Quasiperiodic Superlattices Research Articles

Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Starting from the effective Hamiltonian arising from the tight-binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second-order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second-order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create non-singular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated with quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.

Long‐Lived Acoustic Phonon and Carrier Dynamics in III–V Adiabatic Cavities

AbstractEvidence of strongly confined coherent acoustic phonons inside high quality factor phononic cavities that exhibit tailored phonon potentials is provided. Using GaAs/AlAs quasiperiodic superlattices, functional phonon potentials are realized by adiabatically changing the layer thicknesses along the growth direction. Room temperature ultrafast vibrational spectroscopy reveals discrete phonon modes with frequencies in the range of ≈96–101 GHz. Additionally, it is confirmed that phononic cavities impact the energy loss rate of the photoexcited carriers, as evidenced by time‐resolved photoluminescence measurements. These results highlight the potential of concurrently engineering optoelectronic and phononic properties for a range of novel applications.

Design of quasiperiodic magnetic superlattices and domain walls supporting bound states

We study the simplest Lamé magnetic superlattice in graphene, finding its allowed and forbidden energy bands and band-edge states explicitly. Then, we design quasiperiodic magnetic superlattices supporting bound states using Darboux transformations. This technique enables us to add any finite number of bound states, which we exemplify with the most straightforward cases of one and two bound states in the designed spectrum. The topics of magnetic superlattices and domain walls in gapped graphene turn out to be connected by a unitary transformation in the limit of significantly large oscillation periods. We show that the generated quasiperiodic magnetic superlattices are also linked to domain walls, with the bound states keeping their nature in such a limit.

Second-harmonic and cascaded third-harmonic generation in generalized quasiperiodic poled lithium niobate waveguides.

Lithium niobate (LN) thin film has recently emerged as an important platform for nonlinear optical investigations for its large χ(2) nonlinear coefficients and ability of light localization. In this Letter, we report the first, to the best of our knowledge, fabrication of LN-on-insulator ridge waveguides with generalized quasiperiodic poled superlattices using the electric field polarization technique and microfabrication techniques. Benefiting from the abundant reciprocal vectors, we observed efficient second-harmonic and cascaded third-harmonic signals in the same device, with normalized conversion efficiency of 1735% W-1 cm-2 and 0.41% W-2 cm-4, respectively. This work opens a new direction for nonlinear integrated photonics based on LN thin film.

Flexible dual-wavelength second-harmonic generation in nested quasi-periodic optical superlattice

Flexible dual-wavelength second-harmonic generation in nested quasi-periodic optical superlattice

Thermal transport in periodic and quasiperiodic graphene-hBN superlattice ribbons

Nanostructured superlattices are expected to play a significant role in the next generation of technological devices, specially due to their adjustable physical properties. In terms of heat transport, materials with low thermal conductivities can be useful in thermoelectric devices or heat shields, while materials with high thermal conductivities are fundamental for heat dissipation in miniaturized electronic devices. In general, transport properties are dominated by translational symmetry and the presence of unconventional symmetries might lead to unusual transport characteristics. In this work, we report our results from nonequilibrium molecular dynamics simulations to investigate phonon heat transport in periodic and quasiperiodic graphene-hBN superlattices. The periodic superlattices are built with alternating equal-sized domains of graphene and hBN, while the quasiperiodic case follows the Fibonacci sequence, which lies between periodic and disordered structures. Periodic superlattices can facilitate coherent phonon transport due to constructive interference at the boundaries between the materials. Nonetheless, it is possible to induce a crossover from a coherent to an incoherent transport regime by increasing the length of individual domains, thus adjusting the superlattice period. We also show that the quasiperiodicity can suppress coherent phonon transport in these superlattices. We attribute this behavior to the increased inhomogeneity in the distribution of interfaces, which increases for each Fibonacci generation, hindering coherent phonon transport in the superlattices. The suppression of coherent thermal transport enables a higher degree of control on heat conduction at the nanoscale, and shows potential for application in thermoelectric devices and heat management.

