Band Structure Of Superlattices Research Articles

Engineering Topological States in Nanographenes

Our research focuses on the rational design, deterministic assembly, and detailed investigation of the physical phenomena emerging from quantum confinement effects in graphene nanomaterials. We pursue a highly integrated multidisciplinary program, founded on synthetic bottom-up approaches toward functional materials with precisely defined structure. We control their assembly into hierarchically ordered architectures and evaluate inherent physical properties using modern scanning probe techniques cross multiple length, time, and energy scales. We recently demonstrated the rational design and experimental realization of a graphene nanoribbon (GNR) superlattices that hosts a 1D array of symmetry-protected topological states, thus generating otherwise inaccessible electronic structure.1 This new class of materials can be thought of as an extended form of poly-acetylene wherein highly localized half-filled topological states replace the familiar single occupied p-orbitals along a conjugated π-system. Experimental results and first-principles calculations reveal that the frontier band structure of these GNR superlattices is defined purely by the coupling between adjacent topological interface states and can be tuned all the way from a semiconductor and a metal.2,3 This novel manifestation of 1D topological phases presents an entirely new route to band engineering in 1D materials based on precise control of their electronic topology and is a promising new platform for future studies of 1D quantum spin physics and metallicity in low dimensional carbon nanomaterials. 1. Topological Band Engineering of Graphene Nanoribbons. Rizzo, D. J.; Veber, G.; Cao, T.; Bronner, C.; Chen, T.; Zhao, F.; Rodriguez, H.; Louie, S. G.; Crommie, M. F.; Fischer, F. R. Nature 2018, 560, 204-206. 2. Inducing Metallicity in Graphene Nanoribbons via Zero-Mode Superlattices. Rizzo, D. J.; Veber, G.; Jiang, J.; McCurdy, R.; Cao, T.; Bronner, C.; Chen, T.; Louie, S. G.; Fischer, F. R.; Crommie, M. F. Science 2020, 369, 1597-1603. 3. Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons. McCurdy, R. D.; Delgado, A.; Jiang, J.; Zhu, J.; Wen, E. C. H.; Blackwell, R. E.; Veber, G. C.; Wang, S.; Louie, S. G.; Fischer, F. R. J. Am. Chem. Soc. 2023, 145, 15162-15170.

Electronic transport properties in GaAs/AlGaAs finite superlattice of cylindrical quantum wires

In this paper, we have studied a theoretical and numerical investigation of the electronic properties of finite cylindrical quantum wires (CQWRs), constituted by the periodic alteration of two semiconductor materials of CQWRs GaAs/AlGaAs in the axial direction, the structure sandwiched between two substrates GaAs. The electronic band structure and the electronic transmission spectrum are obtained by means of Green’s function approach, taking into account the impact of connection barriers. Our results reveal that the electronic energy levels of CQWRs consist of alternating passbands and bandgaps. The coincidence of incoming electronic waves with these discrete electronic energy levels leads to electron transport during the CQWRs superlattice. We employed an effective mass model dependent on the cell position in the axial direction to solve the Schrodinger equation. This model was adjusted to reflect variations in the confining potentials while accounting for changes in the radial direction. When the radius of the structure is relatively small the electronic states tend towards higher energies due to geometrical confinement. On the other hand, as the radius increases, the passbands and bandgaps move to lower energies. Similarly, the pseudogaps turn into full gaps, and their width increases, and this feature is also observed when the number of cells increases. This property is due to the interaction between the neighboring electrons and the eigenstates of the CQWRs. In addition, the passbands and band gaps shift to high energy when the barrier concentration increases, and the width of band gaps increases also. Finally, we have demonstrated the theoretical design of an optoelectronic device for filtering electronic waves by geometrical and physical parameters, whose electronic band structure of this finite CQWRs superlattice can be controlled.

Design and Growth of Low Resistivity P-Type AlGaN Superlattice Structure.

This work investigated the impact of periodic thickness and doping region on the doping efficiency of the P-type AlGaN superlattice. In this paper, the band structure of the simulated superlattice was analyzed. The superlattice structure of Al0.1Ga0.3N/Al0.4Ga0.6N, and the AlGaN buffer on the sapphire substrate, achieved a resistivity of ~3.3 Ω·cm. The results indicate that barrier doping and low periodic thickness offer significant advantages in introducing a reduction of the resistivity of P-type AlGaN superlattice structures.

Probing Interlayer Interactions and Commensurate-Incommensurate Transition in Twisted Bilayer Graphene through Raman Spectroscopy.

