Flat Bands and Chiral Optical Response of Moiré Insulators

Opto-twistronic Hall effect in a three-dimensional spiral lattice

Studies of moiré systems have explained the effect of superlattice modulations on their properties, demonstrating new correlated phases1. However, most experimental studies have focused on a few layers in two-dimensional systems. Extending twistronics to three dimensions, in which the twist extends into the third dimension, remains underexplored because of the challenges associated with the manual stacking of layers. Here we study three-dimensional twistronics using a self-assembled twisted spiral superlattice of multilayered WS2. Our findings show an opto-twistronic Hall effect driven by structural chirality and coherence length, modulated by the moiré potential of the spiral superlattice. This is an experimental manifestation of the noncommutative geometry of the system. We observe enhanced light-matter interactions and an altered dependence of the Hall coefficient on photon momentum. Our model suggests contributions from higher-order quantum geometric quantities to this observation, providing opportunities for designing quantum-materials-based optoelectronic lattices with large nonlinearities.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Chiral-magic angle of nanoimprint meta-device

The magic angle of Twistronics has attracted a lot of attention because of its peculiar electrical characteristics. Moiré patterns formed by the superlattice of a twisted bilayer change overall physical properties. Circular dichroism can also be manipulated through the generated moiré pattern. Here, we report a polymer-based twisted bilayer meta-device fabricated by multilayer nanoimprint technology and study the magic angle of chirality. The superlattice of the bilayer meta-device creates moiré patterns and brings unique chiral optical responses. The bilayer nanoimprint technology is developed for metasurfaces with relative twist angles. Via the twist angle control, polymer materials with a low refractive index can manipulate the electric field of the light and reveal the chiral magic angle. Moreover, the shape of the meta-atoms plays a key role in chiral magic angle tuning. The chirality engineering by the reported nanoimprint technology and chiral meta-devices may contribute to applications in chiral imaging, biomedical sensing, lasing, and tunable optical devices.

Recent Advances in Ultrathin Chiral Metasurfaces by Twisted Stacking

Artificial chiral nanostructures have been subjected to extensive research for their unique chiroptical activities. Planarized chiral films of ultrathin thicknesses are in particular demand for easy on-chip integration and improved energy efficiency as polarization-sensitive metadevices. Recently, controlled twisted stacking of two or more layers of nanomaterials, such as 2D van der Waals materials, ultrathin films, or traditional metasurfaces, at an angle has emerged as a general strategy to introduce optical chirality into achiral solid-state systems. This method endows new degrees of freedom, e.g., the interlayer twist angle, to flexibly engineer and tune the chiroptical responses without having to change the material or the design, thus greatly facilitating the development of multifunctional metamaterials. In this review, recent exciting progress in planar chiral metasurfaces are summarized and discussed from the viewpoints of building blocks, fabrication methods, as well as circular dichroism and modulation thereof in twisted stacked nanostructures. The review further highlights the ever-growing portfolio of applications of these chiral metasurfaces, including polarization conversion, information encryption, chiral sensing, and as an engineering platform for hybrid metadevices. Finally, forward-looking prospects are provided.

Moiré bands in twisted trilayer black phosphorene: effects of pressure and electric field

Twist-induced moiré bands and accompanied correlated phenomena have been extensively investigated in twisted hexagonal lattices with weak interlayer coupling. However, the formation of moiré bands in strongly coupled layered materials and their controlled tuning remain largely unexplored. Here, we systematically study the moiré bands in twisted trilayer black phosphorene (TTbP) and the influences of pressure and electric field on them. Moiré states can form in various TTbPs even when the twist angle is larger than 16° similar to that of twisted bilayer bP. However, different TTbPs show different localization patterns depending on the twisting layer, leading to distinct dipolar behaviors. While these moiré states become quasi-one-dimensional (1D) as the twist angle decreases, external pressure causes the crossover of moiré states from quasi-1D to 0D with a dramatic change in localization areas and greatly reduced bandwidth. Interestingly, compared to twisted bilayer and pristine bP, TTbPs show a much larger electric-field induced Stark effect, controllable by either the twist angle or twist layer. Our work thus demonstrates TTbP as an attractive platform to explore moiré-controlled electronic and optical properties, as well as tunable optoelectronic applications.