Thermal conductivity of Thue–Morse and double-period quasiperiodic graphene-hBN superlattices

Semiconductor superlattices can play a significant role in the control of physical properties in modern electronic devices. The wave-particle crossover that the phonons can experience in the process of heat transport is one of the most interesting mechanisms related to this class of materials. However, if on the one hand this is due to the fact that translational symmetry governs transport properties in superlattices, on the other hand an unconventional symmetry may provide a new opportunity to achieve surprising results. In this work, we perform non-equilibrium molecular dynamics simulations to investigate phonon heat transport in quasiperiodic superlattices of graphene-boron nitride, alternating their domains according to the Thue–Morse and Double-Period sequences. Our results reveal that coherent heat transport is suppressed for higher generations of both sequences, similarly to what we recently observed for quasiperiodic graphene-hBN nanoribbons following the Fibonacci sequence. This suppression is caused by the increase of the superlattice period (or quasiperiodic generation) which can lead to phonon localization for different wavelengths, reducing the lattice thermal conductivity. We also obtain a general expression for the thermal conductivity as a function of quasiperiodic generation and supercell size for each of the sequences. These findings open up new horizons for the understanding of thermal transport in quasiperiodic nanomaterials.

Magnetoconductivity in quasiperiodic graphene superlattices

The magnetoconductivity in Fibonacci graphene superlattices is investigated in a perpendicular magnetic field B. It was shown that the B-dependence of the diffusive conductivity exhibits a complicated oscillatory behavior whose characteristics cannot be associated with Weiss oscillations, but rather with Shubnikov-de Haas ones. The absense of Weiss oscillations is attributed to the existence of two incommensurate periods in Fibonacci superlattices. It was also found that the quasiperiodicity of the structure leads to a renormalization of the Fermi velocity v_{F} of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity sigma _{yx} exhibits well defined and robust plateaux, where it takes the unexpected values pm 4e^{2}/hslash left( 2N+1right) , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that sigma _{yx} displays self-similarity for magnetic fields related by tau ^{2} and tau ^{4}, where tau is the golden mean.

Quasi-Phase-Matching Efficiency Optimization for Coupled Second-Order Nonlinear Processes

It is well known how to tailor the conversion efficiency grid of a single quasi-phase-matching (QPM) grating when the involved processes are uncoupled. However, it becomes much more sophisticated in the presence of coupling between multiple processes. In this case, different processes compete for the same QPM “resources” throughout the grating, and one process can outweigh the others over a certain range of interaction. Here we propose the generalized iterative domino (GID) algorithm to meet these challenges for the first time (to our best knowledge). Instead of tailoring the strength of each “global” Fourier coefficient, GID algorithm can properly adjust the spatially varying “local” Fourier coefficients in favor of the final yield. Three methods, including cascaded single-period (C1P) structure, quasi-periodic optical superlattice (QPOS), and hyperfine aperiodic optical superlattice (HAOS) optimized by GID, are numerically and experimentally investigated under the platform of third-harmonic generation (THG). It shows that the THG efficiency of HAOS + GID can exceed the record achieved by C1P structure by 33%. This method is applicable to general wavelength converters involving with multiple coupled nonlinear processes.

Quasiperiodic graphene superlattices: Self-similarity of the Landau level spectra

We have numerically calculated the magnetic subbands of a quasiperiodic Fibonacci graphene superlattice subject to a perpendicular magnetic field. It is shown that, when all energies and lengths are written in units of the cyclotron energy and cyclotron radius, respectively, these subbands exhibit a self-similar behavior at two magnetic fields related by τ4. To see explicitly that behavior, the energy spectrum corresponding to one of the fields must be rigidly shifted upwards in energy and in the lateral direction. It was also found that to obtain a good coincidence between both spectra, one of them must be properly rescaled in energy.