Twisted 2D layered materials have garnered much attention recently as a class of 2D materials whose interlayer interactions and electronic properties are dictated by the relative rotation/twist angle between the adjacent layers. In this work, we explore a prototype of such a twisted 2D system, artificially stacked twisted bilayer graphene (TBLG), where we probe, using Raman spectroscopy, the changes in the interlayer interactions and electron-phonon scattering pathways as the twist angle is varied from 0° to 30°. The long-range Moiré potential of the superlattice gives rise to additional intravalley and intervalley scattering of the electrons in TBLG, which has been investigated through their Raman signatures. Density functional theory (DFT) calculations of the electronic band structure of the TBLG superlattices were found to be in agreement with the resonant Raman excitations across the van Hove singularities in the valence and conduction bands predicted for TBLG due to hybridization of bands from the two layers. We also observe that the relative rotation between the graphene layers has a marked influence on the second order overtone and combination Raman modes signaling a commensurate-incommensurate transition in TBLG as the twist angle increases. This serves as a convenient and rapid characterization tool to determine the degree of commensurability in TBLG systems.

Emergence of Different Replica Dirac Cones and Intra- and Intervalley Scatterings in Short-Wavelength Graphene Superlattices Modulated by an Atomic-Scale Sharp Potential

Here, we calculate the unfolded band structure of short-wavelength graphene superlattices modulated by the atomic-scale sharp potential of a semiconductor surface, using density functional theory. We show that in the case of the superlattice graphene Brillouin zone (SBZ) center folded into the primitive graphene Brillouin zone (GBZ) corner, the emergence of different replica Dirac cones and their scattering behaviors are driven by the substrate-induced potential or atomic-scale disorders as well as by the correlation between the rotation angle of the superlattice and the trigonal warping orientation of the Dirac cone because of the quantum interference associated with the scattering at the SBZ edge. In particular, a superlattice with a rotational angle of φ = 30° (G–N√3 × N√3–R30°, N > 1) facilitates intervalley scattering, whereas an unrotated superlattice (G–N3 × N3) is favorable to intravalley scattering. For a superlattice with a rotational angle in the range of 0 < φ < 30°, the intervalley and intravalley scatterings may be comparable to each other, leading to the emergence of mixed inequivalent replica cones at the SBZ center (or GBZ corner). Interestingly, such inequivalent replica cones facilitate a stronger intervalley scattering at the GBZ corner, compared to the G–N√3 × N√3–R30° and G–N3 × N3 superlattices, thus opening a larger energy gap at the primitive Dirac point. In addition to the inversion symmetry breaking in graphene, we show that intervalley scattering can also generate an energy gap at the secondary Dirac point.

Signature of miniband nodes in magneto-optical properties of one-dimensional superlattice of planar quantum rings

The effect of transverse magnetic field on the band structure, magnetization and inter-miniband magnetoabsorption of a one-dimensional superlattice of planar quantum rings is discussed. The band structure calculations are made in the framework of diagonalization procedure. A complete set of basis functions, reflecting the structure periodicity in superlattice direction and the effect of magnetic field is constructed, considering the Landau gauge of the vector potential in the Hamiltonian. It is shown that the energy minibands reveal repeating nodes that correspond to a degeneration of quantum states. The magnetization of the system mimics the main peculiarities of the same quantity for a single QR, however considerable differences are observed as well. The examination of the magnetoabsorption indicates on the possibility to extract an information about the existence of nodes in the band structure and the arrangement of quantum states in the neighboring minibands.

Localization of ultracold atoms in Zeeman lattices with incommensurate spin-orbit coupling

We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the problem is reduced to description of spinor states in a superlattice. In the absence of a constant Zeeman splitting, the system acquires an additional symmetry, which hinders the localization. However, if the lattices are deep enough, then localized states can appear even for Zeeman field with zero or small mean value. Spatial distribution of localized modes is nearly uniform and is directly related to the topological properties of the effective superlattice: center-of-mass coordinates of modes are determined by Zak phases computed from the superlattice band structure. The best rational approximations feature the `memory' effect: each rational approximation holds the information about the energies and spatial distribution of the modes obtained under preceding, less accurate approximations. Dispersion of low-energy initial wavepackets is characterized by the law $\propto t^\beta$ with $\beta$ varying between $1/2$ at the initial stage and $1$ at longer, but still finite-time, evolution. The dynamics of initial wavepackets, exciting mainly localized modes, manifests quantum revivals.

