Two-dimensional Superlattice Research Articles

Two-dimensional-lattice-confined single-molecule-like aggregates.

Intermolecular distance largely determines the optoelectronic properties of organic matter. Conventional organic luminescent molecules are commonly used either as aggregates or as single molecules that are diluted in a foreigner matrix. They have garnered great research interest in recent decades for a variety of applications, including light-emitting diodes1,2, lasers3-5 andquantum technologies6,7, among others8-10. However, there is still a knowledge gap on how these molecules behave between the aggregation and dilution states. Here we report an unprecedented phase of molecular aggregate that forms in a two-dimensional hybrid perovskite superlattice with a near-equilibrium distance, which we refer to as a single-molecule-like aggregate (SMA). By implementing two-dimensional superlattices, the organic emitters are held in proximity, but, surprisingly, remain electronically isolated, thereby resulting in a near-unity photoluminescence quantum yield, akin to that of single molecules. Moreover, the emitters within the perovskite superlattices demonstrate strong alignment and dense packing resembling aggregates, allowing for the observation of robust directional emission, substantially enhanced radiative recombination and efficient lasing. Molecular dynamics simulations together with single-crystal structure analysis emphasize the critical role of the internal rotational and vibrational degrees of freedom of the molecules in the two-dimensional lattice for creating the exclusive SMA phase. This two-dimensional superlattice unifies the paradoxical properties of single molecules and aggregates, thus offering exciting possibilities for advanced spectroscopic and photonic applications.

Towards the scalable synthesis of two-dimensional heterostructures and superlattices beyond exfoliation and restacking.

Two-dimensional transition metal dichalcogenides, which feature atomically thin geometry and dangling-bond-free surfaces, have attracted intense interest for diverse technology applications, including ultra-miniaturized transistors towards the subnanometre scale. A straightforward exfoliation-and-restacking approach has been widely used for nearly arbitrary assembly of diverse two-dimensional (2D) heterostructures, superlattices and moiré superlattices, providing a versatile materials platform for fundamental investigations of exotic physical phenomena and proof-of-concept device demonstrations. While this approach has contributed importantly to the recent flourishing of 2D materials research, it is clearly unsuitable for practical technologies. Capturing the full potential of 2D transition metal dichalcogenides requires robust and scalable synthesis of these atomically thin materials and their heterostructures with designable spatial modulation of chemical compositions and electronic structures. The extreme aspect ratio, lack of intrinsic substrate and highly delicate nature of the atomically thin crystals present fundamental difficulties in material synthesis. Here we summarize the key challenges, highlight current advances and outline opportunities in the scalable synthesis of transition metal dichalcogenide-based heterostructures, superlattices and moiré superlattices.

The Nested Topological Band-Gap Structure for the Periodic Domain Walls in a Photonic Super-Lattice

We study the nested topological band-gap structure of one-dimensional (1D) photonic super-lattices. One cell of the super-lattice is composed of two kinds of photonic crystals (PhCs) with different topologies so that there is a domain wall (DW) state at the interface between the two PhCs. We find that the coupling of periodic DWs could form a new band-gap structure inside the original gap. The new band-gap structure could be topologically nontrivial, and a topological phase transition can occur if the structural or material parameters of the PhCs are tuned. Theoretically, we prove that the Hamiltonian of such coupled DWs can be reduced to the simple Su–Schrieffer–Heeger (SSH) model. Then, if two super-lattices carrying different topological phases are attached, a new topological interface state can occur at the interface between the two super-lattices. Finally, we find the nested topological band-gap structure in two-dimensional (2D) photonic super-lattices. Consequently, such nested topological structures can widely exist in complex super-lattices. Our work improves the topological study of photonic super-lattices and provides a new way to realize topological interface states and topological phase transitions in 1D and 2D photonic super-lattices. Topological interface states in super-lattices are sensitive to frequency and have high accuracy, which is desired for high-performance filters and high-finesse cavities.

