Symmetric Films Research Articles

Modeling of interfacial diffusion in adjacent flows of polymer films

Adjacent flow of two polymeric fluids occurs in many industrial processes. Under these processes, entangled polymer chains usually undergo extensional flow and shear flow deformation fields, rendering orientation and stretching within polymer chains. In the present paper, the chain stretching ratio and interfacial diffusion in a symmetric bilayer film in the isothermal adjacent flows in a coextrusion process are modeled using the double constraint release with chain stretching model. Extension-dominant and shear-dominant flows are considered separately for ease of the modeling process. Also, the impact of entanglement density on the reptation relaxation is investigated to determine the entanglement density variation and its effect on the stretching ratios and interfacial diffusion. Our findings show that extension-dominant and shear-dominant deformation fields have different impacts on polymer chain stretching, affecting polymer interfacial chain diffusion. Our findings show that while shear flow with the strength of 30 s−1 increases the stretching ratio by 28%, extensional flow with the same strength increases the stretching ratio by 60% of the maximum stretching ratio for polystyrene chains with an average molecular weight of 200 km/mol at 175 °C. Our results show that initial entanglement density is effective on the chain stretching only in the transition step before chains reach equilibriums. This study highlights the impact of flow conditions and chain configuration in polymers on engineering the diffusion of polymer chains at the interface of layered configurations.

Spin-coating ANF based multilayer symmetric composite films for enhanced electromagnetic interference shielding and thermal management

The demand for flexible composite films with electromagnetic interference (EMI) shielding capabilities is rapidly increasing. Balancing high EMI performance with flexibility and portability has become a critical research focus in practical applications. In this study, an optimized strategy for aramid nanofibers (ANF) films was developed using spin-coating and sol–gel techniques. The resulting film features a smooth surface and excellent mechanical properties. ANF, initially an insulator, was transformed into a conductor through the in-situ polymerization of ion-doped polypyrrole (PPy). Leveraging a multilayer structural strategy, we prepared a symmetric composite film, ANF@PPy-(TA-MXene)-AgNWs-(TA-MXene)-ANF@PPy (PMA), using vacuum-assisted filtration and lamination hot pressing. This film, composed of ANF@PPy (PA) as the matrix, tannic acid (TA) modified MXene, and silver nanowires (AgNWs) as fillers, exhibited multiple shielding mechanisms as electromagnetic wave (EMW) passed through its various layers. This multilayer configuration provides significant flexibility in EMW shielding. Moreover, TA-modified MXene expands the lamellar spacing, enhancing the scattering efficiency of EMWs within the film, and serves as a medium connecting the upper and lower layers. This results in the efficient integration of the multilayer structure, synergistically improving both EMI shielding performance and mechanical properties. When the ratio of PA/MXene/AgNWs was 1:3:1, the film demonstrated optimal properties, including an EMI shielding effectiveness of 70.2 dB, thermal conductivity of 4.62 W/(m•K), and tensile strength of 50.2 MPa. Due to the exceptional EMI shielding and thermal properties of the PMA composite film, it holds great potential for applications in artificial intelligence, wearable heaters, and military equipment.

Modelling of evaporative falling-film heat transfer over a horizontal tube

This article focuses on evaporative falling film heat transfer through numerical simulations. A two-dimensional symmetric liquid film flowing outside a single horizontal tube was simulated using the open-source CFD software OpenFOAM. The Tanasawa model was employed to consider mass transfer at the liquid–vapour interface, and the isoAdvector VOF method was used for interface tracking. The simulations explored the impact of film flow rate, tube surface heat flux, and tube diameter on the liquid film thickness and surface heat transfer coefficient. Additionally, the critical heat flux and operational limits were considered. The results demonstrate the accurate reproduction of evaporative falling film heat transfer performance by the present model. The film thickness exhibits a similar profile to adiabatic and sensible falling film heat transfer but provides smaller values. Similarly, the evaporative heat transfer coefficient exhibits significantly higher values and a gentle peripheral variation. The influence of heat flux on evaporative falling film heat transfer is contingent on the film flow rate; it can either enhance or weaken the process. Notably, a larger tube diameter negatively affects heat transfer, suppressing the impact of heat flux, and also increases the risk of liquid film dryout. For a given film flow rate, the average heat transfer coefficient increases initially, reaches a maximum value, and then decreases as the wall heat flux is increased. The peak heat flux, termed critical heat flux, increases with film flow rate but decreases with tube diameter. An operational limit exists where the heat flux is lower than the critical heat flux and the film flow rate is higher than the critical film flow rate; under these conditions, evaporative falling film heat transfer operates in a fully wetting status.

