Floquet bands and photon-induced topological edge states of graphene nanoribbons

Floquet theorem is widely used in the light-driven systems. But many 2 D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work,we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies(including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.     

Preparation of edge states by shaking boundaries

Preparing topological states of quantum matter, such as edge states, is one of the most important directions in condensed matter physics. In this work, we present a proposal to prepare edge states in Aubry–André–Harper (AAH) model with open boundaries, which takes advantage of Lyapunov control to design operations. We show that edge states can be obtained with almost arbitrary initial states. A numerical optimalization for the control is performed and the dependence of control process on the system size is discussed. The merit of this proposal is that the shaking exerts only on the boundaries of the model. As a by-product, a topological entangled state is achieved by elaborately designing the shaking scheme.     

Band structure and edge states of star-like zigzag graphene nanoribbons

Connecting three zigzag graphene nanoribbons(ZGNRs) together through the sp~3 hybrid bonds forms a star-like ZGNR(S-ZGNR). Its band structure shows that there are four edge states at k = 0.5, in which the three electrons distribute at three outside edge sites, and the last electron is shared equally(50%) by two sites near the central site. The lowest conductance step in the valley is 2, two times higher than that of monolayer ZGNR(M-ZGNR). Furthermore, in one quasithree-dimensional hexagonal lattice built, both of the Dirac points and the zero-energy states appear in the band structure along the z-axis for the fixed zero k-point in the x-y plane. In addition, it is an insulator in the x-y plane due to band gap 4 eV, however, for any k-point in the x-y plane the zero-energy states always exist at k_z = 0.5.     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.     

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking(symmetry of sublattices).We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for "local chemical potential" and "local gap".The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states(BSs) has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~+(r),g_m~+(r),and f_m~-(r),g_m~-(r),can be established by SO(2) group.     

Density of states in randomly shaped graphene quantum dots

By numerical diagonalization of honeycomb-lattice tight-binding Hamiltonian we calculate the density of state (DOS) of irregularly shaped graphene quantum dots fabricated in the form of graphene nano-flakes. The finite-size electron confinement and the edge states result in the central peak of DOS that is located at the zero-energy Dirac point. The amplitude and width of the peak are provided by the form of the graphene cluster, but no regular correlation with its shape was found.     

A rigorous proof for non-existence of edge state in the semi-infinite armchair edged graphene

Within the transfer matrix method, we study the conditions for the existence of the edge states in the semi-infinite armchair edged graphene. We discuss zero-energy and non-zero-energy edge states, respectively, and show the non-existence of the edge states in the model analytically and rigorously.     

Analytical study of surface states caused by the edge decoration

Analytical studies of the effect of edge decoration on the energy spectrum of semi-infinite one-dimensional (1D) model and zigzag edged graphene (ZEG) are presented by means of transfer matrix method, in the frame of which the conditions for the existence of edge states are determined. For 1D model, the zero-energy surface state occurs regardless of whether the decorations exist or not, while the non-zero-energy surface states can be induced and manipulated through adjusting the edge decoration. On the other hand, the case for the semi-infinite ZEG model with nearest-neighbour interaction is discussed in the analogous way. The non-zero-energy surface states can be induced by the edge decoration and moreover, the ratio between the edge hopping and the bulk hopping amplitudes should be within a certain threshold.     

Rectifying performance in zigzag graphene nanoribbon heterojunctions with different edge hydrogenations

Using nonequilibrium Green?s functions in combination with the density functional theory, we investigated the electronic transport behaviors of zigzag graphene nanoribbon (ZGNR) heterojunctions with different edge hydrogenations. The results show that electronic transport properties of ZGNR heterojunctions can be modulated by hydrogenations, and prominent rectification effects can be observed. We propose that the edge dihydrogenation leads to a blocking of electronic transfer, as well as the changes of the distribution of the frontier orbital at negative/positive bias might be responsible for the rectification effects. These results may be helpful for designing practical devices based on graphene nanoribbons.     

Correlated states in alternating twisted bilayer-monolayer-monolayer graphene heterostructure

Highly controlled electronic correlation in twisted graphene heterostructures has gained enormous research interests recently, encouraging exploration in a wide range of moiré superlattices beyond the celebrated twisted bilayer graphene. Here we characterize correlated states in an alternating twisted Bernal bilayer-monolayer-monolayer graphene of ～ 1.74°, and find that both van Hove singularities and multiple correlated states are asymmetrically tuned by displacement fields. In particular, when one electron per moiré unit cell is occupied in the electron-side flat band, or the hole-side flat band (i.e., three holes per moiré unit cell), the correlated peaks are found to counterintuitively grow with heating and maximize around 20 K - a signature of Pomeranchuk effect. Our multilayer heterostructure opens more opportunities to engineer complicated systems for investigating correlated phenomena.     

Recent advances of defect-induced spin and valley polarized states in graphene

Electrons in graphene have fourfold spin and valley degeneracies owing to the unique bipartite honeycomb lattice and an extremely weak spin-orbit coupling, which can support a series of broken symmetry states. Atomic-scale defects in graphene are expected to lift these degenerate degrees of freedom at the nanoscale, and hence, lead to rich quantum states, highlighting promising directions for spintronics and valleytronics. In this article, we mainly review the recent scanning tunneling microscopy (STM) advances on the spin and/or valley polarized states induced by an individual atomic-scale defect in graphene, including a single-carbon vacancy, a nitrogen-atom dopant, and a hydrogen-atom chemisorption. Lastly, we give a perspective in this field.     

