Superlattice Period Research Articles

Strain fields in twisted bilayer graphene.

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials.

High-yield exfoliation of 2D semiconductor monolayers and reassembly of organic/inorganic artificial superlattices

<h2>Summary</h2> The scalable preparation of high-purity monolayers is essential for practically integrating two-dimensional (2D) semiconductors in diverse technologies but remains a persistent challenge. Previous efforts to exfoliate 2D layered crystals by the organic ammonium intercalation usually produce few-layer nanosheets owing to a self-retarding effect that hinders the complete intercalation in neighboring layers. Herein, we report a unique "intercalation and separation" chemistry with a constant self-refreshing crystal surface that mitigates the self-retarding effect to ensure a complete intercalation of the bulk crystal, ultimately enabling high-yield solution-phase exfoliation of 2D semiconductor monolayers in excellent purity (e.g., monolayer purity of >95% for In₂Se₃ and InSe). Furthermore, we have assembled large-area organic/inorganic hybrid superlattices with diverse organic molecules and inorganic 2D monolayer crystals, thus creating a family of artificial superlattice materials with atomically modulated chemical compositions, widely tunable superlattice periodicities, and specifically tailorable electronic and thermal properties.

Total-transmission and total-reflection of individual phonons in phononic crystal nanostructures

The control of thermal waves by the phononic crystal exhibits peculiar behaviors different from the particle picture of phonons and thus has attracted increasing interest. However, the wave nature of phonons is only indirectly reflected in most studies via the macroscopic thermal transport coefficient, such as thermal conductivity. In this work, we investigate directly the coherent interference effect in a graphene superlattice structure at the microscopic phonon mode level via wave-packet simulations. The constructive interference and destructive interference between the reflected phonons give rise to valleys and peaks in the transmission coefficient, respectively, leading to the periodic oscillation of the transmission function with the variation of the superlattice period length. More importantly, both total-transmission and total-reflection of individual phonons have been clearly demonstrated. The physical conditions for realizing the phonon interference have been proposed, which are quantitatively in good agreement with independent wave-packet simulations. Our study provides direct evidence for the coherent phonon interference effect, which might be helpful for the regulation of phonon transport based on its wave nature.

Origins of Minimized Lattice Thermal Conductivity and Enhanced Thermoelectric Performance in WS2/WSe2 Lateral Superlattice.

We report a configuration strategy for improving the thermoelectric (TE) performance of two-dimensional transition metal dichalcogenide WS2 based on the experimentally prepared WS2/WSe2 lateral superlattice (LS) crystal. On the basis of density function theory combined with a Boltzmann transport equation, we show that the TE figure of merit zT of monolayer WS2 is remarkably enhanced when forming into a WS2/WSe2 LS crystal. This is primarily ascribed to the almost halved lattice thermal conductivity due to the enhanced anharmonic processes. Electronic transport properties parallel (xx) and perpendicular (yy) to the superlattice period are highly symmetric for both p- and n-doped LS owing to the nearly isotropic lifetime of charger carriers. The spin-orbital effect causes a significant split of conduction band and leads to three-fold degenerate sub-bands and high density of states (DOS), which offers opportunity to obtain a high n-type Seebeck coefficient (S). Interestingly, the separated degenerate sub-bands and upper conduction band in monolayer WS2 form a remarkable stair-like DOS, yielding a higher S. The hole carriers with much higher mobility than electrons reveal the high p-type power factor, and the potential to be good p-type TE materials with optimal zT exceeds 1 at 400 K in WS2/WSe2 LS.

Surface electromagnetic waves in bianisotropic superlattices and homogeneous media

This paper analyzes the existence of surface electromagnetic waves (SEWs) at the interface of bianisotropic bicrystals which are formed of half-infinite periodic superlattices or of homogeneous bianisotropic media. In either case we assume no absorption. Properties of the impedance matrices characterizing such bianisotropic media are established. On this basis, a series of statements is proved on the maximum total number of SEWs in two bicrystals composed of two superlattices or homogeneous media in such a way that the upper (lower) half of one bicrystal complements the lower (upper) part of the other to an infinite periodic superlattice or homogeneous media, respectively. It is shown that in superlattices the maximum number of SEWs at a fixed tangential wave number equals two in the lowest forbidden band (this band begins from zero frequency) and four in any upper forbidden band. It is also proved that at most two SEWs emerge in homogeneous bianisotropic media.