О влиянии «гидрофобности» газовой фазы на образование флотокомплексов в процессах флотации

Introduction. A model of a three-phase system in which, as a result of hetero coagulation from a bulk liquid, its thin layer has formed, the surfaces of which separate the gas and condensed phases with different potentials, is a wetting film. The study of wetting films adds to the knowledge of the nature of the structure-induced surface forces acting in them, which serves to develop the theory of hetero coagulation and is of interest for solving various topical problems of the theory and practice of flotation. The purpose of the work is to study the influence of “hydrophobic” properties of the gas phase on the separation of minerals by flotation with a vapor-air mixture in flotation schemes with jet countercurrent flow of feed and rough concentrate. Materials and Methods. Methods and installations have been developed to investigate the temperature dependence of the equilibrium thickness of wetting films and wetting edge angles. Studies of wetting films are supplemented by measurements of induction time at adhesion of minerals to each other and to an air bubble on a specially designed installation. In-situ flotation experiments were performed on a sample of apatite-nepheline ores. Results. The temperature dependence of the equilibrium thickness of the wetting film has been revealed, which does not contradict the experimentally established decrease of the exponentially decreasing (non-oscillating) part of the cleavage pressure with increasing temperature. It is shown that the temperature dependence of the boundary angles formed by the wetting film on the hydrophobic and hydrophilic surface is multidirectional. The connection between the temperature dependence of the boundary angle and the temperature dependence of the spreading coefficient obtained from Young’s law and determined by multiplication of parameters characterizing the magnitude and long-range action of forces caused by the difference between the structure and properties of the liquid in the boundary layers and their values in the volume is shown. “Hydrophobicity” of the bubble is associated with a smaller range effect of structural repulsion forces compared to hydrophobic attraction forces. By measuring the induction time, it is shown that the “hydrophobicity” of air manifests itself in the difference in the stability of wetting (when hydrophobic and hydrophilic particles adhere to the air bubble) and symmetric (when particles of the same hydrophobicity/hydrophilicity adhere to each other) films as the temperature increases. Discussion. In the framework of the phonon mechanism of surface forces, the dynamic structure of the liquid in the boundary layers (the sign and magnitude of the phonon component of the bowing pressure) determines the selectivity of aggregation and completeness of particle extraction, as well as the stability of symmetric and wetting films from temperature. Conclusion. When discussing the stability of disperse systems, the concepts of additional (to dispersive (van der Waals) and ionic-electrostatic interactions) forces associated with the overlap of boundary layers of liquids with structure parameters changed compared to their bulk values are fruitfully used. Such differences are understood as static deviations of the structure and properties of the liquid induced by the surface. However, the main reason for changes in the stability of wetting films at increasing temperature may be the high sensitivity to temperature of the entire set of rotational and vibrational motions of atoms and molecules of the liquid, i. e., its dynamic structure and the associated phonon component of the wedging pressure. Resume. The results of the study can be used to improve the technological performance of ores enriched by flotation. Consideration of the influence of linear tension on the system with the line of threephase contact will be useful for revealing the peculiarities of flotation of micro-dispersions of minerals by the developed technology.

