.

The study also performed magneto-optical measurements and DFT band structure calculations to rule out pressure-induced modifications to the electronic band structure (e.g., band gap shifts or effective mass changes) as the primary cause of observed spectral shifts.

Key Results

• Rydberg Series Compression: Under increasing hydrostatic pressure, the energy separation between the exciton ground state (1s) and excited states (2s, 3s, etc.) systematically decreased. This "compression" of the Rydberg ladder indicates an enhancement of Coulomb screening.
• Dominance of Dielectric Effects: DFT calculations and magneto-optical data revealed that the electronic band structure of monolayer WSe$_2$ is only marginally affected by pressures up to 3 GPa. The fundamental band gap shifted by only ~10 meV, and the exciton reduced mass remained nearly constant. Consequently, the observed renormalization of the Rydberg series is attributed primarily to changes in the dielectric environment rather than intrinsic electronic structure changes.
• Quantitative Agreement: The theoretical model, which incorporated the pressure-dependent decrease in interlayer distance and the increase in the hBN dielectric constant, showed excellent agreement with the experimental energy separations ($\Delta E_{1s-2s}$ and $\Delta E_{1s-3s}$).
• Intensity Trends: A reduction in the luminescence intensity of excited states relative to the 1s state was observed with increasing pressure. The authors attribute this to a pressure-enhanced carrier relaxation mechanism, where the shrinking energy gap between excited and ground states facilitates faster depopulation of excited states.

Significance and Claims
The paper demonstrates that the exciton Rydberg series in hBN-encapsulated monolayer WSe$_2$ acts as a sensitive and quantitative probe for pressure-induced modifications of dielectric screening in vdW heterostructures. By correlating the systematic compression of the Rydberg ladder with a microscopic dielectric model, the authors establish a methodology to directly measure the dielectric constant of pressurized hBN.

The authors claim this approach establishes a new framework for "dielectric sensing" and "Coulomb engineering" in low-dimensional systems. They posit that excitons in 2D semiconductors can serve as versatile quantum sensors for electrostatic environments under extreme conditions, offering nanoscale spatial sensitivity for determining dielectric properties without the need for fixed sample architectures. This methodology is presented as extensible to other layered materials and heterostructure geometries for investigating external stimuli.