Bandgaps in free‐standing monolayer TiO2: Ab initio diffusion quantum Monte Carlo study

AbstractIn this study, bandgap of the two‐dimensional (2D) TiO2, a transition‐metal oxide, was obtained by the diffusion Monte Carlo (DMC) method for the first time. This genuine 2D monolayer material that includes transition elements has been proven to be very challenging for reliable prediction of the bandgap. In order to improve the description of correlation effects, the DMC method was used to calculate the bandgaps of 2D‐TiO2 in α‐ and β‐phases, and the obtained results were compared with the density functional theory (DFT) calculations. The DMC results obtained from the infinite periodic superlattices predict ∆f of the 2D‐TiO2 in the α‐ and β‐phases to be about 5.54(4) and 5.69(2) eV, respectively, indicating that the available DFT results significantly underestimated the bandgaps of 2D‐TiO2 nanosheets. Considering the recently reported linear scaling relationship between the bandgap ∆f and the exciton binding energy ∆e of 2D semiconductors, (∆e ≈ 0.28∆f), the optical bandgap ∆o was further predicted to be ~3.99 eV for the α‐phase TiO2, and it is consistent with the experimental value (~3.84 eV). The successful application of the quantum Monte Carlo (QMC) method on the 2D‐TiO2 systems implies that QMC may serve as a feasible tool to investigate the electronic properties of the freestanding 2D transition‐metal oxides.

Multigap superconductivity at an unconventional Lifshitz transition in a three-dimensional Rashba heterostructure at the atomic limit

It is well known that the critical temperature of multi-gap superconducting 3D heterostructures at atomic limit (HAL) made of a superlattice of atomic layers with an electron spectrum made of several quantum subbands can be amplified by a shape resonance driven by the contact exchange interaction between different gaps. The $T_C$ amplification is achieved tuning the Fermi level near the singular nodal point at a Lifshitz transition for opening a neck. Recently high interest has been addressed to the breaking of inversion symmetry which leads to a linear-in-momentum spin-orbit induced spin splitting, universally referred to as Rashba spin-orbit coupling (RSOC) also in 3D layered metals. However the physics of multi-gap superconductivity near unconventional Lifshitz transitions in 3D HAL with RSOC, being in a non-BCS regime, is not known. The key result of this work getting the superconducting gaps by Bogoliubov theory and the 3D electron wave functions by solution of the Dirac equation is the feasibility of tuning multi-gap superconductivity by suitably matching the spin-orbit length with the 3D superlattice period. It is found that the presence of the RSOC amplifies both the k dependent anisotropic gap function and the critical temperature when the Fermi energy is tuned near the circular nodal line. Our results suggest a method to effectively vary the effect of RSOC on macroscopic superconductor condensates via the tuning of the superlattice modulation parameter in a way potentially relevant for spintronics functionalities in several existing experimental platforms and tunable materials needed for quantum devices for quantum computing.

Thermal conductivity and interfacial thermal resistance behavior for the polyaniline-boron carbide heterostructure.

In this paper, by employing non-equilibrium molecular dynamics simulations (NEMD), the thermal conductance of the hybrid formed by polyaniline (C3N) and boron carbide (BC3) in both the armchair and zigzag configurations has been investigated. For this purpose, by creating superlattices with different periodic lengths (lp), the thermal conductivity of the entire hybrid at various lengths and also at infinity has been reported. In addition, the thermal conductivity of each sheet and also the interface thermal resistance (ITR) between them under various conditions have been computed and how this changes upon varying the length, width, temperature, uniaxial strain, point vacancy, and circular defects has been recorded and plotted. Based on our findings, the increasing length of the hybrid results in a higher thermal conductance owing to the higher thermal conductivity of each sheet and the lower amount of ITR. However, altering the width does not have a noticeable effect on the thermal transport if the periodic boundary conditions are applied. Moreover, the results revealed that the rising temperature and uniaxial strain reduced the thermal conductivity of each sheet, whereas the ITR increased by increasing the temperature. Also, studying the effect of the presence of defects on the thermal transport demonstrated that increasing the size of the defects or the density leads to considerably lower thermal conductivity of each sheet and also a higher ITR. Our results also revealed the thermal conductivity of hybrid C3N-BC3 can reach 506 W m-1 K-1, which is higher in comparison to other two-dimensional hybrid materials. This result provides valuable information on the thermal transport and phonon behavior for use in nanoelectronic and thermoelectric devices.

