Size effects on atomic collapse in the dice lattice

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices.

Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Quantum simulator to emulate lower-dimensional molecular structure

Bottom-up quantum simulators have been developed to quantify the role of various interactions, dimensionality, and structure in creating electronic states of matter. Here, we demonstrated a solid-state quantum simulator emulating molecular orbitals, based solely on positioning individual cesium atoms on an indium antimonide surface. Using scanning tunneling microscopy and spectroscopy, combined with ab initio calculations, we showed that artificial atoms could be made from localized states created from patterned cesium rings. These artificial atoms served as building blocks to realize artificial molecular structures with different orbital symmetries. These corresponding molecular orbitals allowed us to simulate two-dimensional structures reminiscent of well-known organic molecules. This platform could further be used to monitor the interplay between atomic structures and the resulting molecular orbital landscape with submolecular precision.

Phases of Wilson Lines in Conformal Field Theories

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. This result is universal: in large enough representations, Wilson lines are screened by the charged matter fields. We observe that the onset of the screening instability is associated with fixed-point mergers. We study this phenomenon in a variety of applications. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in 3+1 dimensions and determine the screening cloud due to bosons or fermions. We also study QED in 2+1 dimensions in the large N_{f} limit and identify the nontrivial conformal Wilson lines. We briefly discuss 't Hooft lines in 3+1-dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In non-Abelian gauge theories with S duality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.

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.

Molecular Collapse States in Graphene/WSe_{2} Heterostructure Quantum Dots

In relativistic physics, both atomic collapse in a heavy nucleus and Hawking radiation in a black hole are predicted to occur through the Klein tunneling process that couples particles and antiparticles. Recently, atomic collapse states (ACSs) were explicitly realized in graphene because of its relativistic Dirac excitation with a large "fine structure constant." However, the essential role of the Klein tunneling in the ACSs remains elusive in experiment. Here we systematically study the quasibound states in elliptical graphene quantum dots (GQDs) and two coupled circular GQDs. Bonding and antibonding molecular collapse states formed by two coupled ACSs are observed in both systems. Our experiments supported by theoretical calculations indicate that the antibonding state of the ACSs will change into a Klein-tunneling-induced quasibound state revealing deep connection between the ACSs and the Klein tunneling.

Numerical package for QFT calculations of defect-induced phenomena in graphene

We introduce a computationally efficient method based on the path integral formalism to describe defect-modified graphene. By taking into account the entire Brillouin zone, our approach respects the lattice symmetry and can be used to investigate both short-range and long-range effects. The proposed method's key advantage is that the computational complexity does not increase with the system size, scaling, instead, with the number of defects. Our aim is to make the quantum-field calculations in graphene accessible to the experimental community. We demonstrate our method's capabilities by exploring the well-known graphene-mediated Ruderman-Kittel-Kasuya-Yoshida interaction and by performing a detailed study of the atomic collapse in the presence of defects.

Gate-Tunable Resonance State and Screening Effects for Proton-Like Atomic Charge in Graphene

The ability to create a robust and well-defined artificial atomic charge in graphene and understand its carrier-dependent electronic properties represents an important goal toward the development of graphene-based quantum devices. Herein, we devise a new pathway toward the atomically precise embodiment of point charges into a graphene lattice by posterior (N) ion implantation into a back-gated graphene device. The N dopant behaves as an in-plane proton-like charge manifested by formation of the characteristic resonance state in the conduction band. Scanning tunneling spectroscopy measurements at varied charge carrier densities reveal a giant energetic renormalization of the resonance state up to 220 meV with respect to the Dirac point, accompanied by the observation of gate-tunable long-range screening effects close to individual N dopants. Joint density functional theory and tight-binding calculations with modified perturbation potential corroborate experimental findings and highlight the short-range character of N-induced perturbation.

Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material

Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe₅) and hafnium pentatelluride (HfTe₅), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe₅ can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (E_F). These features are consistent with the theoretical prediction of a magnetic field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

Electronic Quantum Materials Simulated with Artificial Model Lattices

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Coexistence of electron whispering-gallery modes and atomic collapse states in graphene/WSe2 heterostructure quantum dots

The relativistic massless charge carriers with a Fermi velocity of about c/300 in graphene enable us to realize two distinct types of resonances (here, c is the speed of light in vacuum). One is the electron whispering-gallery mode in graphene quantum dots arising from the Klein tunneling of the massless Dirac fermions. The other is the atomic collapse state, which has never been observed in experiment with real atoms due to the difficulty of producing heavy nuclei with charge Z > 170; however, they can be realized near a Coulomb impurity in graphene with a charge Z ≥ 1 because of the "small" velocity of the Dirac excitations. Here we demonstrate that both the electron whispering-gallery modes and atomic collapse states coexist in graphene/WSe₂ heterostructure quantum dots due to the Coulomb-like potential near their edges. By applying a perpendicular magnetic field, we explore the evolution from the atomic collapse states to unusual Landau levels in the collapse regime.

Measuring and Tuning the Potential Landscape of Electrostatically Defined Quantum Dots in Graphene

We use Kelvin probe force microscopy (KPFM) to probe the carrier-dependent potential of an electrostatically defined quantum dot (QD) in a graphene/hexagonal boron nitride (hBN) heterostructure. We show that gate-dependent measurements enable a calibration scheme that corrects for uncertainty inherent in typical KPFM measurements and accurately reconstructs the potential well profile. Our measurements reveal how the well changes with carrier concentration, which we associate with the nonlinear dependence of graphene's work function on carrier density. These changes shift the energy levels of quasi-bound states in the QD which we can measure via scanning tunneling spectroscopy (STS). We show that the experimentally extracted energy levels closely compare with wave functions calculated from the reconstructed KPFM data. This methodology, where KPFM and STS data are simultaneously acquired from 2D materials, allows the quasiparticle response to an electrostatic potential to be determined in a self-consistent way.

On the Impact of Substrate Uniform Mechanical Tension on the Graphene Electronic Structure

Employing density functional theory calculations, we obtain the possibility of fine-tuning the bandgap in graphene deposited on the hexagonal boron nitride and graphitic carbon nitride substrates. We found that the graphene sheet located on these substrates possesses the semiconducting gap, and uniform biaxial mechanical deformation could provide its smooth fitting. Moreover, mechanical tension offers the ability to control the Dirac velocity in deposited graphene. We analyze the resonant scattering of charge carriers in states with zero total angular momentum using the effective two-dimensional radial Dirac equation. In particular, the dependence of the critical impurity charge on the uniform deformation of graphene on the boron nitride substrate is shown. It turned out that, under uniform stretching/compression, the critical charge decreases/increases monotonically. The elastic scattering phases of a hole by a supercritical impurity are calculated. It is found that the model of a uniform charge distribution over the small radius sphere gives sharper resonance when compared to the case of the ball of the same radius. Overall, resonant scattering by the impurity with the nearly critical charge is similar to the scattering by the potential with a low-permeable barrier in nonrelativistic quantum theory.

Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

2D materials open the possibility to study Dirac electrons in complex self-similar geometries. The two-dimensional nature of materials like graphene, silicene, phosphorene and transition-metal dichalcogenides allow the nanostructuration of complex geometries through metallic electrodes, interacting substrates, strain, etc. So far, the only 2D material that presents physical properties that directly reflect the characteristics of the complex geometries is monolayer graphene. In the present work, we show that silicene nanostructured in complex fashion also displays self-similar characteristics in physical properties. In particular, we find self-similar patterns in the conductance, spin polarization and thermoelectricity of Cantor-like silicene structures. These complex structures are generated by modulating electrostatically the silicene local bandgap in Cantor-like fashion along the structure. The charge carriers are described quantum relativistically by means of a Dirac-like Hamiltonian. The transfer matrix method, the Landauer–Büttiker formalism and the Cutler–Mott formula are used to obtain the transmission, transport and thermoelectric properties. We numerically derive scaling rules that connect appropriately the self-similar conductance, spin polarization and Seebeck coefficient patterns. The scaling rules are related to the structural parameters that define the Cantor-like structure such as the generation and length of the system as well as the height of the potential barriers. As far as we know this is the first time that a 2D material beyond monolayer graphene shows self-similar quantum transport as well as that transport related properties like spin polarization and thermoelectricity manifest self-similarity.