Interfacial Charge-Transfer Excitonic Insulator in a Two-Dimensional Organic-Inorganic Superlattice.

Excitonic insulators are long-sought-after quantum materials predicted to spontaneously open a gap by the Bose condensation of bound electron-hole pairs, namely, excitons, in their ground state. Since the theoretical conjecture, extensive efforts have been devoted to pursuing excitonic insulator platforms for exploring macroscopic quantum phenomena in real materials. Reliable evidence of excitonic character has been obtained in layered chalcogenides as promising candidates. However, owing to the interference of intrinsic lattice instabilities, it is still debatable whether those features, such as the charge density wave and gap opening, are primarily driven by the excitonic effect or by the lattice transition. Herein, we develop an intercalation chemistry strategy for obtaining a novel charge-transfer excitonic insulator in organic-inorganic superlattice interfaces that serves as an ideal platform to decouple the excitonic effect from the lattice effect. In this system, we observe a narrow excitonic gap, formation of a charge density wave without periodic lattice distortion, and metal-insulator transition, providing visualized evidence of exciton condensation occurring in thermal equilibrium. Our findings identify self-assembly intercalation chemistry as a new strategy for developing novel excitonic insulators.

Interface Modulation of 2D Superlattice Heterostructures with Oxygen-enriched Sites and Dissolution Restraint for Effective Rare-earth Elements Extraction

Effective recovery of rare earth elements from wastewater is crucial for the modern industry, as well as for protecting the human health and ecosystem. Nevertheless, it is still challenging to realize efficient and selective low-concentration rare earth extraction in systems containing high levels competing metal ions. Here, we report on the fabrication of two-dimensional superlattice heterostructures (VOGO-x) through the alternating restacking of VOPO4 nanosheets and GO-PDDA nanosheets via electrostatic self-assembly. The meticulously organized molecular scale of superlattice heterostructures enable the full exposure of accessible adsorption sites and facilitate the transport of rare earth ions, meanwhile the abundant oxygen-containing phosphate groups within the interlayer can realize selective rare earth ions extraction. Furthermore, the tunable interlayer interaction can promote structure stability to prevent dissolution. Consequently, VOGO-11 possesses excellent rare earth adsorption performance, with a saturated adsorption capacity (Nd(III) 631.52 mg/g, Dy(III) 689.48 mg/g, Lu(III) 716.06 mg/g), high utilization rate of adsorption sites and short adsorption equilibrium time of simply 10 min in the REE aqueous solution. Furthermore, VOGO-11 exhibits outstanding selective rare earth adsorption ability over a wide range of metal ions in the low-concentration simulated wastewater and actual leaching tailings. These results demonstrate the material’s promising potential in capturing rare earth ions and pave the way to the development of two-dimensional superlattice heterostructures through interface modulation for effective rare earth extraction.

Chaos-Assisted Dynamical Tunneling in Flat Band Superwires.

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities.

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

Macroscopic Superlattice Membranes Self-Assembled from Gold Nanobipyramids with Precisely Tunable Tip Arrangements for SERS.

A persistent challenge in utilizing Au nanocrystals for surface-enhanced Raman spectroscopy (SERS) lies in achieving controllable superstructures that maximize SERS performance. Here, a novel strategy is proposed to enhance the SERS performance by precisely adjusting the tip arrangements of Au nanobipyramids (BPs) in two-dimensional (2D) superlattices (SLs). This is achieved through ligand-exchange of Au BPs, followed by liquid-air interfacial assembly, resulting in large-area, transferrable SL membranes. The key to controlling the arrangement of Au BPs in the SLs is the regulation of the amount of free ligands added during self-assembly, which allows for the precise formation of various configurations such as tilted SLs, tip-on-tip SLs, and tip-to-tip SLs. Among these configurations, tip-on-tip SLs exhibit the highest enhancement factor for SERS, reaching an impressive value of 1.95×108, with uniform and consistent SERS signals across a large area. The experimental findings are further corroborated by simulations using the finite element method. This study establishes an efficient method for engineering the microstructure of 2D SLs composed of Au BPs, highlighting the importance of fine-tuning the tip arrangements of Au BPs to regulate SERS performance.

