Miniband Spectrum Research Articles

Full Slonczewski-Weiss-McClure parametrization of few-layer twistronic graphene

We use a hybrid k dot p theory - tight binding (HkpTB) model to describe interlayer coupling simultaneously in both Bernal and twisted graphene structures. For Bernal-aligned interfaces, HkpTB is parametrized using the full Slonczewski-Weiss-McClure (SWMcC) Hamiltonian of graphite, which is then used to refine the commonly used minimal model for twisted interfaces, by deriving additional terms that reflect all details of the full SWMcC model of graphite. We find that these terms introduce some electron-hole asymmetry in the band structure of twisted bilayers, but in twistronic multilayer graphene, they produce only a subtle change of moire miniband spectra, confirming the broad applicability of the minimal model for implementing the twisted interface coupling in such systems.

High-order minibands and interband Landau level reconstruction in graphene moiré superlattices

The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride (G/hBN) heterostructures, the lattice mismatch between the two atomic crystals generates a unique kind of periodic structure known as a moir\'e superlattice. Of particular interests is the emergent phenomena related to the reconstructed band-structure of graphene, such as the Hofstadter butterfly, topological currents, gate dependent pseudospin mixing, and ballistic miniband conduction. However, most studies so far have been limited to the lower-order minibands, e.g. the 1st and 2nd minibands counted from charge neutrality, and consequently the fundamental nature of the reconstructed higher-order miniband spectra still remains largely unknown. Here we report on probing the higher-order minibands of precisely aligned graphene moir\'e superlattices by transport spectroscopy. Using dual electrostatic gating, the edges of these high-order minibands, i.e. the 3rd and 4th minibands, can be reached. Interestingly, we have observed interband Landau level (LL) crossinginducing gap closures in a multiband magneto-transport regime, which originates from band overlap between the 2nd and 3rd minibands. As observed high-order minibands and LL reconstruction qualitatively match our simulated results. Our findings highlight the synergistic effect of minibands in transport, thus presenting a new opportunity for graphene electronic devices.

Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice

We determine the structure of band and gaps in graphene encapsulated in hexagonal boron nitride and subjected to magnetic field of Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one non-dispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling slightly broadened first Landau levels in graphene, suggesting the persistence of $\nu = \pm 2$ quantum Hall effect states. Also, we identify occasional merging point of magnetic minibands which feature Dirac-type dispersion at the consecutive miniband edges.

Superlattice effects in graphene on SiC(0001) and Ir(111) probed by ARPES

We review the angle-resolved photoemission spectroscopy (ARPES) technique and its applications to epitaxially grown graphenes. In particular we discuss the extraction of symmetry-breaking factors associated with superlattice formation due to substrate lattice mismatch. For UHV grown graphene on SiC, which has a quasi-13×13 superlattice (with respect to graphene), no coupling vectors exist to break the chiral symmetry, and a gap at ED is not observed. For graphene on Ir(111), lattice mismatch induces a well-known Moiré pattern with 10×10 (relative to graphene) symmetry. Despite the fact that chirality should be preserved under this symmetry, energy gaps are found at the main as well as the mini-Dirac crossings. A simple tight binding model that neglects chirality can explain the observed miniband spectrum in graphene on Ir(111).

Massless Dirac fermions in a laser field as a counterpart of graphene superlattices

We establish an analogy between spectra of Dirac fermions in laser fields and an electron spectrum of graphene superlattices formed by static one-dimensional periodic potentials. The general relations between a laser-controlled spectrum where electron momentum depends on the quasienergy and a superlattice miniband spectrum in graphene are derived. As an example we consider two spectra generated by a pulsed laser and by a steplike electrostatic potential. We also calculate the graphene excitation spectrum in continuous strong laser fields in the resonance approximation for linear and circular polarizations. Some physical phenomena, including an anomalous energy-gap anisotropy, related to the peculiar graphene energy spectrum in the strong electromagnetic field are discussed.