Simulation of the Band Structure of InAs/GaSb Type II Superlattices Utilizing Multiple Energy Band Theories

Antimonide type II superlattices is expected to overtake HgCdTe as the preferred materials for infrared detection due to their excellent photoelectric properties and flexible and adjustable band structures. Among these compounds, InAs/GaSb type II superlattices represent the most commonly studied materials. However, the sophisticated physics associated with the antimonide-based bandgap engineering concept started at the beginning of the 1990s gave a new impact and interest in the development of infrared detector structures within academic and national laboratories. InAs/GaSb superlattices are a type II disconnected band structure with electrons and holes confined in the InAs and GaSb layers, respectively. The electron miniband and hole miniband can be regulated separately by adjusting the thickness of InAs and GaSb layers, which facilitates the design of superlattice structures and optimizes the value of band offset. In recent years, both domestic and foreign researchers have made many attempts to quickly and accurately predict the bandgaps of superlattice materials before superlattice materials grow. These works constituted a theoretical basis for the effective utilization of the InAs/GaSb system in material optimization and designing new SL structures; they also provided an opportunity for the preparation and rapid development of InAs/GaSb T2SLs. In this paper, we systematically review several widely used methods for simulating superlattice band structures, including the k·p perturbation method, envelope function approximation, empirical pseudopotential method, empirical tight-binding method, and first-principles calculations. With the limitations of different theoretical methods proposed, the simulation methods have been modified and developed to obtain reliable InAs/GaSb SL energy band calculation results. The objective of this work is to provide a reference for designing InAs/GaSb type II superlattice band structures.

Impact of stacking sequence on the tight-binding electronic band structures of (BeX)m/(ZnX)m, X = S, Se and Te superlattices

By using a semi-empirical tight-binding sp3s* method, the results of comprehensive electronic band structures are reported for the zinc-blende beryllium- and zinc-chalcogenides (BeX and ZnX; X = S, Se, Te) as well as their representative (BeX)m/(ZnX)m (001) superlattices (SLs). For the bulk BeX and ZnX materials, the simulations of energy band dispersions Ejk→ have offered the correct band gaps in very good agreement with the first-principles calculations. The band-mixing effect through the interfaces of two constituent compounds (BeX indirect- and ZnX direct-band gap) has played an important role for determining the overall band lineup in the (BeX)m /(ZnX)m SLs over the entire Brillouin zone. Based on the quantum confinement effects, the impact of stacking sequence m ≤ 10 is carefully examined for assessing the band structures of SLs. The results have clearly revealed that the nature of energy bandgaps is quite sensitive to the choice of well (BeX) and barrier (ZnX) layer thickness. Obviously, this intuition has implied that controlling m to achieve direct bandgaps in novel (BeX)m/(ZnX)m SLs is probably an effective way of assessing their potential use in technologically important optoelectronic devices.

Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Bilayer Graphene.

In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at M and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac points in the reconstructed dispersions. For twists θ > 21.8°, the low-energy minigaps are not due to cone anticrossing as is the case at smaller twist angles but rather due to moiré scattering of electrons in one graphene layer on the potential of the other which generates intervalley coupling. Our work demonstrates the robustness of the mechanisms which enable engineering of electronic dispersions of stacks of two-dimensional crystals by tuning the interface twist angles. It also shows that large-angle tBLG hosts electronic minigaps and van Hove singularities of different origin which, given recent progress in extreme doping of graphene, could be explored experimentally.

Bayesian Optimization of Hubbard U’s for Investigating InGaN Superlattices

In this study, we undertake a Bayesian optimization of the Hubbard U parameters of wurtzite GaN and InN. The optimized Us are then tested within the Hubbard-corrected local density approximation (LDA+U) approach against standard density functional theory, as well as a hybrid functional (HSE06). We present the electronic band structures of wurtzite GaN, InN, and (1:1) InGaN superlattice. In addition, we demonstrate the outstanding performance of the new parametrization, when computing the internal electric-fields in a series of [InN]1–[GaN]n superlattices (n = 2–5) stacked up along the c-axis.

Electronic properties of atomically coherent square PbSe nanocrystal superlattice resolved by Scanning Tunneling Spectroscopy

Rock-salt lead selenide nanocrystals can be used as building blocks for large scale square superlattices via two-dimensional assembly of nanocrystals at a liquid-air interface followed by oriented attachment. Here we report Scanning Tunneling Spectroscopy measurements of the local density of states of an atomically coherent superlattice with square geometry made from PbSe nanocrystals. Controlled annealing of the sample permits the imaging of a clean structure and to reproducibly probe the band gap and the valence hole and conduction electron states. The measured band gap and peak positions are compared to the results of optical spectroscopy and atomistic tight-binding calculations of the square superlattice band structure. In spite of the crystalline connections between nanocrystals that induce significant electronic couplings, the electronic structure of the superlattices remains very strongly influenced by the effects of disorder and variability.