Photostimulated Nernst effect in two-dimensional compositional semiconductor superlattices under the influence of confined phonons

The photostimulated Nernst effect in compositional semiconductor superlattices under the influence of a confined acoustic phonon is studied by using the quantum kinetic equation. The case of the confined electron-confined acoustic phonon scattering process is examined in detail. The obtained analytical results reveal that the Nernst coefficient (NC) depends on the external field such as magnetic field B, the frequency Ω, and the amplitude E 0 of the electromagnetic wave in a complicated way but also like a function of the temperature of the system and the period of the superlattice. It also depends on the quantum number m-describing the confined acoustic phonon. The theoretical results are depicted and discussed for GaAs/AlxGa 1 − xAs compositional semiconductors superlattices. The results indicate that the Shubnikov-De hass oscillations have appeared. The confined phonons make the magnitude of the Nernst coefficient higher and more obvious than the case of a bulk phonon. In addition, the magneto-photon resonance condition is also proved. Besides, the Nernst coefficient decreases significantly as the temperature increases. The oscillations Nernst coefficient in a magnetic field are consistent with the previous experimental.

Temperature-dependent morphology and composition of ultra-thin GeSn epilayers prepared by remote plasma enhanced chemical vapor deposition

Two distinct ultra-thin Ge1−xSnx (x ≤ 0.1) epilayers were deposited on (001) Si substrates at 457 and 313 °C through remote plasma-enhanced chemical vapor deposition. These films are considered potential initiation layers for synthesizing thick epitaxial GeSn films. The GeSn film deposited at 313 °C has a thickness of 10 nm and exhibits a highly epitaxial continuous structure with its lattice being compressed along the interface plane to coherently match Si without mismatch dislocations. The GeSn film deposited at 457 °C exhibits a discrete epitaxial island-like morphology with a peak height of ∼30 nm and full-width half maximum (FWHM) varying from 20 to 100 nm. GeSn islands with an FWHM smaller than 20 nm are defect free, whereas those exceeding 25 nm encompass nanotwins and/or stacking faults. The GeSn islands form two-dimensional modulated superlattice structures at the interface with Si. The GeSn film deposited at 457 °C possesses a lower Sn content compared to the one deposited at lower temperature. The potential impact of using these two distinct ultra-thin layers as initiation layers for the direct growth of thicker GeSn epitaxial films on (001) Si substrates is discussed.

Area-selective atomic layer deposition on 2D monolayer lateral superlattices

The advanced patterning process is the basis of integration technology to realize the development of next-generation high-speed, low-power consumption devices. Recently, area-selective atomic layer deposition (AS-ALD), which allows the direct deposition of target materials on the desired area using a deposition barrier, has emerged as an alternative patterning process. However, the AS-ALD process remains challenging to use for the improvement of patterning resolution and selectivity. In this study, we report a superlattice-based AS-ALD (SAS-ALD) process using a two-dimensional (2D) MoS2-MoSe2 lateral superlattice as a pre-defining template. We achieved a minimum half pitch size of a sub-10 nm scale for the resulting AS-ALD on the 2D superlattice template by controlling the duration time of chemical vapor deposition (CVD) precursors. SAS-ALD introduces a mechanism that enables selectivity through the adsorption and diffusion processes of ALD precursors, distinctly different from conventional AS-ALD method. This technique facilitates selective deposition even on small pattern sizes and is compatible with the use of highly reactive precursors like trimethyl aluminum. Moreover, it allows for the selective deposition of a variety of materials, including Al2O3, HfO2, Ru, Te, and Sb2Se3.