Chemical and thermal stability of novel phenyl-BODIPY symmetric dimer thin films

Phenyl-BODIPY-dimers are an increasingly interesting motif whose unique electronic and morphological properties make them excellent candidates for a wide range of applications in materials chemistry, including device design and fabrication. Two dimers based on the meso‑(4-ethynylphenyl)-BODIPY unit were obtained through sequential Sonogashira and Glaser-Hay-type coupling reactions. The synthesized compounds, present a significant advantage in terms of solution stability compared to their monomers. An evaluation of their properties, both in solution and thin films, highlights that these dimers maintain exceptional chemical and structural stability when deposited in films, suggesting their plausible use in coatings and devices. The studied dimers exhibit reduced wettability given their surface roughness, meaning a potential for varied applications. Finally, a tandem analysis that included UV–Vis/fluorescence measurements and quantum chemistry methods was carried out to analyze the optical properties in solution and solid-state helping to gain insight into the optical properties of the synthesized molecules and the effect of π-interacting solvents.

Performance and stability of cellulose triacetate membranes in humid high H2S natural gas feed streams

The current study aims to provide a thorough understanding of the separation performance of the cellulose triacetate (CTA) membrane material in humid high H2S natural gas feed streams. A systematic study of the gas separation performances of CTA polymers has been carried out in self-standing symmetric films and asymmetric hollow fiber membranes. The separation performance in H2S-containing mixtures (CH4/CO2/H2S, 80/5/15 mol%) were evaluated at 30 and 50 °C at 20, 35 and 50 bar, including higher hydrocarbons (butane and toluene) in the presence of various levels of humidity, up to 4500 ppm or 80 % RH, depending on conditions of temperature and pressure. For the first time, the effect of these contaminants and humidity together under sour gas conditions has demonstrated the promising stability of CTA membrane separation performance, both in terms of H2S permeability and H2S/CH4 selectivity. The improvement in H2S permeability is due to a combination of H2S plasticization and competitive sorption making this phenomenon even more attractive and worth studying further.

High Efficiency and Flexible Modulation of Spintronic Terahertz Emitters in Synthetic Antiferromagnets.

Spintronic terahertz (THz) emitters based on synthetic antiferromagnets (SAFs) of FM1/Ru/FM2 (FM: ferromagnet) have shown great potential for achieving coherent superposition and significant THz power enhancement due to antiparallel magnetization alignment. However, key issues regarding the effects of interlayer exchange coupling and net magnetization on THz emissions remain unclear, which will inevitably hinder the performance improvement and practical application of THz devices. In this work, we have investigated the femtosecond laser-induced THz emission in Pt (3)/CoFe (3)/Ru (tRu = 0-3.5)/CoFe (tCoFe = 1.5-10)/Pt (3) (in units of nm) films with compensated and uncompensated magnetic moments. Antiferromagnetic (AF) coupling occurs in the Ru thickness ranges of 0.2-1.1 and 1.9-2.3 nm, with the first peak (tRu = 0.4 nm) of the AF coupling field (Hex) significantly higher than that of the second peak (2.0 nm). Rather high THz amplitude is found for the samples with strong AF coupling. Nevertheless, despite the same remanence ratio of zero, the THz amplitude for the symmetric SAF films declines significantly as the tRu decreases from 0.8 to 0.4 nm, which is mainly ascribed to the noncolinear magnetization vectors due to the increased biquadratic coupling term. Specifically, we demonstrate that an asymmetric SAF structure with a dominant FM layer is more favored than the completely compensated one, which could generate significantly enhanced THz electric field with well-controlled polarity and intensity. In addition, as the temperature decreases, the THz emission intensity increases for the SAF samples of tRu = 0.9 nm with negligible biquadratic coupling, which is contrary to the decreasing trend of the tRu = 0.4 nm sample and has been attributed to the greatly enhanced Hex.