Internal quantum efficiency in 6.1 Å superlattices of 77% for mid-wave infrared emitters

Two new superlattices with high internal quantum efficiency at high injection, InAs/AlGaInSb and InAs/GaInSb/InAs/AlAsSb, are presented and compared with state-of-the-art InAs/GaSb and InAs/InAsSb superlattices. The internal quantum efficiency peaks at 44% and 77% for the InAs/AlGaInSb and InAs/GaInSb/InAs/AlAsSb samples, respectively, which suggests that they are excellent candidates for high-efficiency mid-wave infrared LEDs. These values have been measured without invoking the ABC model to eliminate the assumption of Boltzmann statistics. The calculated superlattice band structures are used qualitatively to explain the internal quantum efficiency results.

Dirac equation and energy levels of electrons in one-dimensional wells: Plane wave expansion method

Abstract The band structure of an electron in one-dimensional crystals is obtained using the Dirac equation. At low energies, the Dirac equation solved for a periodic 1D potential corresponds to the obtention of the band structure of a 1D graphene periodic superlattice. The plane wave expansion method was used to obtain the theoretical solution to the problem as an eigenvalues equation, which is solved with a standard matrix diagonalization numerical method. Results are presented for the case of the Dirac–Kronig–Penney model for a rectangular potential of width w and depth V a . It is firstly shown that the bands structures, calculated in the first Brillouin zone, using the Schrodinger and Dirac equations, give practically the same results for | V a | ≤ 0 . 01 e r , where e r is the electron’s rest energy. Then, a comparison between the limits of the two lowest bands obtained with Schrodinger and Dirac formalisms is presented as a function of the ratio a p ∕ w for a fixed depth, where a p is the potential’s period. Later, since the energies given by the Dirac equation form two subsets separated by a gap Δ for any value of the potential amplitude V a , it was studied and found that the width of this gap is reduced when the magnitude of the potential is increased, i.e., for V a ≈ | ± 2 m e c 2 | , Δ ≈ 0 . 001 m e c 2 . It was also studied a structure with local periodicity a l embedded in a periodic one. This crystal allows to study both, localized and surfaces states. In the first case, the deepness V c of the central potential is varied and two localized states appear at the forbidden gap between the two lower bands. In the second one, the width w s of the lateral wells is varied and two-degenerated surface modes appear.

First-principles on the energy band mechanism for modifying conduction property of graphene nanomeshes

By means of first-principles electronic structure calculations, the ordered graphene nanomeshes with patterned hexagonal vacancy holes are theoretically studied to explore the modification mechanism of electrical conduction on graphene atomic monolayers. According to pseudopotential plane wave first-principles scheme based on density functional theory, the band structures of graphene nanomeshes are calculated to analyze the electrical conductance in correlation with the superlattice symmetry and vacancy hole magnetism. Based on the structural features and topological magnetism of Y-shaped nodes between the nanopores on the atomic monolayer of graphene, the graphene nanomeshes are classified into three types. The quadruplet degeneracy and splitting of electronic states at Brillouin zone center are investigated by comparing the band structures of graphene nanomeshes and analogical superlattices. The effects of inversion symmetry and supercell size on the opening band-gap at Dirac cone are elaborately analyzed with the consideration of antiferromagnetic coupling and hydrogen passivation at the magnetic edge of nanopores on graphene nanomeshes. The band-structure calculation results indicate that the (3&lt;i&gt;m&lt;/i&gt;, 3&lt;i&gt;n&lt;/i&gt;) (&lt;i&gt;m&lt;/i&gt; and &lt;i&gt;n&lt;/i&gt; are integers) superlattices have fourfold degenerate electronic states at center point of Brillouin zone, which can be effectively splitted by regularly arranging porous atomic vacancy to make the (3&lt;i&gt;m&lt;/i&gt;, 3&lt;i&gt;n&lt;/i&gt;) nanomesh, resulting in adjustable band-gap no matter whether or not the sublattices keeping in equivalence. In the nanomeshes formed by patterned holes with magnetic edge, the antiferromagnetic coupling adds a quantum parameter to the inversion symmetry so as to break the sublattice equivalence, opening band-gap at the twofold degenerate &lt;i&gt;K&lt;/i&gt; point. Nevertheless, the hydrogen passivation at the edge of magnetic nanopores will convert the magnetic graphene nanomeshes into non-magnetic and eliminate the band-gap at &lt;i&gt;K&lt;/i&gt; point. The band-gap of graphene nanomeshes could also be controlled by changing the density of nanopores, suggesting a graphene nanomaterial with adjustable band-gap that can be designed by controlling the mesh pore spacing. The graphene nanomeshes represent a new mechanism of forming band-gap and thus promise a strategy for achieving special electrical properties of graphene nanostructures. These results also theoretically demonstrate that the nano-graphene is a prospective candidate with flexibly adjustable electrical properties for realizing multivariate applications in new-generation nano-electronics.