Functional nanoporous graphene superlattice

Two-dimensional (2D) superlattices, formed by stacking sublattices of 2D materials, have emerged as a powerful platform for tailoring and enhancing material properties beyond their intrinsic characteristics. However, conventional synthesis methods are limited to pristine 2D material sublattices, posing a significant practical challenge when it comes to stacking chemically modified sublattices. Here we report a chemical synthesis method that overcomes this challenge by creating a unique 2D graphene superlattice, stacking graphene sublattices with monodisperse, nanometer-sized, square-shaped pores and strategically doped elements at the pore edges. The resulting graphene superlattice exhibits remarkable correlations between quantum phases at both the electron and phonon levels, leading to diverse functionalities, such as electromagnetic shielding, energy harvesting, optoelectronics, and thermoelectrics. Overall, our findings not only provide chemical design principles for synthesizing and understanding functional 2D superlattices but also expand their enhanced functionality and extensive application potential compared to their pristine counterparts.

Nonlinear Landau Fan Diagram for Graphene Electrons Exposed to a Moiré Potential.

Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and field. This fan looks identical, irrespective of the dispersion and field dependence of the Landau level energy. This is no surprise because the position of conductance minima depends solely on the level degeneracy that is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they also create just linear fans for identical reasons. Here, we report conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule and form nonlinear trajectories in the density-field plane. We attribute this anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown-induced open orbits.

Symmetry-controllable assembly of Au nanooctahedron superlattice membranes for SERS.

We present a novel approach to adjust the symmetry of Au octahedral nanocrystals in two-dimensional superlattices. By modifying the content of free polymeric ligands added in the nanocrystal solution, we achieve Au nanocrystal superlattices with tip-on-tip arrangements that significantly enhance the surface-enhanced Raman spectroscopy performance.

Controllable synthesis of star-shaped FeCoMnOx nanocrystals and their self-assembly into superlattices with low-packing densities.

We present a novel method for synthesizing monodisperse, star-shaped FeCoMnOx nanocrystals with tunable concavity. Through liquid-air interfacial assembly, these colloidal nanostars can form two-dimensional superlattices, which are characterized by low packing densities. Notably, the ability to adjust the degree of concavity of nanostars allows for the tuning of the packing symmetry of the assembled superlattices.

Defect-Regulated Two-Dimensional Superlattice of Holey g-C3N4-TiO2 Nanohybrids: Contrasting Influence of Vacancy Content on Hybridization Impact and Photocatalyst Performance.

Defect engineering provides an effective way to explore efficient nanostructured catalysts. Herein, we synthesize defect-regulated two-dimensional superlattices comprising interstratified holey g-C3N4 and TiO2 monolayers with tailorable interfacial coupling. Using this interfacial-coupling-controlled hybrid system, a strong interdependence among vacancy content, performance, and interfacial coupling was elucidated, offering key insights for the design of high-performance catalysts. The defect-optimized g-C3N4-TiO2 superlattice exhibited higher photocatalytic activity toward visible-light-induced N2 fixation (∼1.06 mmol g-1 h-1) than defect-unoptimized and disorderly assembled g-C3N4-TiO2 homologues. The high photocatalytic performance of g-C3N4-TiO2 was attributed to the hybridization-induced defect creation, facilitated hydrogenation of adsorbed nitrogen, and improvement in N2 adsorption and charge transport. A comparison of the defect-dependent photocatalytic activity of g-C3N4, g-C3N4 nanosheets, and g-C3N4-TiO2 revealed the presence of optimal defect content for improving photocatalytic performance and the continuous increase of hybridization impact with the defect content. Sophisticated mutual influence among defect, electronic coupling, and photocatalytic ability underscores the importance of defect fine control in exploring high-performance hybrid photocatalysts. Along with the DFT calculation, the excellent photocatalyst performance of defect-optimized g-C3N4-TiO2 can be ascribed to the promotion of the uphill *N hydrogenation step as well as to enhancement of N2 adsorption, charge transfer kinetics, and mass transports.

One-Dimensionally Arranged Quantum-Dot Superstructures Guided by a Supramolecular Polymer Template.