Nanoporous Double-Gyroid Structure from ABC Triblock Terpolymer Thick Films

The creation of nanostructured materials with a triply periodic minimal surface (TPMS), defined as a zero mean curvature surface having periodicity in three-dimensional space, is an emerging solution to optimize transport (i.e., the ion-conductivity and hydraulic permeability) through the next-generation of electrolyte and ultrafiltration (UF) membranes. Here, we used an amphiphilic ABC-type block copolymer (BCP) (namely, polystyrene-block-poly(2-vinylpyridine)-block-poly(ethylene oxide) (PS-b-P2VP-b-PEO)) to generate symmetric thick films (~8 μm) composed entirely of a TPMS-based structure, consisting of a PS matrix with a double gyroid (DG) minimal surface and hydrophilic stimuli-responsive (P2VP/PEO) nanochannels. To produce the core/shell DG-structured monoliths, we used a process combining the nonsolvent-induced phase separation (NIPS) process with a solvent vapor annealing (SVA) treatment. From such symmetric ABC-type BCP-thick films generated by NIPS-SVA, a mean hydraulic permeability as high as 514 L h-1 m-2 bar-1 was measured. This mean value was revealed to be nearly equal to that of asymmetric PS-b-P2VP-b-PEO membranes manufactured by NIPS, which have a substructure with an implicit irregular and random distribution of the internal pore structure and a skin layer with P2VP/PEO nanopores arranged into a hexagonal array.

Six-band rotationally symmetric tunable absorption film based on AlCuFe quasicrystals

In this paper, a six-band rotationally symmetric tunable absorption film based on AlCuFe quasicrystals is proposed. The absorption film has a symmetrically excited electric field, which makes it have good polarization incoherence. After calculating the relative impedance of the absorption film using parameter inversion, it is obvious that the absorption film is consistent with the impedance matching theory. In addition, by changing the physical parameters of the absorption film and adjusting the Fermi energy, it can be found that the absorption film has good tunability. By changing the refractive index of the working environment of the absorption film, it can be seen that the absorption film has extremely high refractive index sensitivity. Overall, the absorption film is tunable, polarization incoherent, and has good sensing performance, which makes the absorption film have strong application prospects in many fields.

3D Architectural MXene‐based Composite Films for Stealth Terahertz Electromagnetic Interference Shielding Performance

AbstractThe terahertz frequency range is gaining popularity in security, stealth technology, and the future 6G network communication. For the control of severe terahertz electromagnetic interference (EMI) pollution, frequency‐selective stealth‐capable shielding materials are being explored to mask terahertz signals. For the realization of masking terahertz signals, the robustness, lightweight, and shape‐conformable materials with excellent terahertz EMI shielding/absorption are crucial. Here, the study reports the fabrication of 3D symmetric pyramidal architectural MXene composite films with frequency‐selective stealth performance characteristics via the facile drop casting method. With the high absorption capability of 2D MXene layers, the MXene composite films exhibit substantial terahertz stealth performance. 3D pyramidal microstructure design leads to frequency selective surface‐assisted reflection resonance in the frequency range of 0.6–1.1 THz. The MXene composite film demonstrates an outstanding maximum terahertz shielding effectiveness (SE) of up to 70.4 dB and a specific SE of 0.55 dB µm−1. These terahertz SE values exceed all of those for MX‐based shielding material designs reported in the literature. The investigation will open a new direction toward developing terahertz EMI shielding thin films with easy integration into any surface for stealth capabilities.

Solidification dynamics of polymer membrane by solvent extraction: Spontaneous stratification

Nonsolvent-induced phase separation is widely used to create polymer membranes, but its demixing process is generally understood by liquid-liquid separation. In this work, the solidification dynamics of polymer solutions for membrane formation are explored through dissipative particle dynamics simulations. The shrinkage of the symmetric film of polymer solution is monitored, and the evolutions of the concentration profiles of polymer, solvent, and nonsolvent are analyzed. Additionally, the evolution of the degree of crystallinity (local alignment) and the morphology of the developing membrane are also studied. Three regions can be identified: (i) interfacial region, (ii) dense layer, and (iii) middle region. The demixing process associated with liquid-solid separation is found to be caused by the extraction of solvent and concentration of polymers rather than nonsolvent-induced separation. Our results provide valuable insights into directional solidification and spontaneous stratification of the membrane, driven by solvent loss and oversaturation (beyond the maximum solubility of polymer).