Topological phase transitions in superlattice based on 2D Dirac crystals with anisotropic dispersion

Superlattice based on the system of periodically spaced 2D Dirac materials with anisotropic electron dispersion has been studied. Topological transition between semi-metallic phase and band-insulator in the electronic structure of considered superlattice has been investigated. The system of the minigaps and minibands has been shown to appear in band structure of considered superlattice. The dependences of the minigaps and conduction miniband widths on the superlattice parameters have been analyzed. The approximate explicit form of the electron spectrum which can explain the topological transition has been derived. The renormalization of electron velocities near the Dirac points of superlattice band structure has been shown. • Superlattice based on 2D Dirac crystals with anisotropic dispersion is studied. • Electron dispersion is obtained for considered superlattice. • Topological transition between semi-metallic phase and band-insulator is shown. • Explicit analytical expression for energy spectrum is derived. • Topological phase transition can be explained by means of analytical expression.

Erratum to: Band structures of symmetrical graphene superlattice with cells of three regions

Some sentences of the abstract have been removed by mistake. The correct abstract is given below. We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different physical parameters. We numerically analyze such relation and show that there exist three zones: bound, unbound and forbidden states. In the central zone of the band structures, we determine and enumerate the vertical Dirac points (ky = 0), opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points. The publisher apologizes for the inconvenience.

Band structure of monolayer of graphene, silicene and silicon-carbide including a lattice of empty or filled holes

We have developed a -orbital tight-binding Hamiltonian model taking into account the nearest neighbors to study the effect of antidot lattices (two dimensional honeycomb lattice of atoms including holes) on the band structure of silicene and silicon carbide (SiC) sheets. We obtained that the band structure of the silicene antidot superlattice strongly depends on the size of embedded holes, and the band gap of the silicene antidot lattice increases by increasing of holes diameter. The band gap of SiC antidot lattice, except for the lattice of the small unit cell, is independent of the holes diameter and also depends on the distance between holes. We obtained that, the band gap of the SiC antidot lattice is the same as the band gap of the corresponding sheet without hole. Also, the electronic properties of the SiC antidot superlattice occupied either by carbon or by silicon atoms are investigated, numerically. Furthermore, we study the effect of occupation of graphene antidot by Si atoms and vice versa. Also, we have calculated the band structure of graphene and silicene antidot lattice filled by Si + C atoms. Finally, we compute the band structure of the SiC antidot lattice including the holes which are filled by C or by Si atoms. Really, in this paper we have generalized the method of paper[] about graphene antidot with empty holes to the cases of filled holes by different atoms and also to the case of silicene and silicon carbide antidot lattices.

Topological band engineering of graphene nanoribbons.

Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk1,2. Most advances in this field have focused on topological insulators and related topological crystalline insulators3 in two dimensions4-6 and three dimensions7-10, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs)11. The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a [Formula: see text] invariant12 (that is, an index of either 0 or 1, indicating two topological classes-similar to quasi-one-dimensional solitonic systems13-16). Interfaces between topologically distinct GNRs characterized by differentvalues of [Formula: see text] are predicted to support half-filled, in-gap localized electronic states that could, in principle, be used as a tool for material engineering11. Here we present the rational design and experimental realization of a topologically engineered GNR superlattice that hosts a one-dimensional array of such states, thus generating otherwise inaccessible electronic structures. This strategy also enables new end states to be engineered directly into the termini of the one-dimensional GNR superlattice. Atomically precise topological GNR superlattices were synthesized from molecular precursors on a gold surface, Au(111), under ultrahigh-vacuum conditions and characterized by low-temperature scanning tunnelling microscopy and spectroscopy. Our experimental results and first-principles calculations reveal that the frontier band structure(the bands bracketing filled and empty states) of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This manifestation of non-trivial one-dimensional topological phases presents a route to band engineering in one-dimensional materials based on precise control of their electronic topology, and is a promising platform for studies of one-dimensional quantum spin physics.

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different physical parameters. We numerically analyze such relation and show that there exist three zones: bound, unbound and forbidden states. In the central zone of the band structures, we determine and enumerate the vertical Dirac points, opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.