Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Controllable quantum scars induced by spin-orbit couplings in quantum dots

Spin-orbit couplings (SOCs), originating from the relativistic corrections in the Dirac equation, offer nonlinearity in the classical limit and are capable of driving chaotic dynamics. In a nanoscale quantum dot confined by a two-dimensional parabolic potential with SOCs, various quantum scar states emerge quasi-periodically in the eigenstates of the system, when the ratio of confinement energies in the two directions is nearly commensurable. The scars, displaying both quantum interference and classical trajectory features on the electron density, due to relativistic effects, serve as a bridge between the classical and quantum behaviors of the system. When the strengths of Rashba and Dresselhaus SOCs are identical, the chaos in the classical limit is eliminated as the classical Hamilton's equations become linear, leading to the disappearance of all quantum scar states. Importantly, the quantum scars induced by SOCs are robust against small perturbations of system parameters. With precise control achievable through external gating, the quantum scar induced by Rashba SOC is fully controllable and detectable.

Visualizing a single wavefront dislocation induced by orbital angular momentum in graphene

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains challenging. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularities, and result in robust single-wavefront dislocations in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes.

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules

Materials such as graphene and topological insulators host massless Dirac fermions that enable the study of relativistic quantum phenomena. Single quantum dots and coupled quantum dots formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique testbed to study atomic and molecular physics in the ultrarelativistic regime (particle speed close to the speed of light). Here we use a scanning tunnelling microscope to create and probe single and coupled electrostatically defined graphene quantum dots to unravel the magnetic-field responses of artificial relativistic nanostructures. We observe a giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV T^-1 and ~600μ_B (μ_B, Bohr magneton) in single graphene quantum dots. For coupled graphene quantum dots, Aharonov-Bohm oscillations and a strong Van Vleck paramagnetic shift of ~20 meV T^-2 are observed. Our findings provide fundamental insights into relativistic quantum dot states, which can be potentially leveraged for use in quantum information science.

Hexagonal-borocarbonitride (h-BCN) based heterostructure photocatalyst for energy and environmental applications: A review

Formulation of heterojunction with remarkable high efficiency by utilizing solar light is promising to synchronously overcome energy and environmental crises. In this concern, hexagonal-borocarbonitride (h-BCN) based Z-schemes have proved potential candidates due to their spatially separated oxidation and reduction sites, robust light-harvesting ability, high charge pair migration and separation, and strong redox ability. H-BCN has emerged as a hotspot in the research field as a metal-free photocatalyst with a tunable bandgap range of 0-5.5 eV. The BCN photocatalyst displayed synergistic benefits of both graphene and boron nitride. Herein, the review demonstrates the current state-of-the-art in the Z-scheme photocatalytic application with a special emphasis on the predominant features of their photoactivity. Initially, fundamental aspects and various synthesis techniques are discussed, including thermal polymerization, template-assisted, and template-free methods. Afterward, the reaction mechanism of direct Z-scheme photocatalysts and indirect Z-scheme (all-solid-state) are highlighted. Moreover, the emerging Step-scheme (S-scheme) systems are briefly deliberated to understand the charge transfer pathway mechanism with an induced internal electric field. This review critically aims to comprehensively summarize the photo-redox applications of various h-BCN-based heterojunction photocatalysts including CO₂ photoreduction, H₂ evolution, and pollutants degradation. Finally, some challenges and future direction of h-BCN-based Z-scheme photocatalyst in environmental remediation are also proposed.

Model for Nanopore Formation in Two-Dimensional Materials by Impact of Highly Charged Ions

We present a first qualitative description of the atomic dynamics in two-dimensional (2D) materials induced by the impact of slow, highly charged ions. We employ a classical molecular dynamics simulation for the motion of the target atoms combined with a Monte Carlo model for the diffusive charge transport within the layer. Depending on the velocity of charge transfer (hopping time or hole mobility) and the number of extracted electrons which, in turn, depends on the charge state of the impinging ions, we find regions of stability of the 2D structure as well as parameter combinations for which nanopore formation due to Coulomb repulsion is predicted.