A study of the GaAs/AlAs(001) superlattice spectrum within the abrupt- and smooth-boundary models

The electron states and miniband spectra of (GaAs) m (AlAs) n (001) superlattices related to the Г- and X z -valleys of conduction bands of bulk GaAs and AlAs crystals are considered within the framework of simplified abrupt- and smooth-heteroboundary models. The models are constructed on the basis of calculations made by the pseudopotential method. It is shown that the proposed models describe the results of the corresponding exact calculations in the approximation of the abrupt and smooth boundaries reasonably well. It is found that the difference between the smooth-boundary and abrupt-boundary models becomes pronounced in the case of superlattices with thin layers, where this difference results in a qualitatively different dispersion of lower minibands.

Magnetically induced Bragg scattering of electrons in quantum-dot crystals

We demonstrate a novel manifestation of dynamic Bragg reflection in artificial quantum-dot crystals that is driven by the application of a magnetic field. This backscattering is coherently cascaded as the number of dots in the structure is increased, causing a superlinear damping of the electron wave function and the appearance of a series of gaps in the miniband spectrum. The evolution of the dynamic miniband structure as the magnetic field is varied gives rise to behavior analogous to a metal-insulator transition, which is manifest as a dramatic resonance in the magneto-resistance of the structures.

Energy states in short-period symmetrical and asymmetrical (GaAs)N/(AlAs)M superlattices: The effect of the boundary conditions

Obtained experimental data on low-temperature photoluminescence are used to numerically simulate the energy states in symmetrical and asymmetrical short-period (GaAs)N/(AlAs)M superlattices with the (001) orientation. The matrix formalism in the envelope-function method is employed to study trends in the behavior of the miniband spectrum in models with different boundary conditions. It is shown that correct information about the type of transitions in the materials under consideration can be obtained even if the boundary conditions are diagonal. The effect of corrections on the miniband spectrum that arise when mixing of the states belonging to the Γ and X valleys is taken into account and a δ-functional potential localized at the heterointerface is present is studied.

Electronic and optical properties of AlAs/AlxGa1−x As(110) superlattices

Electronic states in the conduction band of (AlAs)M(AlxGa1−x As)N(110) superlattices are investigated for various M and N. It is shown that electronic properties of these structures are mainly determined by electrons of two pairs of valleys, namely, either Γ-X Z or X X –X Y . Calculations based on the developed model of joining the envelope functions were carried out. Miniband spectra, symmetry, and localization of wave functions, as well as probabilities of miniband-to-miniband infrared absorption, are determined and analyzed. It is shown that, in the case of the X X –X Y pair of valleys, the absorption probabilities are high not only for polarization of light along the growth axis of the superlattice but also for the normal incidence of an optical wave on the structure surface.

Electron states in (AlAs)M(AlxGa1−x As)N superlattices

Electronic states have been studied for energies within the conduction band of (AlAs)M(AlxGa1−x As)N (111) superlattices. Calculations were carried out in terms of the model of the matching of envelope functions at heterointerfaces, generalized to the case of the structures under consideration. Miniband spectra, symmetry and localization of wave functions, and the probabilities of interband IR absorption were analyzed. The probabilities are shown to be substantial not only for light polarized along the superlattice growth axis, but also for normal incidence on the structure surface. The superlattices studied are shown to be promising materials for IR photodetectors.

Miniband spectra of (AlAs)M(GaAs)N(111) superlattices

Electron states in the conduction band of (111)-oriented (AlAs)M(GaAs)N superlattices (SLs) with M≥N and N<10 are considered. The properties of such SLs are mainly governed by the X-valley electrons in AlAs and the L-valley electrons in GaAs. The calculations are carried out using a previously developed model for the envelope-function matching at heterointerfaces. Miniband spectra, symmetry, and localization of the wave functions, as well as the probabilities of interminiband infrared absorption, are calculated and analyzed. It is shown that the absorption probabilities may be high not only for a light wave polarized along the SL axis, but also for a light wave incident normally to the surface of the structure. It is found that, for analysis of infrared absorption, it is important to take into account the contribution to the wave functions from X5 valence-band states.

Quantized adiabatic charge transport in a carbon nanotube.

The coupling of a semimetallic carbon nanotube to a surface acoustic wave (SAW) is proposed as a vehicle to realize quantized adiabatic charge transport. We demonstrate that electron backscattering from a periodic SAW potential can be used to induce a miniband spectrum at energies near the Fermi level. Within the framework of Luttinger liquid theory, electron interaction is shown to enhance minigaps and thereby improve current quantization.