Second harmonic generation in the plasmon-polariton gap of quasiperiodic metamaterial photonic superlattices

Second harmonic generation in the plasmon-polariton gap of quasiperiodic metamaterial photonic superlattices

The energy spectra of the graphene-based quasi-periodic superlattice

The spectra of the Dirac quasi-electrons transmission through the Fibonacci quasi-periodical superlattice (SL) are calculated and analyzed in the continuum model with the help of the transfer matrix method. The onedimensional SL based on a monolayer graphene modulated by the Fermi velocity barriers is studied. A new quasi-periodical factor is proposed to be considered. We show that the Fibonacci quasi-periodic modulation in graphene superlattices with the velocity barriers can be effectively realized by virtue of a difference in the velocity barrier values (no additional factor is needed and we keep in mind that not each factor can provide the quasi-periodicity). This fact is true for a case of normal incidence of quasi-electrons on a lattice. In contrast to the case of other types of the graphene SL spectra studied reveal the remarkable property, namely the periodic character over all the energy scale and the transmission coefficient doesn’t tend asymptotically to unity at rather large energies. Both the conductance (using the known Landauer-Buttiker formula) and the Fano factor for the structure considered are also calculated and analyzed. The dependence of spectra on the Fermi velocity magnitude and on the external electrostatic potential as well as on the SL geometrical parameters (width of barriers and quantum wells) is analyzed. Using the quasi-periodical SL one can control the transport properties of the graphene structures in a wide range. The obtained results can be used for applications in the graphene-based electronics.

Spin wave propagation spectra in Octonacci one-dimensional magnonic quasicrystals

In this paper, we study spin wave propagation in quasiperiodic magnonic superlattices that follow the so-called Octonacci quasiperiodic sequence, where the N-th stage can be obtained through the recurrence rule SN=SN-1SN-2SN-1, for N⩾3, and starting with S1=A and S2=B. The multilayered magnonic nanostructure is composed of two simple cubic ferromagnetic materials, labeled A and B, which interact through bilinear and biquadratic exchange couplings at their interfaces. The ferromagnetic materials are described by the Heisenberg model, and a transfer matrix treatment is employed, with the calculations performed for the exchange-dominated regime, taking the random phase approximation (RPA) into account. The obtained numerical results show the effects of both (i) the Octonacci quasiperiodic sequence and (ii) the biquadratic exchange coupling on the band structure and transmission spectra of spin waves. Comparisons are also performed with the spectra found in other periodic and quasiperiodic structures.

Interparticle spacing dependence of magnetic anisotropy and dipolar interaction of Ni nanocrystals embedded in epitaxial BaTiO3 matrix

A quasi-periodic superlattice was designed, consisting of the epitaxial BaTiO3 single crystal matrix and the Ni nanocrystals (NCs). For the in-plane Ni NCs the statistical interparticle spacing (R) with a log-normal distribution was controlled ranging from 9 to 28 nm. With the decrease of R, the preferential orientation of the Ni NCs was changed from (001) to (111), inducing the transition of magnetic anisotropy from the out-of-plane to the in-plane direction. Increasing the in-plane R modulated the collective magnetic behavior by effectively lowering the interparticle dipolar coupling. For the Ni NCs/BaTiO3 system, it displayed a noninteracting system in the out-of-plane, and possesses an in-plane tunability between the interacting (R < 21 nm) and noninteracting (R ≥ 21 nm) system according to change the R. The increase of in-plane anisotropy energy induced the enhancement of dipole-dipole interaction among the Ni NCs.

Shot noise and electronic properties in the inversion-symmetric Weyl semimetal resonant structure

Using the transfer matrix method, the authors combine the analytical formula with numerical calculation to explore the shot noise and conductance of massless Weyl fermions in the Weyl semimetal resonant junction. By varying the barrier strength, the structure of the junction, the Fermi energy, and the crystallographic angle, the shot noise and conductance can be tuned efficiently. For a quasiperiodic superlattice, in complete contrast to the conventional junction case, the effect of the disorder strength on the shot noise and conductance depends on the competition of classical tunneling and Klein tunneling. Moreover, the delta barrier structure is also vital in determining the shot noise and conductance. In particular, a universal Fano factor has been found in a single delta potential case, whereas the resonant structure of the Fano factor perfectly matches with the number of barriers in a delta potential superlattice. These results are crucial for engineering nanoelectronic devices based on this topological semimetal material.

