States In Superlattices Research Articles

The nontrivial states in one-dimensional nonlinear bichromatic superlattices

We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of the lattice with their chemical potential located in the linear gap regime and are sensitive to the phase parameter of the superlattice potential. We further demonstrate that the topological property of the nonlinear Bloch bands can be characterized by topological Chern numbers defined in the extended two-dimensional parameter space. In addition, we discuss that the composition relations between the nolinear Bloch waves and gap solitions for the nonlinear superlattices. The stabilities of edge solitons are also studied.

Local Density of States in One-dimensional Photonic Crystals and Sinusoidal Superlattices

We have calculated the local density of states (LDOS) for four Brillouin zones of a superlattice for a plane source depending on its location relative to the change in the profile of dielectricpermeability ɛ(z) of the superlattice. It is shown that the LDOS for the cases of sinusoidal and rectangular profiles of ɛ(z) are close to each other in the first and second Brillouin zones, and sharp differences between them appear beginning with the third zone. Radical changes in the LDOS occur in a rectangular superlattice with different thicknesses of adjacent layers. In this case, the function LDOS has a sharp jump at the edges of the allowed bands in the transition from one layer to another. The effects studied theoretically in this paper, can be detected and studied experimentally by the intensively developing currently methods of nanooptics.

Alternating superlattice textures in driven nanomagnets

Nanomagnets driven with uniform electric currents exhibit a wide variety of spatial textures. In the present work, we investigate alternating superlattice states in nanomagnets, which are spatially periodic textures composed by several spatial modes that oscillate in time. The magnetic system is described in the continuum approach by the Landau–Lifshitz–Gilbert–Slonczewski equation, and direct numerical simulations of this model allow us to characterize the alternating patterns. As a result of this temporal oscillation, textures alternate between different shapes. In particular, we focus on two types of textures, namely a superhexagon and a square-like pattern, which are composed by six and two dominant Fourier modes, respectively. Based on an appropriate modal decomposition, we reveal that the mechanism that originates the alternating superhexagon is a homoclinic bifurcation. In addition, we show that the oscillatory square-like texture emerges through a supercritical Andronov–Hopf bifurcation.

Depth-Resolved Composition and Electronic Structure of Buried Layers and Interfaces in a LaNiO3/SrTiO3 Superlattice from Soft- and Hard- X-ray Standing-Wave Angle-Resolved Photoemission

LaNiO3 (LNO) is an intriguing member of the rare-earth nickelates in exhibiting a metal-insulator transition for a critical film thickness of about 4 unit cells [Son et al., Appl. Phys. Lett. 96, 062114 (2010)]; however, such thin films also show a transition to a metallic state in superlattices with SrTiO3 (STO) [Son et al., Appl. Phys. Lett. 97, 202109 (2010)]. In order to better understand this transition, we have studied a strained LNO/STO superlattice with 10 repeats of [4 unit-cell LNO/3 unit-cell STO] grown on an (LaAlO3)0.3(Sr2AlTaO6)0.7 substrate using soft x-ray standing-wave-excited angle-resolved photoemission (SWARPES), together with soft- and hard- x-ray photoemission measurements of core levels and densities-of-states valence spectra. The experimental results are compared with state-of-the-art density functional theory (DFT) calculations of band structures and densities of states. Using core-level rocking curves and x-ray optical modeling to assess the position of the standing wave, SWARPES measurements are carried out for various incidence angles and used to determine interface-specific changes in momentum-resolved electronic structure. We further show that the momentum-resolved behavior of the Ni 3d eg and t2g states near the Fermi level, as well as those at the bottom of the valence bands, is very similar to recently published SWARPES results for a related La0.7Sr0.3MnO3/SrTiO3 superlattice that was studied using the same technique (Gray et al., Europhysics Letters 104, 17004 (2013)), which further validates this experimental approach and our conclusions. Our conclusions are also supported in several ways by comparison to DFT calculations for the parent materials and the superlattice, including layer-resolved density-of-states results.

Magnetic-field-induced spontaneous superlattice formation via spinodal decomposition in epitaxial strontium titanate thin films

Applying magnetic fields during growth of ceramic thin films creates a tipping point that spontaneously produces stress-based ferromagnets. While atoms in a normal crystal lattice are spaced closely together, researchers can now make ‘superlattices’ consisting of nanometer-wide strips of different crystals periodically stacked on top of each other. In semiconductors, thin films can be induced to form superlattices by tweaking the deposition conditions. Now, Naoki Wakiya from Shizuoka University in Japan and co-workers have replicated this feat for thin films of strontium titanate, an insulating oxide with magnetic and superconducting capabilities. The team used a pulsed laser to deposit strontium titanate onto a substrate and a strong magnetic field to stretch the usual crystal framework. The compressive stress in the new thin film initiates a transformation to a superlattice state and room-temperature ferroelectric behavior.