Transport study in high mobility GaAs/AlGaAs lateral superlattices

We report transport measurements in high mobility GaAs/AlGaAs heterostructures with lateral surface-induced periodic potentials. A modulation period of 1900 Å was produced with Schottky gates located above the two-dimensional electron gas. Both commensuration and Shubnikov–de Haas oscillations were observed. Nonlinear conductance (dI/dVds) measurements revealed a sharp feature near zero source-drain voltage. With zero magnetic field this feature is a conductance dip while finite B turns it into a conductance peak. We suggest that the conductance features result from Zener tunneling through a tilted miniband spectrum caused by the superlattice potential.

On wave propagation in periodic structures with smoothly varying parameters

A theory of wave propagation in periodic structures with smoothly varying parameters is developed. Consideration is provided for the case when both periodicity and modulation are in one dimension. The theory is based on the Wannier-function expansion. As an example, it is shown that electromagnetic waves can propagate along effective waveguides, which are interpreted in terms of defect modes. Related effects such as anomalous scattering, self-channeling (gap solitons) in nonlinear periodic media), and miniband spectra are discussed.

Wannier-Stark resonances under strong localization conditions in natural silicon-carbide superlattices

A detailed experimental investigation is made of the electronic transport under conditions of Wannier-Stark localization of carriers in a natural superlattice of hexagonal polytypes of silicon carbide. The 4H and 6H polytypes, which possess different superlattice and miniband spectrum parameters, are employed. Direct measurements of the electronic current versus the average electric field in the active region of the sample revealed a series of regions of negative differential conductivity in fields ranging from 500 to 2100 kV/cm. Analysis of the results shows that the observed current resonances are associated with the development of the Wannier-Stark quantization process and are due to conduction mechanisms such as hopping conduction, induced between the levels of a Wannier-Stark ladder by a resonant electron-phonon interaction, and the resonant interminiband tunneling from the first into the second miniband.

Disorder-induced localization in superlattices

Abstract Purposely disordered GaAs/AlxGa1−x As short period superlattices, followed by an enlarged well, were grown by molecular beam epitaxy. Selective excitation photoluminescence and photoluminescence excitation measurements were performed to study the energy dependence of the motion of resonantly photocreated excitons in disordered superlattices. The disorder was introduced as a random succession of different well widths distributed according to a Gaussian function. We report the existence of different energy regions in the superlattice bands, corresponding to extended and spatially confined (localized) states. A calculation of the superlattice miniband spectrum suggests that the coupling between similar wells although on different spatial region atlows excitonic diffusion for some energies. We compare different samples with different disorder distribution. The role of the enlarged well in driving the vertical diffusion is discussed.

Periodic and purposely disordered superlattices: The effect of continuous and discrete disorder distribution.

Selective-excitation photoluminescence measurements were performed on purposely disordered superlattices to study the energy dependence of the motion of resonantly photocreated excitons in disordered superlattices. The disorder was introduced as a random succession of different well widths distributed according to a Gaussian function. We compare the continuous and the discrete Gaussian distributions of the disorder. In the latter case, we report the existence of different energy regions in the superlattice bands, corresponding to extended and spatially confined (localized) states. A calculation of the superlattice miniband spectrum and of the localization lengths for the different energy states suggests that the coupling between similar wells, although on different spatial regions, allows excitonic diffusion for some energies in the discrete Gaussian-disordered superlattice. According to calculations, a continuous Gaussian distribution yields only localized states.

Photoluminescence of disorder-induced localized states in GaAs/AlxGa1-xAs superlattices.

Purposely disordered GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As superlattices, followed by an enlarged well, were grown by molecular-beam epitaxy. Selective-excitation photoluminescence measurements were performed to study the energy dependence of the motion of resonantly photocreated excitons in disordered superlattices. We report the existence of different energy regions in the superlattice bands, corresponding to extended and spatially confined (localized) states induced by disorder. The temperature dependence of the photoluminescence spectra suggests the existence of activation energies for the localized states. This reflects itself by an increase in the propagation rate of excitons by increasing the temperature. We compare qualitatively the experimental findings with a calculation of the superlattice miniband spectrum.