Tuning the Fano factor of graphene via Fermi velocity modulation

In this work we investigate the influence of a Fermi velocity modulation on the Fano factor of periodic and quasi-periodic graphene superlattices. We consider the continuum model and use the transfer matrix method to solve the Dirac-like equation for graphene where the electrostatic potential, energy gap and Fermi velocity are piecewise constant functions of the position x. We found that in the presence of an energy gap, it is possible to tune the energy of the Fano factor peak and consequently the location of the Dirac point, by a modulation in the Fermi velocity. Hence, the peak of the Fano factor can be used experimentally to identify the Dirac point. We show that for higher values of the Fermi velocity the Fano factor goes below 1/3 at the Dirac point. Furthermore, we show that in periodic superlattices the location of Fano factor peaks is symmetric when the Fermi velocity vA and vB is exchanged, however by introducing quasi-periodicity the symmetry is lost. The Fano factor usually holds a universal value for a specific transport regime, which reveals that the possibility of controlling it in graphene is a notable result.

A method to calculate thermal conductivity of a nonperiodic system, bamboo Si1−xGex nanowire with axially degraded components

For a nonperiodic system, a bamboo Si1−x Ge x nanowire with axially degraded components, it is impossible to obtain its phonon dispersion relations through lattice dynamic or the first principle calculation. Therefore, we present a simple and available method to solve this problem. At first, the Si1−x Ge x nanowire with axially degraded component is divided into several sections according to its component distribution like bamboos’ sections formed in the growth process. For each section with a given x value, we constructed a pseudo-cell to calculate its phonon dispersion relations. Thermal conductances of junctions and of each section are then calculated by the phonon mismatch model and the phonon transmission probability with diffusive and ballistic portions. The dependences of thermal conductivity on the length of each section and the gradient of degraded component between sections are presented. We studied thermal conductivity dependence on temperature, length and diameter of the Si1−x Ge x nanowire with axially degraded component. And we found κ ~ l 0.8, in which the exponent 0.8 is ascribed to the competition between phonons ballistic and diffusive transport. Furthermore, thermal conductivities along axial (100), (110), and (111) directions are discussed in detail. The method provides a simple and available tool to study thermal conductivity of a non-period system, such as a quasiperiodic superlattice or a nanowire with axially degraded component.

Periodic to quasi-periodic graphene superlattice transition by Fermi velocity modulation

Graphene superlattices have attracted great research interest in the last years, since it is possible to manipulate the electronic properties of graphene in these structures. They can be periodic, quasi-periodic or disordered, each one presenting different electronic properties. In this work we investigate the possibility of transforming a periodic and quasi-periodic graphene superlattice one into another by a Fermi velocity modulation. We analyzed finite and infinite superlattices. We considered an one-dimensional superlattice and show that the transformation can be perfectly done for charge carriers moving in the direction of the superlattice. However, for oblique moving, some features can not be transformed by the Fermi velocity. The results obtained here are relevant for the development of novel graphene-based electronic devices.

Three-colour entanglement produced by the single-pass quasi-phase-matching fourth harmonic generation

Three-colour continuous-variable entanglement produced by single-pass cascaded quasi-phase-matching fourth harmonic generation is investigated. The fourth harmonic can be generated through cascaded double-frequency processes in a quasiperiodic optical superlattice by using quasi-phase-matching technology. The conversion dynamics of the cascaded double-frequency processes is studied using quantum stochastic methods. The nature of the entanglement is discussed by applying a necessary and sufficient criterion for continuous-variable entanglement. Strong three-colour entanglement among the fundamental, second-, and fourth-harmonic beams with a double frequency interval can be produced without an optical oscillator cavity. This is experimentally feasible and has potential applications in quantum communication and computation networks.

Transport and Conductance in Fibonacci Graphene Superlattices with Electric and Magnetic Potentials

We investigate the electron transport and conductance properties in Fibonacci quasi-periodic graphene superlattices with electrostatic barriers and magnetic vector potentials. It is found that a new Dirac point appears in the band structure of graphene superlattice and the position of the Dirac point is exactly located at the energy corresponding to the zero-averaged wave number. The magnetic and electric potentials modify the energy band structure and transmission spectrum in entirely diverse ways. In addition, the angular-dependent transmission is blocked by the potential barriers at certain incident angles due to the appearance of the evanescent states. The effects of lattice constants and different potentials on angular-averaged conductance are also discussed.