Monolayer Boron Nitride: Hyperspectral Imaging in the Deep Ultraviolet

The optical response of 2D materials and their heterostructures is the subject of intense research with advanced investigation of the luminescence properties in devices made of exfoliated flakes of few- down to one-monolayer thickness. Despite its prevalence in 2D materials research, hexagonal boron nitride (hBN) remains unexplored in this ultimate regime because of its ultrawide bandgap of about 6 eV and the technical difficulties related to performing microscopy in the deep-ultraviolet domain. Here, we report hyperspectral imaging at wavelengths around 200 nm in exfoliated hBN at low temperature. In monolayer boron nitride, we observe direct-gap emission around 6.1 eV. In marked contrast to transition metal dichalcogenides, the photoluminescence signal is intense in few-layer hBN, a result of the near unity radiative efficiency in indirect-gap multilayer hBN.

Enhanced tunable second harmonic generation from twistable interfaces and vertical superlattices in boron nitride homostructures

Broken symmetries induce strong even-order nonlinear optical responses in materials and at interfaces. Unlike conventional covalently bonded nonlinear crystals, van der Waals (vdW) heterostructures feature layers that can be stacked at arbitrary angles, giving complete control over the presence or lack of inversion symmetry at a crystal interface. Here, we report highly tunable second harmonic generation (SHG) from nanomechanically rotatable stacks of bulk hexagonal boron nitride (BN) crystals and introduce the term twistoptics to describe studies of optical properties in twistable vdW systems. By suppressing residual bulk effects, we observe SHG intensity modulated by a factor of more than 50, and polarization patterns determined by moiré interface symmetry. Last, we demonstrate greatly enhanced conversion efficiency in vdW vertical superlattice structures with multiple symmetry-broken interfaces. Our study paves the way for compact twistoptics architectures aimed at efficient tunable frequency conversion and demonstrates SHG as a robust probe of buried vdW interfaces.

Plasmon-Enhanced Near-Field Chirality in Twisted van der Waals Heterostructures

It is shown that chiral plasmons, characterized by a longitudinal magnetic moment accompanying the longitudinal charge plasmon, lead to electromagnetic near-fields that are also chiral. For twisted bilayer graphene, we estimate that the near-field chirality of screened plasmons can be several orders of magnitude larger than that of the related circularly polarized light. The chirality also manifests itself in a deflection angle that is formed between the direction of the plasmon propagation and its Poynting vector. Twisted van der Waals heterostructures might thus provide a novel platform to promote enantiomer-selective physio-chemical processes in chiral molecules without the application of a magnetic field or external nanopatterning that break time-reversal, mirror plane, or inversion symmetry, respectively.

Chiral Plasmons with Twisted Atomic Bilayers

van der Waals heterostructures of atomically thin layers with rotational misalignments, such as twisted bilayer graphene, feature interesting structural moiré superlattices. Because of the quantum coupling between the twisted atomic layers, light-matter interaction is inherently chiral; as such, they provide a promising platform for chiral plasmons in the extreme nanoscale. However, while the interlayer quantum coupling can be significant, its influence on chiral plasmons still remains elusive. Here we present the general solutions from full Maxwell equations of chiral plasmons in twisted atomic bilayers, with the consideration of interlayer quantum coupling. We find twisted atomic bilayers have a direct correspondence to the chiral metasurface, which simultaneously possesses chiral and magnetic surface conductivities, besides the common electric surface conductivity. In other words, the interlayer quantum coupling in twisted van der Waals heterostructures may facilitate the construction of various (e.g., bi-anisotropic) atomically-thin metasurfaces. Moreover, the chiral surface conductivity, determined by the interlayer quantum coupling, determines the existence of chiral plasmons and leads to a unique phase relationship (i.e., ±π/2 phase difference) between their transverse-electric (TE) and transverse-magnetic (TM) wave components. Importantly, such a unique phase relationship for chiral plasmons can be exploited to construct the missing longitudinal spin of plasmons, besides the common transverse spin of plasmons.