Atomically resolved electronic properties in single layer graphene on α-Al2O3 (0001) by chemical vapor deposition

Metal-free chemical vapor deposition (CVD) of single-layer graphene (SLG) on c-plane sapphire has recently been demonstrated for wafer diameters of up to 300 mm, and the high quality of the SLG layers is generally characterized by integral methods. By applying a comprehensive analysis approach, distinct interactions at the graphene-sapphire interface and local variations caused by the substrate topography are revealed. Regions near the sapphire step edges show tiny wrinkles with a height of about 0.2 nm, framed by delaminated graphene as identified by the typical Dirac cone of free graphene. In contrast, adsorption of CVD SLG on the hydroxyl-terminated α-Al₂O₃ (0001) terraces results in a superstructure with a periodicity of (2.66 ± 0.03) nm. Weak hydrogen bonds formed between the hydroxylated sapphire surface and the π-electron system of SLG result in a clean interface. The charge injection induces a band gap in the adsorbed graphene layer of about (73 ± 3) meV at the Dirac point. The good agreement with the predictions of a theoretical analysis underlines the potential of this hybrid system for emerging electronic applications.

Characterization and Manipulation of Intervalley Scattering Induced by an Individual Monovacancy in Graphene

Intervalley scattering involves microscopic processes that electrons are scattered by atomic-scale defects on the nanoscale. Although central to our understanding of electronic properties of materials, direct characterization and manipulation of range and strength of the intervalley scattering induced by an individual atomic defect have so far been elusive. Using scanning tunneling microscope, we visualize and control intervalley scattering from an individual monovacancy in graphene. By directly imaging the affected range of monovacancy-induced intervalley scattering, we demonstrate that it is inversely proportional to the energy; i.e., it is proportional to the wavelength of massless Dirac fermions. A giant electron-hole asymmetry of the intervalley scattering is observed because the monovacancy is charged. By further charging the monovacancy, the bended electronic potential around the monovacancy softens the scattering potential, which, consequently, suppresses the intervalley scattering of the monovacancy.

Realizing Valley-Polarized Energy Spectra in Bilayer Graphene Quantum Dots via Continuously Tunable Berry Phases

The Berry phase plays an important role in determining many physical properties of quantum systems. However, tuning the energy spectrum of a quantum system via Berry phase is comparatively rare because the Berry phase is usually a fixed constant. Here, we report the realization of an unusual valley-polarized energy spectra via continuously tunable Berry phases in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about π to 2π by perpendicular magnetic fields. When the Berry phase equals π or 2π, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of π, large and continuously tunable valley-polarized energy spectra are realized. Our result reveals the Berry phase's essential role in valleytronics and the observed valley splitting, on the order of 10 meV at a magnetic field of 1 T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics.

Growth of wafer-scale graphene-hexagonal boron nitride vertical heterostructures with clear interfaces for obtaining atomically thin electrical analogs

Two-dimensional (2D) integrated circuits based on graphene (Gr) heterostructures have emerged as next-generation electronic devices. However, it is still challenging to produce high-quality and large-area Gr/hexagonal boron nitride (h-BN) vertical heterostructures with clear interfaces and precise layer control. In this work, a two-step metallic alloy-assisted epitaxial growth approach has been demonstrated for producing wafer-scale vertical hexagonal boron nitride/graphene (h-BN/Gr) heterostructures with clear interfaces. The heterostructures maintain high uniformity while scaling up and thickening. The layer number of both h-BN and graphene can be independently controlled by tuning the growth process. Furthermore, conductance measurements confirm that electrical hysteresis disappears on h-BN/Gr field-effect transistors, which is attributed to the h-BN dielectric surface. Our work blazes a trail toward next-generation graphene-based analog devices.