Strong influence of non-ideality of electrodes on stability of single domain state in ferroelectric-paraelectric superlattices

We study the phase stabilities with respect to small perturbations in ferroelectric-paraelectric superlattices and show that nature of the electrodes characterized by a deviation from the ideal behavior strongly influences the possibility to obtain single-domain state in ferroelectric-paraelectric superlattices. To demonstrate this, we analyze the limit of stability of the paraelectric and the single domain state in ferroelectric-paraelectric superlattices in contact with top and bottom electrodes with finite screening lengths. The combined analytical and numerical analyses of one bilayer and two bilayer systems are carried out using the Landau-Ginzburg-Devonshire formalism and equations of electrostatics. The BaTiO3/SrTiO3 system was considered as an example. Unlike the case of ideal electrodes where the stability limits are independent of the system size, the stability analysis in a multilayer with real electrodes should take into account explicitly the number of the repeating units that makes the algebra very cumbersome, forcing us to consider systems with one and two bilayer stacks only. Extrapolating the difference between the two systems to the cases of many repeating units gives us the possibility to make qualitative but feasible predictions related to those with many repeating units. We observe that in systems with nearly equal thicknesses of the ferroelectric and paraelectric layers, the electrodes with realistic screening lengths lead to dramatic widening of the parametric region where the single-domain state is absolutely unstable expelling the single-domain state to unphysical layer thicknesses and temperatures. This region grows when one goes from a single bilayer to two bilayer system, implying that obtaining a single domain state becomes even less feasible in systems with many bilayers. When electrode properties approach that of ideal in addition to increasing the volume fraction of the ferroelectric component, the effect of growth of the region of absolute instability of the single domain state may remain very strong for relatively thin repeating units (a few nanometers). This tendency will continue with increasing the number of the repeating units.

Valence Band Profile in Two-Dimensional Silicon-Oxygen Superlattices Probed by Internal Photoemission

Energy distribution of electron states in two-dimensional superlattices (SLs) of crystalline silicon layers separated by monolayers (MLs) of oxygen atoms is studied using internal photoemission (IPE) spectroscopy. SLs made of 1, 2 or 5 periods of one ML of O in between 25, 15, 7, 3 or ∼1 nm thick Si layers were studied by using IPE from these SLs into 20-nm thick Al2O3 dielectric deposited on top of the SL. We observed the reduction of direct optical transition intensity in Si-O SLs when decreasing the Si thickness to 1 nm, indicative of the Si electronic structure distortion inside the SLs. The field dependence of IPE spectral threshold indicates the absence of both the change in Si-O SLs VB energy and any additional field-induced band bending across the SLs. Further, electron spin resonance indicates the absence of additional Si dangling bonds in the Si-O SLs within the sensitivity limit of ≈1011 cm−2. These findings suggest that Si-O SLs enhance the carrier mobility by breaking the crystal symmetry and tuning the location of the channel to the region where electrons or holes travel without additional scattering.

Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice

Recent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by a manifold in momentum space with the topology of a single twist Möbius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves.

Influence of Fermi velocity engineering on electronic and optical properties of graphene superlattices

Abstract In this paper, using Kronig–Penney model, the electronic states in graphene-based superlattices with various substrates and considering exact electron Fermi velocity values are investigated. The analysis of our results clearly indicates that the difference between Fermi velocity values of gaped and gapless graphene regions determines the patency rate of band gap. Also, using transfer matrix method (TMM) the absorbance spectrum of mentioned structures is calculated. The more important result is that the absorbance of these structures is significantly near zero.

Kaleidoscope of symmetry-protected topological phases in one-dimensional periodically modulated lattices

We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase $\pi$ or the emergence of a pair of degenerate boundary states. It is shown that there may exist three types of topological phases, which are protected by the inversion symmetry, the chiral symmetry, and both of them, respectively, depending on the modulations, the odd or even modulation period. The connection between the hopping and potential modulations is also discussed. Furthermore, we demonstrate that the topological phase protected by the inversion symmetry can be realized in the interacting boson systems trapped in the same superlattices. The results are very possibly studied experimentally in the superlattice systems engineered with state-of-art technologies.

Electrical flicker-noise generated by filling and emptying of impurity states in injectors of quantum-cascade lasers

Free running line-widths (>100 kHz), much broader than intrinsic line-widths ∼100 Hz, of existing quantum-cascade lasers are governed by strong flicker frequency-noise originating from electrical flicker noise. Understanding of microscopic origins of the electrical flicker noises in quantum-cascade lasers is crucially important for the reduction of strength of flicker frequency-noise without assistances of any type of feedback schemes. In this article, an ad hoc model that is based on fluctuating charge-dipoles induced by electron trappings and de-trappings at indispensable impurity states in injector super-lattices of a quantum-cascade laser is proposed, developing theoretical framework based on the model. The validity of the present model is evaluated by comparing theoretical voltage-noise power spectral densities based on the model with experimental ones obtained by using mid-infrared quantum-cascade lasers with designed impurity-positioning. The obtained experimental results on flicker noises, in comparison with the theoretical ones, shed light on physical mechanisms, such as the inherent one due to impurity states in their injectors and extrinsic ones due to surface states on the ridge-walls and due to residual deep traps, for electrical flicker-noise generation in existing mid-infrared quantum-cascade lasers. It is shown theoretically that quasi-delta doping of impurities in their injectors leads to strong suppression of electrical flicker noise by minimization of the dipole length at a certain temperature, for instance ∼300 K and, in turn, is expected to result in substantial narrowing of the free running line-width down below 10 kHz.

