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Abstract The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other. 

The far‐infrared (far‐IR) remains a relatively underexplored region of the electromagnetic spectrum extending roughly from 20 to 100 µm in free‐space wavelength. Research within this range has been restricted due to a lack of optical materials that can be optimized to reduce losses and increase sensitivity, as well as by the long free‐space wavelengths associated with this spectral region. Here the exceptionally broad Reststrahlen bands of two Hf‐based transition metal dichalcogenides (TMDs) that can support surface phonon polaritons (SPhPs) within the mid‐infrared (mid‐IR) into the terahertz (THz) are reported. In this vein, the IR transmission and reflectance spectra of hafnium disulfide (HfS₂) and hafnium diselenide (HfSe₂) flakes are measured and their corresponding dielectric functions are extracted. These exceptionally broad Reststrahlen bands (HfS₂: 165 cm⁻¹; HfSe₂: 95 cm⁻¹) dramatically exceed that of the more commonly explored molybdenum‐ (Mo) and tungsten‐ (W) based TMDs (≈5–10 cm⁻¹), which results from the over sevenfold increase in the Born effective charge of the Hf‐containing compounds. This work therefore identifies a class of materials for nanophotonic and sensing applications in the mid‐ to far‐IR, such as deeply sub‐diffractional hyperbolic and polaritonic optical antennas, as is predicted via electromagnetic simulations using the extracted dielectric function.

 

Phonon polaritons in van der Waals materials reveal significant confinement accompanied with long propagation length: important virtues for tasks pertaining to the control of light and energy flow at the nanoscale. While previous studies of phonon polaritons have relied on relatively thick samples, here reported is the first observation of surface phonon polaritons in single atomic layers and bilayers of hexagonal boron nitride (hBN). Using antenna‐based near‐field microscopy, propagating surface phonon polaritons in mono‐ and bilayer hBN microcrystals are imaged. Phonon polaritons in monolayer hBN are confined in a volume about one million times smaller than the free‐space photons. Both the polariton dispersion and their wavelength–thickness scaling law are altered compared to those of hBN bulk counterparts. These changes are attributed to phonon hardening in monolayer‐thick crystals. The data reported here have bearing on applications of polaritons in metasurfaces and ultrathin optical elements.