The electronic shell and supershell structure of triangular graphene quantum dots has been studied using density functional and tight-binding methods. The density functional calculations demonstrate that the electronic structure close to the Fermi energy is correctly described with a simple tight-binding model where only the p_z orbitals perpendicular to the graphene layer are included. The results show that (i) both at the bottom and at the top of the p_z band a supershell structure similar to that of free electrons confined in a triangular cavity is seen, (ii) close to the Fermi level the shell structure is that of free massless particles, (iii) triangles with armchair edges show an additional sequence of levels ('ghost states') absent for triangles with zigzag edges while the latter exhibit edge states, and (iv) the observed shell structure is rather insensitive to the edge roughness.
We investigate quantum transport properties of triangular graphene flakes with zigzag edges by using first principles calculations. Triangular graphene flakes have large magnetic moments which vary with the number of hydrogen atoms terminating its edge atoms and scale with its size. Electronic transmission and current-voltage characteristics of these flakes, when contacted with metallic electrodes, reveal spin valve and remarkable rectification features. The transition from ferromagnetic to antiferromagnetic state under bias voltage can, however, terminate the spin polarizing effects for speci…
The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at …
Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every angle is energetically favorable. Recent experiments on rotation-tunable electronics reveal the existence of a discrete set of angles at which the rotation-tunable electronics assume the most stable configurations. Nevertheless, a quantitative map for locating these intrinsically preferred twist angles in twisted bilayer system has not been available, posing challenges for the on-demand design of twisted electronics that are intrinsically stable at desired twist angles. Here …
Graphene nano-flakes (GNFs) are predicted to host spin-polarized metallic edge states, which are envisioned for exploration of spintronics at the nanometer scale. To date, experimental realization of GNFs is only in its infancy because of the limitation of precise cutting or synthesizing methods at the nanometer scale. Here, we use low temperature scanning tunneling microscope (STM) to manipulate coronene molecules on a Cu(111) surface to build artificial triangular and hexagonal GNFs with either zigzag or armchair type of edges. We observe that the metallic edge states only exist in the GNFs …
Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than to the energy level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy level structure. The susceptibility at charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structure…
The structure stability and electronic properties of edge carboxylated hexagonal and triangular graphene quantum dots are investigated by using density functional theory. The calculated binding energies show that the hexagonal clusters with armchair edges have the highest stability among all other flakes. The binding energy of carboxylated graphene quantum dots increases by increasing the number of attached carboxyl groups. Our study shows that the total dipole moment significantly increases by adding COOH with the highest values observed in triangular clusters. The edge states in triangular g…
Graphene can develop large magnetic moments in custom crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nano-systems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulene-like graphene systems and demonstrate that they possess a spin $S=1$ ground state. Scanning tunnelling spectroscopy identifies the fingerprint of an underscreened $S=1$ Kondo state on \rev{these} flakes at low temperatu…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the disorder strength, level distribution evolves from Poissonian to Wigner, indicating the transition to quantum chaos. The unitary ensemble (with the twofold valley degeneracy) is observed for triangular flakes with zigzag or Klein edges and potential varying smoothly on the scale of atomic separation. For small number of edge defects, the unitary-to-orthogonal s…
Graphite surfaces can be manipulated by several methods to create graphene structures of different shapes and sizes. Scanning tunneling microscopy (STM) can be used to create these structures either through mechanical contact between the tip and the surface or through electro-exfoliation. In the latter, the mechanisms involved in the process of exfoliation with an applied voltage are not fully understood. Here we show how a graphite surface can be locally exfoliated in a systematic manner by applying an electrostatic force with a STM tip at the edge of a terrace, forming triangular flakes seve…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($θ$) close to 0$^\circ$ and at both the valence and conduction band edges for $θ$ close to 60$^\circ$, and have distinct origins. For$ θ$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moiré superlattice is…
A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correc…
Straintronic devices made of carbon-based materials have been pushed up due to the graphene high mechanical flexibility and the possibility of interesting changes in transport properties. Properly designed strained systems have been proposed to allow optimized transport responses that can be explored in experimental realizations. In multi-terminal systems, comparisons between schemes with different geometries are important to characterize the modifications introduced by mechanical deformations, specially if the deformations are localized at a central part of the system or extended in a large r…
The electronic properties of graphene superlattices have attracted intense interest that was further stimulated by the recent observation of novel many-body states at "magic" angles in twisted bilayer graphene (BLG). For very small ("marginal") twist angles of 0.1 deg, BLG has been shown to exhibit a strain-accompanied reconstruction that results in submicron-size triangular domains with the Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, marginally-twisted BLG is predicted to remain conductive due to a triangular netwo…
We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moiré band filling $ν=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moiré Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU…
The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing to write the Hamiltonian in terms of a $2\times 2$ matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle o…
Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level [Phys. Rev. B 85, 245424 (2012)]. Atomic-scale disorder induce the scattering of charge carriers between the valleys and restores the spectral fluctuations of GOE. A simplified description of such a nonstandard GUE-GOE transition, employing the mixed ensemble o…
We devise a model to explain why twisted bi-layer graphene (TBLG) exhibits insulating behavior when $ν=2,3$ charges occupy a unit moiré cell, a feature attributed to Mottness, but not for $ν=1$, clearly inconsistent with Mott insulation. We compute $r_s=E_U/E_K$, where $E_U$ and $E_K$ are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density $10^4$ higher than in the experiments and (ii) a transition to a series of Wigner crystalline states exists as a function of $ν$. We find, for $ν=1$, $r_s$ fails to cross the threshold ($r_s = 37$) for the…
We explore in detail the electronic phases of a system consisting of three non-colinear arrays of coupled quantum wires, each rotated 120 degrees with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a $s$-wave or $d \pm id$ superconductor, a charge density wave insulator, a two-dimensional Fermi liquid, and a 2D Luttinger liquid (also known as smectic metal or sliding Luttinger liquid). The model provides an effective description of electronic interactions in small-angle twisted bilayer graphene and we discuss its im…
We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized -- yet valley polarized -- Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-si…
We study the electronic and magnetic properties of multilayer quantum dots (MQDs) of graphite in the nearest-neighbor approximation of tight-binding model. We calculate the electronic density of states and orbital susceptibility of the system as function of the Fermi level location. We demonstrate that properties of MQD depend strongly on the shape of the system, on the parity of the layer number and on the form of the cluster edge. The special emphasis is given to reveal the new properties with respect to the monolayer quantum dots of graphene. The most interesting results are obtained for th…
Density functional theory calculations are performed on phosphorene quantum dots having different shapes and edge terminations to investigate their structure stability, electronic properties, and gas sensing ability. All the selected phosphorene dots, namely hexagonal and triangular flakes with armchair and zigzag terminations, have positive binding energies which insure their stability even though the bond lengths are much longer than those in the infinite phosphorene layer. It is found that all the selected hydrogen passivated quantum dots have a wide energy gap. In contrast, the partial pas…
Atomic-Scale Imaging of Lattice Relaxation and Topological Flat Bands in Helical Trilayer Graphene
National Institute for Materials Science（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Southern University of Science and Technology（南方科技大学）