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.

Quantitative study of electronic whispering gallery modes in electrostatic-potential induced circular graphene junctions

Electronic whispering gallery modes (EWGMs) have been recently observed in several circular graphene junctions, pn and pp', created in scanning tunneling microscopy experiments. By computing the local density of states within the Dirac-Weyl formalism for massless fermions we demonstrate that the EWGMs may really be emerged in any type of the electrostatic-potential induced circular graphene junctions, including uni-junctions (e.g. np- or pp'-junctions) as well as bipolar-junctions (e.g. pnp-heterojunctions). Surprisingly, quantitative analyses show that for all the EWGMs identified (regardless of junction types) the quality (Q) factors seem to be ≤10², very small compared to those in ordinary optical whispering gallery modes microresonators, while the corresponding mode radii may tunably be in nanometer-scale. Our theoretical results are in good agreement with existent experimental data, putting a question to the application potential of the EWGMs identified.

Guiding Dirac Fermions in Graphene with a Carbon Nanotube

Relativistic massless charged particles in a two-dimensional conductor can be guided by a one-dimensional electrostatic potential, in an analogous manner to light guided by an optical fiber. We use a carbon nanotube to generate such a guiding potential in graphene and create a single mode electronic waveguide. The nanotube and graphene are separated by a few nanometers and can be controlled and measured independently. As we charge the nanotube, we observe the formation of a single guided mode in graphene that we detect using the same nanotube as a probe. This single electronic guided mode in graphene is sufficiently isolated from other electronic states of linear Dirac spectrum continuum, allowing the transmission of information with minimal distortion.

Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5

Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρxx ) and the Hall traces (ρyx ) of HfTe5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρxx and ρyx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.

Nitrogen cluster doping for high-mobility/conductivity graphene films with millimeter-sized domains

Directly incorporating heteroatoms into the hexagonal lattice of graphene during growth has been widely used to tune its electrical properties with superior doping stability, uniformity, and scalability. However the introduction of scattering centers limits this technique because of reduced carrier mobilities and conductivities of the resulting material. Here, we demonstrate a rapid growth of graphitic nitrogen cluster-doped monolayer graphene single crystals on Cu foil with remarkable carrier mobility of 13,000 cm² V^-1 s^-1 and a greatly reduced sheet resistance of only 130 ohms square^-1. The exceedingly large carrier mobility with high n-doping level was realized by (i) incorporation of nitrogen-terminated carbon clusters to suppress the carrier scattering and (ii) elimination of all defective pyridinic nitrogen centers by oxygen etching. Our study opens up an avenue for the growth of high-mobility/conductivity doped graphene with tunable work functions for scalable graphene-based electronic and device applications.

Strong magnetophonon oscillations in extra-large graphene

Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene’s low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures.

Increasing the size of mesoscopic devices based on van der Waals heterostructures triggers additional quantum effects. Here, the authors observe distinct magnetoresistance oscillations in graphene/h-BN Hall bars only in devices wider than 10 μm due to resonant scattering of charge carriers by transverse acoustic phonons in graphene.

Frustrated supercritical collapse in tunable charge arrays on graphene

The photon-like behavior of electrons in graphene causes unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential. We report bottom-up synthesis of atomically-precise one-dimensional (1D) arrays of point charges on graphene that allow exploration of a new type of supercritical confinement of graphene carriers. The arrays were synthesized by arranging F₄TCNQ molecules into a 1D lattice on back-gated graphene, allowing precise tuning of both the molecular charge and the array periodicity. While dilute arrays of ionized F₄TCNQ molecules are seen to behave like isolated subcritical charges, dense arrays show emergent supercriticality. In contrast to compact supercritical clusters, these extended arrays display both supercritical and subcritical characteristics and belong to a new physical regime termed "frustrated supercritical collapse". Here carriers in the far-field are attracted by a supercritical charge distribution, but their fall to the center is frustrated by subcritical potentials in the near-field, similar to trapping of light by a dense cluster of stars in general relativity.