Equally Spaced Quantum States in van der Waals Epitaxy-Grown Nanoislands

Pursuing the confinement of linearly dispersive relativistic Fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van der Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially "simulate" the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Pérot fittings based on the relativistic Fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.

Demonstration of Controlled Hydrogen Release Using Rh@GQDs during Hydrolysis of NH3BH3

Achieving the controlled release of H₂ through an effective approach still faces many challenges. Herein, high-quality graphene quantum dots (GQDs) are synthesized from a new precursor, 1,2,4-trihydroxy benzene, and a multifunctional platform of Rh@GQDs is further developed for the controlled H₂ evolution upon the hydrolysis of NH₃BH₃ (AB). More importantly, the designing concepts of multistep and stepless speed controls have been introduced in the domains of both H₂ evolution for the first time. Through a novel designing protocol, the rate of H₂ evolution can be freely regulated and constantly varied on demand by means of chelation between Zn²⁺ and ethylene diamine tetraacetic acid (EDTA). The density functional theory calculation indicates that Zn²⁺ has the priority to be adsorbed onto Rh(100) due to its larger adsorption energy (107.98 kcal·mol^-1) than that of AB (36.36 kcal·mol^-1). A controlling mechanism is presented such that Zn²⁺ will cover the active sites of the nanocatalyst to prevent the H₂ evolution, and EDTA can chelate Zn²⁺ to reactivate the nanocatalyst for the production of H₂, greatly facilitating use of this strategy in other catalytic reactions. Moreover, it is demonstrated that the protocol is equally valid for diverse hydrogen storage materials. Therefore, this work not only establishes whole new concepts for the controlled production of H₂ but also explains their mechanism, thus remarkably advancing the utilization of H₂ energy and significantly enlightening the controlled process of catalysis.

Epitaxial Intercalation Growth of Scalable Hexagonal Boron Nitride/Graphene Bilayer Moiré Materials with Highly Convergent Interlayer Angles

Vertically stacked two-dimensional van der Waals (vdW) heterostructures with specific interlayer angles exhibit peculiar physical properties. Nowadays, most of the stacked layers are fabricated by mechanical exfoliation followed by precise transfer and alignment with micrometer spatial accuracy. This stringent ingredient of sample preparation limits the productivity of device fabrication and the reproducibility of device performance. Here, we demonstrate the one-pot chemical vapor deposition growth of hexagonal boron nitride (hBN)/graphene bilayers with a high-purity moiré phase. The epitaxial intercalation of graphene under a hydrogen-terminated hBN template leads to convergent interlayer angles of less than 0.5°. The near 0° stacking angle shows almost 2 orders of magnitude higher likelihood of occurrence compared with angles larger than 0.5°. The bilayers show a substantial enhancement of carrier mobility compared with monolayer graphene owing to protection from the top hBN layer. Our work proposes a large-scale fabrication method of hBN/graphene bilayers with a high uniformity and controlled interlayer rotation and will promote the production development for high-quality vdW heterostructures.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Strongly Absorbing Nanoscale Infrared Domains within Strained Bubbles at hBN-Graphene Interfaces

Graphene has great potential for use in infrared (IR) nanodevices. At these length scales, nanoscale features, and their interaction with light, can be expected to play a significant role in device performance. Bubbles in van der Waals heterostructures are one such feature, which have recently attracted considerable attention, thanks to their ability to modify the optoelectronic properties of two-dimensional (2D) materials through strain. Here, we use scattering-type scanning near-field optical microscopy (sSNOM) to measure the nanoscale IR response from a network of variously shaped bubbles in hexagonal boron nitride (hBN)-encapsulated graphene. We show that within individual bubbles there are distinct domains with strongly enhanced IR absorption. The IR domain boundaries coincide with ridges in the bubbles, which leads us to attribute them to nanoscale strain domains. We further validate the strain distribution in the graphene by means of confocal Raman microscopy and vector decomposition analysis. This shows intricate and varied strain configurations, in which bubbles of different shape induce more bi- or uniaxial strain configurations. This reveals pathways toward future strain-based graphene IR devices.

Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference

Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2π. This nontrivial topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties. Here we show that the quantum interference due to intervalley scattering induced by single-atom vacancies or impurities provides insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct valleys with opposite chirality undergo a rotation of pseudospin that results in the Friedel oscillation with wavefront dislocations. The number of dislocations reflects the information about pseudospin texture and hence can be used to measure the Berry phase. As demonstrated both experimentally and theoretically, the Friedel oscillation, depending on the single-atom vacancy or impurity at different sublattices, can exhibit N=4, 2, or 0 additional wavefronts, characterizing the 2π Berry phase of the bilayer graphene. Our results provide a comprehensive study of the intervalley quantum interference in bilayer graphene and can be extended to multilayer graphene, shedding light on the pseudospin physics.

Comprehensive Electrostatic Modeling of Exposed Quantum Dots in Graphene/Hexagonal Boron Nitride Heterostructures

Recent experimental advancements have enabled the creation of tunable localized electrostatic potentials in graphene/hexagonal boron nitride (hBN) heterostructures without concealing the graphene surface. These potentials corral graphene electrons yielding systems akin to electrostatically defined quantum dots (QDs). The spectroscopic characterization of these exposed QDs with the scanning tunneling microscope (STM) revealed intriguing resonances that are consistent with a tunneling probability of 100% across the QD walls. This effect, known as Klein tunneling, is emblematic of relativistic particles, underscoring the uniqueness of these graphene QDs. Despite the advancements with electrostatically defined graphene QDs, a complete understanding of their spectroscopic features still remains elusive. In this study, we address this lapse in knowledge by comprehensively considering the electrostatic environment of exposed graphene QDs. We then implement these considerations into tight binding calculations to enable simulations of the graphene QD local density of states. We find that the inclusion of the STM tip's electrostatics in conjunction with that of the underlying hBN charges reproduces all of the experimentally resolved spectroscopic features. Our work provides an effective approach for modeling the electrostatics of exposed graphene QDs. The methods discussed here can be applied to other electrostatically defined QD systems that are also exposed.

Movable Valley Switch Driven by Berry Phase in Bilayer-Graphene Resonators

Berry phase, the geometric phase accumulated over a closed loop in parameter space during an adiabatic cyclic evolution, has been demonstrated to play an important role in many quantum systems since its discovery. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2π, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene p-n junction resonators. In our experiment, the resonators are generated by combining the electric field of a scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2π continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer-graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.

Valley Polarization and Inversion in Strained Graphene via Pseudo-Landau Levels, Valley Splitting of Real Landau Levels, and Confined States

It is quite easy to control spin polarization and the spin direction of a system via magnetic fields. However, there is no such direct and efficient way to manipulate the valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. Pseudomagnetic fields, which are quite different from real magnetic fields, point in opposite directions at the two distinct valleys of graphene. Therefore, the coexistence of pseudomagnetic fields and real magnetic fields leads to imbalanced effective magnetic fields at two distinct valleys of graphene. This allows us to control the valley in graphene as conveniently as the electron spin. In this work, we report a consistent observation of valley polarization and inversion in strained graphene via pseudo-Landau levels, splitting of real Landau levels, and valley splitting of confined states using scanning tunneling spectroscopy. Our results highlight a pathway to valleytronics in strained graphene-based platforms.