Effects of size polydispersity on electron mobility in a two-dimensional quantum-dot superlattice

We found that the transitions between delocalized electronic states in quantum-dot superlattices with smaller size dispersion can account for higher electron mobility. In particular, we solved for the quantum states of a two-dimensional quantum-dot (QD) superlattice using a one-electron approximation. Electron transport properties were studied by considering hopping transitions among coupled delocalized electronic states. Molecular dynamics simulations were employed to introduce disorders in superlattice configurations as a function of QD size and size dispersion for calculation of electron mobility. The interparticle spacing, size, and temperature dependence of the electron mobility can be well explained within the framework of our analysis.

Effect of interdiffusion on electronic states in one-layer quantum ring superlattice

The effect of interdiffusion on band structure and Bloch amplitudes of two dimensional superlattice composed of initially cylindrical quantum rings is investigated in the framework of adiabatic approach and using transformation to in-plane momentum space. It is shown that the adiabatic approximation is applicable even if the ring’s height is equal to its radius, because of weak localization of electron in the superlattice plane comparing with the localization in perpendicular direction. The consideration of the dependence of effective mass on spatial coordinate and time leads to the energy correction up to 10meV. It is shown that energy minibands rise and become wider due to interdiffusion and the dependence of Bloch amplitudes on quasimomentum direction is more pronounced in the case of diffused potential profile.

Anomalous confined electron states in graphene superlattices

We show that periodic scalar potentials can induce the localization of some electronic states in graphene. Particularly, localized states are found at energies outside the potential variation range and embedded in the continuum spectrum of delocalized ones. The picture of the connection of wave functions with typical symmetries defined in relevant-edge nanoribbons is employed to explain the formation of the electronic structure and to characterize/classify eigen-states in graphene superlattices.

Determination of ground-state and low-energy structures of perovskite superlattices from first principles

In the development of first-principles high-throughput searches for materials with desirable functional properties, there is a clear need for an efficient method to determine the ground state and low-energy alternative structures of superlattices. A method based on a simple strategy -- to generate starting structures based on low-energy structures of the constituent compounds, which are then optimized via structural relaxation calculations -- is proposed. This "stacking method" is demonstrated on the 2:2 PbTiO$_3$/SrTiO$_3$ superlattice, which has been the subject of recent experimental and theoretical interest. Considerations relevant to wider use of the method are discussed.

Dot-bound and dispersive states in graphene quantum dot superlattices

We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a numerically exact kernel polynomial expansion technique. Analyzing the local density of states and the momentum resolved photoemission spectrum we find clear evidence for a series of quasi-bound states at the dots, which can be probed by optical measurements. We further analyze the interplay of the superlattice structure with dot localized modes on the electron energy dispersion. Effects of disordered dot lattices are discussed too.

Superlattice structures of silicene-based armchair nanoribbons by density functional theory calculation

Based on the DFT calculations, the various types of ASiSLs, which are the periodically repeated junctions made of ASiNRs with different widths, have been investigated. The band structures of ASiSLs were modulated by the size and strain of superlattices. The length of the narrow and wide nanoribbons plays interesting roles in the modulation of the electronic structures of ASiSLs. It could alter the band structure, and modify the distribution of the localized and dispersive states of superlattices. With the stain increased, the related energy gaps of ASiSLs will change, which are significantly different with that of the constituent nanoribbons.

Observation of accelerating Wannier–Stark beams in optically induced photonic lattices

We generate optical beams analogous to the Wannier-Stark states in semiconductor superlattices and observe that the two main lobes of the WS beams self-bend (accelerate) along two opposite trajectories in a uniform one-dimensional photonic lattice. Such self-accelerating features exist only in the presence of the lattice and are not observed in a homogenous medium. Under the action of nonlinearity, however, the beam structure and acceleration cannot be preserved. Our experimental observations are in qualitative agreement with theoretical predictions.

Dissipative structures induced by spin-transfer torques in nanopillars.

Macroscopic magnetic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Pattern formation from a uniform magnetization state, induced by the combination of a spin-polarized current and an external magnetic field, is studied for spin-transfer nano-oscillator devices. The system is described in the continuous limit by the Landau-Lifshitz-Gilbert equation. The bifurcation diagram of the quintessence parallel state, as a function of the external field and current, is elucidated. We have shown analytically that this state exhibits a spatial supercritical quintic bifurcation, which generates in two spatial dimensions a family of stationary stripes, squares, and superlattice states. Analytically, we have characterized their respective stabilities and bifurcations, which are controlled by a single dimensionless parameter. This scenario is confirmed numerically.

Stability of the steady state in a strongly coupled semiconductor superlattice described using a semiclassical approach

The stability of the steady state of a semiconductor superlattice described using a semiclassical approach is analyzed. It is shown that generation arises due to the appearance of perturbations characterized by a positive increment of growth. The relationship between the frequency of the current oscillations and the frequency of the perturbation oscillation is determined.