Critical nucleus charge in a superstrong magnetic field

Due to strong enhancement of loop effects in a superstrong magnetic field (B ≫ m2=e3) the Coulomb potential becomes screened. This phenomenon dramatically changes the dependence of the electron energy levels on magnetic field. In particular, the freezing of energy levels occurs so the ground energy level of light ions can never reach the lower continuum (become critical), no matter how strong the field is. Therefore, the magnetic field affects the critical nucleus charge Zcr in two ways: i. it makes the electron movement essentially one-dimensional diminishing the value of Zcr; ii. it makes the potential weaker increasing the value of critical charge. The phenomenon of critical charge itself is also discussed.

Collisions of noble gas atoms with graphene and a graphene nanodome

The collisions of noble gas atoms with graphene and a graphene nanodome were investigated by employing first principles molecular dynamics calculations. By analyzing the electron-related properties of the collision process, the atom dynamics and the deformation of the graphene/nanodome, our results show a difference between the elastic properties of the nanodome and graphene. Generally, the nanodome can more easily revert to its initial conformation. The final kinetic energy, E_f, of the atom that collides with the nanodome is larger than the E_f of the atom that collides with graphene. In addition, the relationship between the initial kinetic energy of the atom, E_k0, and its corresponding proportion of energy loss, χ, is linear (except for the Kr atom). Our research will probably contribute to the investigation of the 2D materials' mechanical properties and their surface morphology. Moreover, due to its novel mechanical properties, the graphene nanodome is an extraordinary nano-architecture which can be employed to protect nano-devices from damage and injury.

Orthogonality catastrophe and fractional exclusion statistics

We show that the N-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

Deep Learning of Atomically Resolved Scanning Transmission Electron Microscopy Images: Chemical Identification and Tracking Local Transformations

Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level precision. This progress has been accompanied by an exponential increase in the size and quality of data sets produced by microscopic and spectroscopic experimental techniques. These developments necessitate adequate methods for extracting relevant physical and chemical information from the large data sets, for which a priori information on the structures of various atomic configurations and lattice defects is limited or absent. Here we demonstrate an application of deep neural networks to extract information from atomically resolved images including location of the atomic species and type of defects. We develop a "weakly supervised" approach that uses information on the coordinates of all atomic species in the image, extracted via a deep neural network, to identify a rich variety of defects that are not part of an initial training set. We further apply our approach to interpret complex atomic and defect transformation, including switching between different coordination of silicon dopants in graphene as a function of time, formation of peculiar silicon dimer with mixed 3-fold and 4-fold coordination, and the motion of molecular "rotor". This deep learning-based approach resembles logic of a human operator, but can be scaled leading to significant shift in the way of extracting and analyzing information from raw experimental data.

Fano resonances in bilayer graphene superlattices

In this work, we address the ubiquitous phenomenon of Fano resonances in bilayer graphene. We consider that this phenomenon is as exotic as other phenomena in graphene because it can arise without an external extended states source or elaborate nano designs. However, there are not theoretical and/or experimental studies that report the impact of Fano resonances on the transport properties. Here, we carry out a systematic assessment of the contribution of the Fano resonances on the transport properties of bilayer graphene superlattices. Specifically, we find that by changing the number of periods, adjusting the barriers height as well as modifying the barriers and wells width it is possible to identify the contribution of Fano resonances on the conductance. Particularly, the coupling of Fano resonances with the intrinsic minibands of the superlattice gives rise to specific and identifiable changes in the conductance. Moreover, by reducing the angular range for the computation of the transport properties it is possible to obtain conductance curves with line-shapes quite similar to the Fano profile and the coupling profile between Fano resonance and miniband states. In fact, these conductance features could serve as unequivocal characteristic of the existence of Fano resonances in bilayer graphene.