Colloidal quantum dots (QDs) exhibit important photophysical properties, such as long-range energy diffusion, miniband formation, and collective photoluminescence, when aggregated into well-defined superstructures, such as three-dimensional (3D) and two-dimensional (2D) superlattices. However, the construction of one-dimensional (1D) QD superstructures, which have a simpler arrangement, is challenging; therefore, the photophysical properties of 1D-arranged QDs have not been studied previously. Herein, we report a versatile strategy to obtain 1D-arranged QDs using a supramolecular polymer (SP) template. The SP is composed of self-assembling cholesterol derivatives containing two amide groups for hydrogen bonding and a carboxyl group as an adhesion moiety on the QDs. Upon mixing the SP and dispersed QDs in low-polarity solvents, the QDs self-adhered to the SP and self-arranged into 1D superstructures through van der Waals interactions between the surface organic ligands of the QDs, as confirmed by transmission electron microscopy. Furthermore, we revealed efficient photoinduced fluorescence resonance energy transfer between the 1D-arranged QDs by an in-depth analysis of the emission spectra and decay curves.

Tuning perovskite nanocrystal superlattices for superradiance in the presence of disorder.

The cooperative emission of interacting nanocrystals is an exciting topic fueled by recent reports of superfluorescence and superradiance in assemblies of perovskite nanocubes. Several studies estimated that coherent coupling is localized to a small fraction of nanocrystals (10-7-10-3) within the assembly, raising questions about the origins of localization and ways to overcome it. In this work, we examine single-excitation superradiance by calculating radiative decays and the distribution of superradiant wave function in two-dimensional CsPbBr3 nanocube superlattices. The calculations reveal that the energy disorder caused by size distribution and large interparticle separations reduces radiative coupling and leads to the excitation localization, with the energy disorder being the dominant factor. The single-excitation model clearly predicts that, in the pursuit of cooperative effects, having identical nanocubes in the superlattice is more important than achieving a perfect spatial order. The monolayers of large CsPbBr3 nanocubes (LNC = 10-20nm) are proposed as model systems for experimental tests of superradiance under conditions of non-negligible size dispersion, while small nanocubes (LNC = 5-10nm) are preferred for realizing the Dicke state under ideal conditions.

Two-Dimensional Artificial Ge Superlattice Confining in Electronic Kagome Lattice Potential Valleys.

Constructing two-dimensional (2D) artificial superlattices based on single-atom and few-atom nanoclusters is of great interest for exploring exotic physics. Here we report the realization of two types of artificial germanium (Ge) superlattice self-confined by a R25.3° superstructure of bismuth (Bi) induced electronic kagome lattice potential valleys. Scanning tunneling microscopy measurements demonstrate that Ge atoms prefer to be confined in the center of the Bi electronic kagome lattice, forming a single-atom superlattice at 120 K. In contrast, room temperature grown Ge atoms and clusters are confined in the sharing triangle corner and the center, respectively, of the kagome lattice potential valleys, forming an artificial honeycomb superlattice. First-principle calculations and Mulliken population analysis corroborate that our reported atomically thin Bi superstructure on Au(111) has a kagome surface potential valley with the center of the inner Bi hexagon and the space between the outer Bi hexagons being energetically favorable for trapping Ge atoms.

Heterodimensional superlattices based on two-dimensional materials

Two-dimensional (2D) superlattices are promising candidates for future technological applications due to their unique electronic structure and exotic properties. Heterodimensional superlattices, consisting of 2D and other dimensional (0D, 1D, 2D, 3D) structural units, extend the applications of 2D superlattices to spintronics, thermoelectrics, and energy storage. In this perspective, we highlight the recent progress in heterodimensional superlattices based on 2D materials. First, we introduce the classification and properties of heterodimensional superlattices, including 3D/2D, 1D/2D, 2D/0D, and hybrid multidimensional superlattices. Second, the potential applications of 2D heterodimensional superlattices are discussed. Finally, we point out the current challenges and provide an outlook in the field of heterodimensional superlattices.