Orbital electronic heat capacity of hydrogenated monolayer and bilayer graphene

The tight-binding Harrison model and Green's function approach have been utilized in order to investigate the contribution of hybridized orbitals in the electronic density of states(DOS) and electronic heat capacity(EHC) for four hydrogenated structures, including monolayer chair-like, table-like, bilayer AA- and finally AB-stacked graphene. After hydrogenation, monolayer graphene and bilayer graphene are behave as semiconducting systems owning a wide direct band gap and this means that all orbitals have several states around the Fermi level. The energy gap in DOS and Schottky anomaly in EHC curves of these structures are compared together illustrating the maximum and minimum band gaps are appear for monolayer chair-like and bilayer AA-stacked graphane, respectively. In spite of these, our findings show that the maximum and minimum values of Schottky anomaly appear for hydrogenated bilayer AA-stacked and monolayer table-like configurations, respectively.     

单层与双层石墨烯的光学吸收性质研究

采用紧束缚模型分别描述单层、双层石墨烯的能带结构, 利用光子-电子相互作用的二阶微扰理论分别计算单光子和双光子吸收系数.计算结果表明: 单层石墨烯单光子吸收系数为常数, 约为6.8×10⁷ m^-1, 即单层石墨烯对入射光的吸收率约为2.3%; 双层石墨烯的单光子吸收比单层石墨烯的单光子吸收强, 且随入射光波长呈分段性变化.单层石墨烯的双光子吸收系数与波长λ⁴成正比; 双层石墨烯双光子吸收系数在红外波段(～ 3100 nm处)有一个很强的共振吸收峰. 研究结果可为石墨烯材料在光电子器件的研究和制作方面提供指导. 关键词： 石墨烯 光学吸收 紧束缚模型     

Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states

The dual-channel nearly perfect absorption is realized by the coupled modes of topological interface states (TIS) in the near-infrared range. An all-dielectric layered heterostructure composed of photonic crystals (PhC)/graphene/PhC/graphene/PhC on GaAs substrate is proposed to excite the TIS at the interface of adjacent PhC with opposite topological properties. Based on finite element method (FEM) and transfer matrix method (TMM), the dual-channel absorption can be modulated by the periodic number of middle PhC, Fermi level of graphene, and angle of incident light (TE and TM polarizations). Especially, by fine-tuning the Fermi level of graphene around 0.4 eV, the absorption of both channels can be switched rapidly and synchronously. This design is hopefully integrated into silicon-based chips to control light.     

Synthesis of high-quality monolayer graphene by low-power plasma

The growth of high-quality graphene on copper substrates has been intensively investigated using chemical vapor deposition (CVD). It, however, has been considered that the growth mechanism is different when graphene is synthesized using a plasma CVD. In this study, we demonstrate a dual role of hydrogen for the graphene growth on copper using an inductively coupled plasma (ICP) CVD. Hydrogen activates surface-bound carbon for the growth of high-quality monolayer graphene. In contrast, the role of an etchant is to manipulate the distribution of the graphene grains, which significantly depends on the plasma power. Atomic-resolution transmission electron microscopy study enables the mapping of graphene grains, which uncovers the distribution of grains and the number of graphene layers depending on the plasma power. In addition, the variation of electronic properties of the synthesized graphene relies on the plasma power.     

Electrical conductivity and resonant states of doped graphene considering next-nearest neighbor interaction

The next-nearest neighbor interaction (NNN) is included in a tight-binding Kubo formula calculation of the electronic spectrum and conductivity of doped graphene. As a result, we observe a wide variation of the behavior of the conductivity, as happens in carbon nanotubes, since the Fermi energy and the resonance peak are not shifted by the same amount when the NNN interaction is included. This finding may have a profound effect on the idea of explaining the minimal conductivity of graphene as a consequence of impurities or defects. Finally, we also estimate the mean free path and relaxation time due to resonant impurity scattering.     

Quasibound states in graphene quantum-dot nanostructures generated by concentric potential barrier rings

We study the quasibound states in a graphene quantum-dot structure generated by the single-, double-, and triple-barrier electrostatic potentials. It is shown that the strongest quasibound states are mainly determined by the innermost barrier. Specifically, the positions of the quasibound states are determined by the barrier height, the number of the quasibound states is determined by the quantum-dot radius and the angular momentum, and the localization degree of the quasibound states is influenced by the width of the innermost barrier, as well as the outside barriers. Furthermore, according to the study on the double- and triple-barrier quantum dots, we find that an effective way to generate more quasibound states with even larger energy level spacings is to design a quantum dot defined by many concentric barriers with larger barrier-height differences. Last, we extend our results into the quantum dot of many barriers, which gives a complete picture about the formation of the quasibound states in the kind of graphene quantum dot created by many concentric potential barrier rings.     

Edge magnetization in Bernal-stacked trilayer zigzag graphene nanoribbons

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.