Вертикальная проводимость сверхрешетки в продольном сильном магнитном поле при внутризонных и межзонных переходах

The influence of interband and intraband transitions on oscillations of the vertical conductivity of superlattices in a strong magnetic field is considered. It was found that for the charged impurity scattering intraband transitions dominate in magnetic fields up to 2 T, and with a further increase in the magnetic field, interband transitions control. The conductivity oscillations are determined by a ratio of the magnetic length to the superlattice period and the effective mass anisotropy.

Real-space Raman spectroscopy of graphene isotope superlattices

We report the Raman spectroscopy of 12C/13C graphene isotope superlattices synthesized by chemical vapour deposition. At large periods the Raman spectra corresponds to the sum of the bulk 12C and 13C contributions. However, at small periods we observe the formation of mixed 12C/13C modes for Raman processes that involve two phonons, which results in the tripling of the 2D and 2D' Raman peaks. This tripling can be well understood in the framework of real space Raman spectroscopy, where the two emitted phonons stem from different regions of the superlattice. The intensity of the mixed peak increases as the superlattice half period approaches the mean free path of the photo-excited electron-hole pairs. By varying the superlattice period between 6 and 225 nm we have a direct measure of the photo-excited electron mean free path, which was found to be 18 nm for suspended graphene and 7 nm for graphene on SiO2 substrates.

Interferences of electrostatic moiré potentials and bichromatic superlattices of electrons and excitons in transition metal dichalcogenides

Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multilayers. We show examples of bichromatic moiré potentials for valley electrons, holes, and interlayer trions in MX2/M’X’2/MX2 trilayers, which can be strain switched from multi-orbital periodic superlattices to quasi-periodic disordered landscape. The trilayer moiré also hosts two independently configurable triangular superlattices of neutral excitons with opposite electric dipoles. These findings greatly enrich the versatility and controllability of TMDs moiré as a quantum simulation platform.

Renormalization Group Study of Hidden Symmetry in Twisted Bilayer Graphene with Coulomb Interactions.

We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated nonperturbatively. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian is determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step. We also calculate exactly the exciton energy spectrum from the Coloumb interactions projected onto the renormalized narrow bands. The resulting softening of the collective modes marks the propinquity of the enlarged ("hidden") U(4)×U(4) symmetry in the magic angle twisted bilayer graphene.

Thermal conductivities of different period Si/Ge superlattices

Thermoelectric materials, which can convert wasted heat into electricity, have attracted considerable attention because they provide a solution to energy problems. The Si/Ge superlattices have shown tremendous promise as effective thermoelectric materials. The period lengths of the Si/Ge superlattices can effectively tailor the phonon's transport behaviors and control their thermal conductivities. In this paper, three kinds of Si/Ge superlattices with different period length distributions (uniform, gradient, random) are constructed. The non-equilibrium molecular dynamics (NEMD) method is used to calculate the thermal conductivities of Si/Ge superlattices under the different period length distributions. The effect of the sample’s total length and temperature on the superlattice's thermal conductivity are studied. The simulation result shows that the thermal conductivity of gradient and random periodical Si/Ge superlattices are significantly reduced at room temperature compared with that of the uniform period Si/Ge superlattices. Phonons are transported by wave or particle properties in the different periodical superlattices. The thermal conductivity of uniform period superlattices has an obvious size effect with the increasing of the sample total length. In contrast, the thermal conductivity of gradient, random periodical Si/Ge superlattices are weakly dependent on the sample’s total length. At the same time, temperature is an important factor affecting the heat transport properties. We find that the temperature affects the thermal conductivities of the three kinds of superlattices in different ways. With the increase of the temperature, (i) the thermal conductivity of uniform periodical superlattices shows an obvious temperature effect; (ii) the thermal conductivity of the gradient and random periodical Si/Ge superlattices are nearly unchanged due to the competition between phonon localization weakness and phonon-phonon scattering enhancement. In addition, the phonon densities of states of superlattices with three different periodical length distributions are calculated. We find that in the picture of uniform periodical Si/Ge superlattices, the number of pronounced peaks quickly decreases as the period length increases, particularly at higher frequencies. This indicates that as the period length increases, fewer coherent phonons will be formed over the superlattices. Moreover, the scattering mechanisms of phonons for gradient and random periodical Si/Ge superlattices are basically the same at 100 K and 500 K. These findings provide a developmental way to further reduce the thermal conductivity of superlattices.