Tuning a circular p-n junction in graphene from quantum confinement to optical guiding

The photon-like propagation of the Dirac electrons in graphene, together with its record-high electronic mobility, can lead to applications based on ultrafast electronic response and low dissipation. However, the chiral nature of the charge carriers that is responsible for the high mobility also makes it difficult to control their motion and prevents electronic switching. Here, we show how to manipulate the charge carriers by using a circular p-n junction whose size can be continuously tuned from the nanometre to the micrometre scale. The junction size is controlled with a dual-gate device consisting of a planar back gate and a point-like top gate made by decorating a scanning tunnelling microscope tip with a gold nanowire. The nanometre-scale junction is defined by a deep potential well created by the tip-induced charge. It traps the Dirac electrons in quantum-confined states, which are the graphene equivalent of the atomic collapse states (ACSs) predicted to occur at supercritically charged nuclei. As the junction size increases, the transition to the optical regime is signalled by the emergence of whispering-gallery modes, similar to those observed at the perimeter of acoustic or optical resonators, and by the appearance of a Fabry-Pérot interference pattern for junctions close to a boundary.

Bielectron vortices in two-dimensional Dirac semimetals

Searching for new states of matter and unusual quasi-particles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasi-particles which are described by ultrarelativistic Dirac-like equations, are of a significant current interest from both a fundamental and applied physics perspective. Here we show that a pair of two-dimensional massless Dirac–Weyl fermions can form a bound state independently of the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler’s inverse distance law. This leads to the emergence of a new type of energetically favorable quasiparticle: bielectron vortices, which are double-charged and reside at zero-energy. Their bosonic nature allows for condensation and may give rise to Majorana physics without invoking a superconductor. These novel quasi-particles arguably explain a range of poorly understood experiments in gated graphene structures at low doping.

Two-dimensional Dirac semimetals are known to host fermionic excitations which can mimic physics usually found in ultrarelativistic quantum mechanics. Here, the authors unveil the existence of another type of quasiparticle, bielectron vortices, which are bosonic and may give rise to new types of condensates.

Observing a scale anomaly and a universal quantum phase transition in graphene

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ‘Efimov physics’. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.

When the continuous scale symmetry of a quantum system is broken, anomalies occur which may lead to quantum phase transitions. Here, the authors provide evidence for such a quantum phase transition in the attractive Coulomb potential of vacancies in graphene, and further envision its universality for diverse physical systems.

Quantum Dots in Graphene Nanoribbons

Graphene quantum dots (GQDs) hold great promise for applications in electronics, optoelectronics, and bioelectronics, but the fabrication of widely tunable GQDs has remained elusive. Here, we report the fabrication of atomically precise GQDs consisting of low-bandgap N = 14 armchair graphene nanoribbon (AGNR) segments that are achieved through edge fusion of N = 7 AGNRs. The so-formed intraribbon GQDs reveal deterministically defined, atomically sharp interfaces between wide and narrow AGNR segments and host a pair of low-lying interface states. Scanning tunneling microscopy/spectroscopy measurements complemented by extensive simulations reveal that their energy splitting depends exponentially on the length of the central narrow bandgap segment. This allows tuning of the fundamental gap of the GQDs over 1 order of magnitude within a few nanometers length range. These results are expected to pave the way for the development of widely tunable intraribbon GQD-based devices.

Electron dynamics in graphene with spin-orbit couplings and periodic potentials

We use both continuum and lattice models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. A number of special things occur when the Kane-Mele and Rashba couplings are equal in magnitude. In the absence of a potential, the dispersion then consists of both massless Dirac and massive Dirac states. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at all those points, but if the two spin-orbit couplings are equal, some of the Dirac points remain gapless. We show that the massless and massive states respond differently to a potential barrier; the massless states transmit perfectly through the barrier at normal incidence while the massive states reflect from it. In the presence of a single potential barrier, we show that there are states localized along the barrier. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.

Self-similar conductance patterns in graphene Cantor-like structures

Graphene has proven to be an ideal system for exotic transport phenomena. In this work, we report another exotic characteristic of the electron transport in graphene. Namely, we show that the linear-regime conductance can present self-similar patterns with well-defined scaling rules, once the graphene sheet is subjected to Cantor-like nanostructuring. As far as we know the mentioned system is one of the few in which a self-similar structure produces self-similar patterns on a physical property. These patterns are analysed quantitatively, by obtaining the scaling rules that underlie them. It is worth noting that the transport properties are an average of the dispersion channels, which makes the existence of scale factors quite surprising. In addition, that self-similarity be manifested in the conductance opens an excellent opportunity to test this fundamental property experimentally.

