[Paper Review] Negative refraction in hyperbolic hetero-bicrystals

Aaron Sternbach, S. Moore+13 more|arXiv (Cornell University)|Sep 30, 2022

Liquid Crystal Research Advancements4 citations

TL;DR

This study demonstrates negative refraction of phonon polaritons at the interface between two hyperbolic van der Waals materials—molybdenum trioxide (MoO₃) and isotopically pure hexagonal boron nitride (h¹¹BN)—using infrared light. At a specific frequency ω₀, the polaritons form collimated rays that follow closed diamond-shaped trajectories due to strong coupling and polaritonic level repulsion, revealing regions of both positive and negative dispersion interrupted by multiple gaps.

ABSTRACT

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons - hybrids of infrared photons and lattice vibrations - form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide ($MoO_3$) and isotopically pure hexagonal boron nitride ($h^{11}BN$). At a special frequency $ω_0$, these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic level repulsion and strong coupling.

Motivation & Objective

• To observe negative refraction of phonon polaritons at the interface of two natural hyperbolic van der Waals crystals.
• To investigate the emergence of closed-loop trajectories in polaritonic modes due to negative refraction.
• To map the dispersion relations of polariton eigenmodes and identify regions of positive and negative dispersion.
• To explore the role of polaritonic level repulsion and strong coupling in creating multiple band gaps.

Proposed method

• Fabricated a planar heterostructure composed of molybdenum trioxide (MoO₃) and isotopically pure hexagonal boron nitride (h¹¹BN).
• Used infrared nano-imaging to visualize the propagation of phonon polaritons across the interface between the two materials.
• Measured the dispersion of polariton modes by analyzing the spatial profile and phase of the emitted radiation at different frequencies.
• Identified the frequency ω₀ at which negative refraction leads to closed diamond-shaped trajectories in the polariton rays.
• Analyzed the system's eigenmodes to detect regions of positive and negative dispersion separated by multiple gaps.
• Employed theoretical modeling based on polaritonic level repulsion and strong coupling to explain the observed band gap formation.

Experimental results

Research questions

• RQ1 Can negative refraction of phonon polaritons be experimentally observed at the interface of two natural hyperbolic van der Waals materials?
• RQ2 What is the role of strong coupling and polaritonic level repulsion in shaping the dispersion relation of polariton modes?
• RQ3 At what frequency does negative refraction lead to closed, circulating trajectories of phonon polaritons?
• RQ4 How do multiple band gaps emerge in the polariton spectrum due to the interplay of dispersion and coupling?
• RQ5 What is the spatial and spectral signature of the transition between positive and negative dispersion in the system?

Key findings

• Negative refraction of phonon polaritons was experimentally visualized at the MoO₃/h¹¹BN interface using infrared nano-imaging.
• At a specific frequency ω₀, polariton rays formed closed diamond-shaped trajectories due to negative refraction.
• The system exhibited alternating regions of positive and negative dispersion, separated by multiple band gaps.
• The band gaps originated from polaritonic level repulsion and strong coupling between the modes in the two materials.
• The dispersion relations showed clear evidence of avoided crossings, confirming strong coupling effects.
• The observed behavior was consistent with theoretical predictions based on hyperbolic dispersion and polariton hybridization.