Nanoscale boron carbonitride semiconductors for photoredox catalysis

The conversion of solar energy to chemical energy achieved by photocatalysts comprising homogeneous transition-metal based systems, organic dyes, or semiconductors has received significant attention in recent years. Among these photocatalysts, boron carbon nitride (BCN) materials, as an emerging class of metal-free heterogeneous semiconductors, have extended the scope of photocatalysts due to their good performance and Earth abundance. The combination of boron (B), carbon (C), and nitrogen (N) constitutes a ternary system with large surface area and abundant activity sites, which together contribute to the good performance for reduction reactions, oxidation reactions and orchestrated both reduction and oxidation reactions. This Minireview reports the methods for the synthesis of nanoscale hexagonal boron carbonitride (h-BCN) and describes the latest advances in the application of h-BCN materials as semiconductor photocatalysts for sustainable photosynthesis, such as water splitting, reduction of CO₂, acceptorless dehydrogenation, oxidation of sp³ C-H bonds, and sp² C-H functionalization. h-BCN materials may have potential for applications in other organic transformations and industrial manufacture in the future.

Real Space Observation of Electronic Coupling between Self-Assembled Quantum Dots

The control of quantum coupling between nano-objects is essential to quantum technologies. Confined nanostructures, such as cavities, resonators, or quantum dots, are designed to enhance interactions between electrons, photons, or phonons, giving rise to new properties, on which devices are developed. The nature and strength of these interactions are often measured indirectly on an assembly of dissimilar objects. Here, we adopt an innovative point of view by directly mapping the coupling of single nanostructures using scanning tunneling microscopy and spectroscopy (STM and STS). We take advantage of the unique capabilities of STM/STS to map simultaneously the nano-object's morphology and electronic density in order to observe in real space the electronic coupling of pairs of In(Ga)As/GaAs self-assembled quantum dots (QDs), forming quantum dot molecules (QDMs). Differential conductance maps d I/d V ( E, x, y) demonstrate the presence of an effective electronic coupling, leading to bonding and antibonding states, even for dissymmetric QDMs. The experimental results are supported by numerical simulations. The actual geometry of the QDMs is taken into account to determine the strength of the coupling, showing the crucial role of quantum dot size and pair separation for device growth optimization.

Sub-10 nm stable graphene quantum dots embedded in hexagonal boron nitride

Graphene quantum dots (GQDs), a zero-dimensional material system with distinct physical properties, have great potential in the applications of photonics, electronics, photovoltaics, and quantum information. In particular, GQDs are promising candidates for quantum computing. In principle, a sub-10 nm size is required for GQDs to present the intrinsic quantum properties. However, with such an extreme size, GQDs have predominant edges with lots of active dangling bonds and thus are not stable. Satisfying the demands of both quantum size and stability is therefore of great challenge in the design of GQDs. Herein we demonstrate the fabrication of sub-10 nm stable GQD arrays by embedding GQDs into large-bandgap hexagonal boron nitride (h-BN). With this method, the dangling bonds of GQDs were passivated by the surrounding h-BN lattice to ensure high stability, meanwhile maintaining their intrinsic quantum properties. The sub-10 nm nanopore array was first milled in h-BN using an advanced high-resolution helium ion microscope and then GQDs were directly grown in them through the chemical vapour deposition process. Stability analysis proved that the embedded GQDs show negligible property decay after baking at 100 °C in air for 100 days. The success in preparing sub-10 nm stable GQD arrays will promote the physical exploration and potential applications of this unique zero-dimensional in-plane quantum material.

Unique Spin Vortices and Topological Charges in Quantum Dots with Spin-orbit Couplings

Spin textures of one or two electrons in a quantum dot with Rashba or Dresselhaus spin-orbit couplings reveal several intriguing properties. We show here that even at the single-electron level stable spin vortices with tunable topological charges exist. These topological textures appear in the ground state of the dots. The textures are stabilized by time-reversal symmetry breaking and are robust against the eccentricity of the dot. The topological charge is directly related to the sign of the z component of the spin in a large dot, allowing a direct probe of its topological properties. This would clearly pave the way to possible future topological spintronics. The phenomenon of spin vortices persists for the interacting two-electron dot in the presence of a magnetic field.