Nonmonotonic crossover in electronic phase separated manganite superlattices driven by the superlattice period

Studying manganite superlattices ${[{(\mathrm{LCMO})}_{2n}/{(\mathrm{PCMO})}_{n}]}_{t}$ made of ${\mathrm{La}}_{0.625}{\mathrm{Ca}}_{0.375}\mathrm{Mn}{\mathrm{O}}_{3}$ (LCMO) and ${\mathrm{Pr}}_{0.625}{\mathrm{Ca}}_{0.375}\mathrm{Mn}{\mathrm{O}}_{3}$ (PCMO), we found an unexpected behavior varying the period $n$. At small $n$, the ensemble is a three-dimensional ferromagnetic metal due to interfacial charge transfer. At large $n$, the LCMO layers dominate transport. However, rather than a smooth interpolation between these limits a sharp transport and magnetic anomaly is found at an intermediate critical PCMO thickness ${n}^{*}$. Magnetic force microscopy reveals that the phase-separation length scale also maximizes at ${n}^{*}$ where, unexpectedly, it becomes comparable to that of the ${({\mathrm{La}}_{1--y}{\mathrm{Pr}}_{y})}_{0.625}{\mathrm{Ca}}_{0.375}\mathrm{Mn}{\mathrm{O}}_{3}$ (LPCMO) alloy. We conjecture the phenomenon originates in a disorder-related length scale: Large charge-ordered clusters as in LPCMO can only nucleate when Pr-rich regions reach a critical size related to ${n}^{*}$.

Anisotropic thermal conductivity of AlGaN/GaN superlattices

High thermal conductivity is an important parameter for nitride-based power electronic and deep-UV light emitters. Especially in the latter case short period superlattices and multicomponent alloys are used and the knowledge of the thermal properties of the binary compounds is sufficient. In-plane and cross-plane thermal conductivity of AlGaN/GaN superlattices were measured by differential two-wire 3ω method in the temperature range from 147 to 325 K. Samples were grown by metalorganic vapor phase epitaxy; the structure quality and accuracy of superlattice structures preparation were verified by means of HRXRD and transmission electron microscopy. It was observed, that value of thermal conductivities decrease with decreasing period thickness, while temperature dependencies differ from each other—in-plane thermal conductivity decreases, and cross-plane—increases with increasing temperature. Callaway method was used for thermal conductivity calculation; dependence of boundary scattering rate on the phonon wavelength was taken into account. Minimum thermal conductivity was added to calculated values to include the influence of high frequency acoustic phonons and optical phonons on the heat transport. Calculations are in good agreement with experimental results.

Engineering of impact ionization characteristics in In0.53Ga0.47As/Al0.48In0.52As superlattice avalanche photodiodes on InP substrate

We report on engineering impact ionization characteristics of In0.53Ga0.47As/Al0.48In0.52As superlattice avalanche photodiodes (InGaAs/AlInAs SL APDs) on InP substrate to design and demonstrate an APD with low k-value. We design InGaAs/AlInAs SL APDs with three different SL periods (4 ML, 6 ML, and 8 ML) to achieve the same composition as Al0.4Ga0.07In0.53As quaternary random alloy (RA). The simulated results of an RA and the three SLs predict that the SLs have lower k-values than the RA because the electrons can readily reach their threshold energy for impact ionization while the holes experience the multiple valence minibands scattering. The shorter period of SL shows the lower k-value. To support the theoretical prediction, the designed 6 ML and 8 ML SLs are experimentally demonstrated. The 8 ML SL shows k-value of 0.22, which is lower than the k-value of the RA. The 6 ML SL exhibits even lower k-value than the 8 ML SL, indicating that the shorter period of the SL, the lower k-value as predicted. This work is a theoretical modeling and experimental demonstration of engineering avalanche characteristics in InGaAs/AlInAs SLs and would assist one to design the SLs with improved performance for various SWIR APD application.