Space charge and screening in bilayer graphene

Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge Ze is accompanied by a reconstruction of the ground state: valence band electrons (for Z  >  0) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is a flat neutral object resembling the regular atom except that for [Formula: see text] it is described by a strictly linear Thomas-Fermi theory. This theory also predicts that the bilayer's static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.

Initiating and imaging the coherent surface dynamics of charge carriers in real space

The tip of a scanning tunnelling microscope is an atomic-scale source of electrons and holes. As the injected charge spreads out, it can induce adsorbed molecules to react. By comparing large-scale 'before' and 'after' images of an adsorbate covered surface, the spatial extent of the nonlocal manipulation is revealed. Here, we measure the nonlocal manipulation of toluene molecules on the Si(111)-7 × 7 surface at room temperature. Both the range and probability of nonlocal manipulation have a voltage dependence. A region within 5-15 nm of the injection site shows a marked reduction in manipulation. We propose that this region marks the extent of the initial coherent (that is, ballistic) time-dependent evolution of the injected charge carrier. Using scanning tunnelling spectroscopy, we develop a model of this time-dependent expansion of the initially localized hole wavepacket within a particular surface state and deduce a quantum coherence (ballistic) lifetime of ∼10 fs.

Tunable Plasmonic Reflection by Bound 1D Electron States in a 2D Dirac Metal

We show that the surface plasmons of a two-dimensional Dirac metal such as graphene can be reflected by linelike perturbations hosting one-dimensional electron states. The reflection originates from a strong enhancement of the local optical conductivity caused by optical transitions involving these bound states. We propose that the bound states can be systematically created, controlled, and liquidated by an ultranarrow electrostatic gate. Using infrared nanoimaging, we obtain experimental evidence for the locally enhanced conductivity of graphene induced by a carbon nanotube gate, which supports this theoretical concept.

Atomic-Scale Spectroscopy of Gated Monolayer MoS2

The electronic properties of semiconducting monolayer transition-metal dichalcogenides can be tuned by electrostatic gate potentials. Here we report gate-tunable imaging and spectroscopy of monolayer MoS2 by atomic-resolution scanning tunneling microscopy/spectroscopy (STM/STS). Our measurements are performed on large-area samples grown by metal-organic chemical vapor deposition (MOCVD) techniques on a silicon oxide substrate. Topographic measurements of defect density indicate a sample quality comparable to single-crystal MoS2. From gate voltage dependent spectroscopic measurements, we determine that in-gap states exist in or near the MoS2 film at a density of 1.3 × 10(12) eV(-1) cm(-2). By combining the single-particle band gap measured by STS with optical measurements, we estimate an exciton binding energy of 230 meV on this substrate, in qualitative agreement with numerical simulation. Grain boundaries are observed in these polycrystalline samples, which are seen to not have strong electronic signatures in STM imaging.

Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy

Defects play a key role in determining the properties and technological applications of nanoscale materials and, because they tend to be highly localized, characterizing them at the single-defect level is of particular importance. Scanning tunnelling microscopy has long been used to image the electronic structure of individual point defects in conductors, semiconductors and ultrathin films, but such single-defect electronic characterization remains an elusive goal for intrinsic bulk insulators. Here, we show that individual native defects in an intrinsic bulk hexagonal boron nitride insulator can be characterized and manipulated using a scanning tunnelling microscope. This would typically be impossible due to the lack of a conducting drain path for electrical current. We overcome this problem by using a graphene/boron nitride heterostructure, which exploits the atomically thin nature of graphene to allow the visualization of defect phenomena in the underlying bulk boron nitride. We observe three different defect structures that we attribute to defects within the bulk insulating boron nitride. Using scanning tunnelling spectroscopy we obtain charge and energy-level information for these boron nitride defect structures. We also show that it is possible to manipulate the defects through voltage pulses applied to the scanning tunnelling microscope tip.

