Electron-electron interactions in artificial graphene

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.

Artificial Graphene on Si Substrates: Fabrication and Transport Characteristics

Artificial graphene (AG) based on a honeycomb lattice of semiconductor quantum dots (QDs) has been of great interest for exploration and applications of massless Dirac Fermions in semiconductors thanks to the tunable interplay between the carrier interactions and the honeycomb topology. Here, an innovative strategy to realize AG on Si substrates is developed by fabricating a honeycomb lattice of Au nanodisks on a Si/GeSi quantum well. The lateral potential modulation induced by the nanoscale Au/Si Schottky junction results in the formation of quantum dots arranged in a honeycomb lattice to form AG. Nonlinear current-voltage curves of the AG reveal conductance phase transitions with switch on/off voltages, a large electric hysteresis loop, and a strong sharp current peak accompanied by a group of differential-conductance peaks and negative differential conductance around the switch-on voltage, which can be modulated by temperature and light. These features are interpreted by a model based on the Coulomb blockade effect, the collective resonant tunneling, and the coupling of holes in the AG. Our results not only demonstrate an approach to the formation but also will greatly stimulate the characterizations and the applications of innovative semiconductor-based AG.

Observation of Flat Bands in Gated Semiconductor Artificial Graphene

Flat bands near M points in the Brillouin zone are key features of honeycomb symmetry in artificial graphene (AG) where electrons may condense into novel correlated phases. Here we report the observation of van Hove singularity doublet of AG in GaAs quantum well transistors, which presents the evidence of flat bands in semiconductor AG. Two emerging peaks in photoluminescence spectra tuned by backgate voltages probe the singularity doublet of AG flat bands and demonstrate their accessibility to the Fermi level. As the Fermi level crosses the doublet, the spectra display dramatic stability against electron density, indicating interplays between electron-electron interactions and honeycomb symmetry. Our results provide a new flexible platform to explore intriguing flat band physics.

Engineering Metal-spxy Dirac Bands on the Oxidized SiC Surface

The ability to construct 2D systems, beyond materials' natural formation, enriches the search and control capability of new phenomena, for instance, the synthesis of topological lattices of vacancies on metal surfaces through scanning tunneling microscopy. In the present study, we demonstrate that metal atoms encaged in a silicate adlayer on silicon carbide is an interesting platform for lattice design, providing a ground to experimentally construct tight-binding models on an insulating substrate. Based on the density functional theory, we have characterized the energetic and electronic properties of 2D metal lattices embedded in the silica adlayer. We show that the characteristic band structures of those lattices are ruled by surface states induced by the metal-s orbitals coupled by the host-p_xy states, giving rise to sp_xy Dirac bands neatly lying within the energy gap of the semiconductor substrate.

Normal and Anomalous Diffusion in Soft Lorentz Gases

Motivated by electronic transport in graphenelike structures, we study the diffusion of a classical point particle in Fermi potentials situated on a triangular lattice. We call this system a soft Lorentz gas, as the hard disks in the conventional periodic Lorentz gas are replaced by soft repulsive scatterers. A thorough computational analysis yields both normal and anomalous (super)diffusion with an extreme sensitivity on model parameters. This is due to an intricate interplay between trapped and ballistic periodic orbits, whose existence is characterized by tonguelike structures in parameter space. These results hold even for small softness, showing that diffusion in the paradigmatic hard Lorentz gas is not robust for realistic potentials, where we find an entirely different type of diffusion.

Coexisting Honeycomb and Kagome Characteristics in the Electronic Band Structure of Molecular Graphene

We uncover the electronic structure of molecular graphene produced by adsorbed CO molecules on a copper (111) surface by means of first-principles calculations. Our results show that the band structure is fundamentally different from that of conventional graphene, and the unique features of the electronic states arise from coexisting honeycomb and Kagome symmetries. Furthermore, the Dirac cone does not appear at the K-point but at the Γ-point in the reciprocal space and is accompanied by a third, almost flat band. Calculations of the surface structure with Kekulé distortion show a gap opening at the Dirac point in agreement with experiments. Simple tight-binding models are used to support the first-principles results and to explain the physical characteristics behind the electronic band structures.

Finite-size effects and interactions in artificial graphene formed by repulsive scatterers

We carry out a numerical real-space study on electrons confined in a two-dimensional triangular lattice of repulsive scattering centres. The system represents a qualitative model of molecular graphene, where the electron gas is confined between the scattering molecules in a hexagonal configuration. Our main interest is, on one hand, in the comparability of a finite system (flake) and a fully periodic one, and, on the other hand, in the role of the Coulombic electron-electron interactions and the relative strength of the scattering centres. Our real-space study shows in detail how the density of states of the fully periodic system-containing the Dirac point-is gradually formed as the size of the flake is increased. Good qualitative agreement with the experimental density of states is obtained. Our study confirms the minor role of the electron-electron interactions with selected system parameters, and shows in detail that large scattering amplitudes are required to obtain a distinctive Dirac point in the density of states.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Scalable tight-binding model for graphene

Artificial graphene consisting of honeycomb lattices other than the atomic layer of carbon has been shown to exhibit electronic properties similar to real graphene. Here, we reverse the argument to show that transport properties of real graphene can be captured by simulations using "theoretical artificial graphene." To prove this, we first derive a simple condition, along with its restrictions, to achieve band structure invariance for a scalable graphene lattice. We then present transport measurements for an ultraclean suspended single-layer graphene pn junction device, where ballistic transport features from complex Fabry-Pérot interference (at zero magnetic field) to the quantum Hall effect (at unusually low field) are observed and are well reproduced by transport simulations based on properly scaled single-particle tight-binding models. Our findings indicate that transport simulations for graphene can be efficiently performed with a strongly reduced number of atomic sites, allowing for reliable predictions for electric properties of complex graphene devices. We demonstrate the capability of the model by applying it to predict so-far unexplored gate-defined conductance quantization in single-layer graphene.

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices offer a tunable platform for studying massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band-structure engineering and cooperative effects leads to spectacular manifestations in tunnelling and optical spectroscopies.