Ameliorating the optical and structural properties of InAs quantum dot heterostructures through digital alloy capping materials: Theory and experiment

Abstract In this study, we have employed a unique technique called digital alloy capping to grow the strain reducing capping layer on InAs quantum dots (QDs). Four different capping materials have been considered, i.e. two ternary (InxGa1-xAs and GaAs1-xSbx) and two quaternary (InxAlyGa1-x-yAs and InxGa1-xAs1-ySby) alloys. Experimental investigations are carried out for InAs QDs capped with InGaAs capping material along with a detailed theoretical study of other capping materials. Distinct short period superlattices are grown with different compositions of capping materials namely digital alloy capping layer (DACL) with specific thicknesses, instead of a thick capping material (namely analog alloy capping layer (AACL)). The compositions of capping material in DACL structures is chosen in a way to minimize the lattice mismatch within the interfaces of QD layer, sub-capping layers and top GaAs layer. QDs capped with DACL provide reduced strain, and emission at telecommunication wavelengths which are confirmed from the experimental and simulation studies. The biaxial and hydrostatic strain has been computed to understand the strain distribution within the heterostructures. This study unveils the effectiveness of the DACL over AACL, and therefore motivates to design futuristic optoelectronic devices with this technique.

Surface electromagnetic waves in anisotropic superlattices

This paper studies the existence of electromagnetic surface waves localized on a boundary of half-infinite periodic superlattices formed by an arbitrary periodic sequence of layers of homogeneous or functionally graded materials with generally anisotropic dielectric permittivity and magnetic permeability tensors. The geometry in question implies either two superlattices attached together to form a photonic bicrystal or else a superlattice in contact with vacuum or any other homogeneous dielectric or metal. Using the formalism of transfer and impedance matrices, a series of statements is proved on the maximum number of surface waves which may exist within a forbidden band at a fixed tangential wave number. This number embraces possible occurrences of surface waves in a given bicrystal and in its counterpart obtained by swapping the upper and lower superlattices. A maximum total number of surface waves in both these structures with an arbitrary arrangement of their unit cells is 2 in the lowest forbidden band (extending from zero frequency) and 4 in any upper forbidden band. The same statements apply to the case where one of the half spaces is occupied by a homogeneous material. A factor 2 smaller number of surface waves occur in a bicrystal composed of superlattices with a symmetric arrangement of unit cells. The existence considerations are further specialized for the surface waves with TE and TM polarizations.

Observation of an Unidentified Phonon Peak in SiGe Alloys and Superlattices Using Molecular Dynamics Simulation

Molecular dynamics was applied to a variety of SiGe alloys and superlattice structures in order to investigate the production of an unidentified phonon mode. The mode in question, observed in the resulting phonon dispersion relations, was produced around 2.5 – 5 THz. The corresponding spectral energy density data for the SiGe alloys produced varying intensities around this region, with a higher intensity tending towards lower thermal conductivity values. The unidentified mode was produced by the alloy and the non-periodic superlattice structures, whereas in the case of the periodic superlattices, the mode is less conspicuous. Regarding the SiGe compound, the mode was not produced. It is concluded that the atomic disorder within the alloys and non-periodic superlattices induce a stronger intensity of the unidentified mode.

Stoneley-type waves in anisotropic periodic superlattices

The paper investigates the existence of interfacial (Stoneley-type) acoustic waves localised at the internal boundary between two semi-infinite superlattices which are adjoined with each other to form one-dimensional phononic bicrystal. Each superlattice is a periodic sequence of perfectly bonded homogeneous and/or functionally graded layers of general anisotropy. Given any asymmetric arrangement of unit cells (periods) of superlattices, it is found that the maximum number of interfacial waves, which can emerge at a fixed tangential wavenumber for the frequency varying within a stopband, is three for the lowest stopband and six for any upper stopband. Moreover, we show that this number of three or six waves in the lowest or upper stopband, is actually the maximum for the number of waves occurring per stopband in a given bicrystal plus their number in the “complementary” bicrystal, which is obtained by swapping upper and lower superlattices of the initial one (so that both bicrystals have the same band structure). An example is provided demonstrating attainability of this upper bound, i.e. the existence of six interfacial waves in a stopband. The results obtained under no assumptions regarding the material anisotropy are also specified to the case of monoclinic symmetry leading to acoustic mode decoupling.