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Owing to its relativistic low-energy charge carriers, the interaction between graphene and various impurities leads to a wealth of new physics and degrees of freedom to control electronic devices. In particular, the behavior of graphene's charge carriers in response to potentials from charged Coulomb impurities is predicted to differ significantly from that of most materials. Scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) can provide detailed information on both the spatial and energy dependence of graphene's electronic structure in the presence of a charged impurity. The design of a hybrid impurity-graphene device, fabricated using controlled deposition of impurities onto a back-gated graphene surface, has enabled several novel methods for controllably tuning graphene's electronic properties. Electrostatic gating enables control of the charge carrier density in graphene and the ability to reversibly tune the charge and/or molecular states of an impurity. This paper outlines the process of fabricating a gate-tunable graphene device decorated with individual Coulomb impurities for combined STM/STS studies. These studies provide valuable insights into the underlying physics, as well as signposts for designing hybrid graphene devices.

Giant enhancement of the optical second-harmonic emission of WSe(2) monolayers by laser excitation at exciton resonances

We show that the light-matter interaction in monolayer WSe_{2} is strongly enhanced when the incoming electromagnetic wave is in resonance with the energy of the exciton states of strongly Coulomb bound electron-hole pairs below the electronic band gap. We perform second harmonic generation (SHG) spectroscopy as a function of laser energy and polarization at T=4  K. At the exciton resonance energies we record an enhancement by up to 3 orders of magnitude of the SHG efficiency, due to the unusual combination of electric dipole and magnetic dipole transitions. The energy and parity of the exciton states showing the strong resonance effects are identified in 1- and 2-photon photoluminescence excitation experiments, corroborated by first principles calculations. Targeting the identified exciton states in resonant 2-photon excitation allows us to maximize k-valley coherence and polarization.

Structure stability and high-temperature distortion resistance of trilayer complexes formed from graphenes and boron nitride nanosheets

The molecular dynamics was employed to study the structure stability and high-temperature distortion resistance of a trilayer complex formed by a monolayer graphene sandwiched in bilayer boron nitride nanosheets (BN-G-BN) and graphenes (G-G-G). The investigation shows that the optimal interlayer distances are about 0.347 nm for BN-G-BN and 0.341 nm for G-G-G. Analysis and comparison of the binding energy, van der Waals interactions between layers and radial distribution function (RDF) revealed that the BN-G-BN achieves a more stable combined structure than G-G-G. The interlayer graphene in the trilayer complex nanosheets, especially the graphene in BN-G-BN, is more integrated than monolayer graphenes in a crystal structure. The structures at high temperature of 1500 K show that the BN-G-BN exhibits less distortion than G-G-G; especially, fixing the atomic positions on up-down layers can obviously further reduce structural deformation of interlayer graphene. The result further indicates that the high-temperature distortion resistance of interlayer graphene in the trilayer complex is related to both material type and conditions of constraints at the up-down layers.

Graphene on hexagonal boron nitride

The field of graphene research has developed rapidly since its first isolation by mechanical exfoliation in 2004. Due to the relativistic Dirac nature of its charge carriers, graphene is both a promising material for next-generation electronic devices and a convenient low-energy testbed for intrinsically high-energy physical phenomena. Both of these research branches require the facile fabrication of clean graphene devices so as not to obscure its intrinsic physical properties. Hexagonal boron nitride has emerged as a promising substrate for graphene devices as it is insulating, atomically flat and provides a clean charge environment for the graphene. Additionally, the interaction between graphene and boron nitride provides a path for the study of new physical phenomena not present in bare graphene devices. This review focuses on recent advancements in the study of graphene on hexagonal boron nitride devices from the perspective of scanning tunneling microscopy with highlights of some important results from electrical transport measurements.

Fermi-edge transmission resonance in graphene driven by a single Coulomb impurity

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude ≈e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Electric-dipole-induced universality for Dirac fermions in graphene

We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.

Screening charged impurities and lifting the orbital degeneracy in graphene by populating Landau levels

We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy, we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate voltage. At low occupation the impurity is screened, becoming essentially invisible. Screening diminishes as states are filled until, for fully occupied Landau levels, the unscreened impurity significantly perturbs the spectrum in its vicinity. In this regime we report the first observation of Landau-level splitting into discrete states due to lifting the orbital degeneracy.