Multichannel nonreciprocal thermal radiation with Weyl semimetal and photonic crystal heterostructure

A novel scheme for achieving multichannel nonreciprocal thermal radiation, which is in the form of a photonic crystal heterostructure sandwiched between two symmetric dielectric spacers and Weyl semimetal film backed with a metal film, is proposed and studied. A dual-channel nonreciprocal thermal emitter is first designed and studied as an illustration. It is found that near-perfect nonreciprocal radiations are realized at two different wavelengths at the same time. The underlying physical origin of this phenomenon is disclosed by investigating the magnetic field distribution. In addition, the novel dual-channel nonreciprocal radiation performance is robust to variations in geometric parameters, which will benefit real fabrication and application. What's more, the scheme can be easily expanded to achieve multi-band nonreciprocal radiation with the channel number larger than two by simply increasing the sequence order of the photonic crystal heterostructure. The scheme proposed in this paper provides a new possibility to develop novel multichannel nonreciprocal thermal emitters.

An 8-inch commercial aluminum nitride MEMS platform for the co-existence of Lamb wave and film bulk acoustic wave resonators

This work investigates a co-design approach for fundamental symmetric Lamb wave (S0) resonators (LWR) and film bulk acoustic wave resonators (FBAR) in a commercial 8-inch aluminum nitride (AlN) microelectromechanical system (MEMS) platform to enable multi-band operation. The platform utilizes surface micromachining to define local release cavities, providing an undercut-free solution for acoustic resonators to achieve a high quality factor (Q). However, being based on a standardized platform initially tailored for FBAR devices, many design considerations and trade-offs need to be investigated for the co-existence between LWR and FBAR design. Hence, to capture the optimal design window for S0 LWRs while analyzing its performance impact on existing FBARs, the electrode configuration and its thickness are thoroughly investigated by the finite element method. In this work, a 2.2 GHz FBAR, a 700 MHz S0 LWR, and a 2.19 GHz S0 Lamé LWR are demonstrated for performance evaluation across different types of devices in this platform. The measurement results revealed a baseline performance for the FBAR device with an electromechanical coupling factor () of 6.73% and Q of 3017 at 2.2 GHz, resulting in a high figure-of-merit (FoM = ) over 200. In comparison, the 700 MHz S0 LWR exhibits a high Q of 2532 as well and a of 1.1% (FoM = 27.8), while the 2.19 GHz S0 Lamé LWR also exhibits a high Q of 1752 and a of 2.44% (FoM = 42.7), respectively. These performance indexes are all comparable with the current state-of-the-art, revealing the excellent potential of this AlN MEMS platform being implemented for future LWR development design or even mass production.

The joint impact of crystal-cell thickness and biaxial ([110]) strain on the ferroelectricity of KNbO[formula omitted] in bulk/thin-film form

Due to robust spontaneous Polarization (P), ferroelectric materials are extensively used in numerous applications such as power consumption, exhaustion-free capacitor, and energy harvesting. Herein, we focus on the possibility of controlling the ferroelectric properties of the bulk/thin films of KNbO3 perovskite oxide via unit cell thickness and strain engineering using ab-initio calculations. First, the thermodynamic stability of the bulk and thin film structures is determined by computing the formation enthalpies and surface energies using Convex Hull analysis, respectively, which affirms their experimental realization. It is demonstrated that bulk structure is stable against its competing KO and NbO2 phases, while NbO2-NbO2 symmetric film is more energetically stable to grow in the lab as compared to others. Moreover, mechanical stability of the structures is confirmed by calculating the elastic constants. The estimated value of (P) for the bulk motif is 37.4 μC cm−2, which is in a good agreement with experimentally observed value. Thin films with larger slab thickness display more structural distortion, which enhances the P magnitude. For possible [KO-NbO2] (asymmetric) and [KO-KO]/[NbO2-NbO2] (symmetric) slabs, P gradually increases from 11.77 to 26.87 μC cm−2 and 8.59 to 16.43/23.38 to 27.42 μC cm−2 as the KNO unit cell thickness increases from 1 to 5 (1.86 nm) and 1.5 to 5.5 (2.05 nm), respectively. Interestingly, it is found that -5% compressive strain increases the P value of bulk KNO up to 31% than that of unstrained one. Similarly, the P amplitude in KO-NbO2 (1.86 nm thick) and KO-KO/NbO2-NbO2 (2.05 nm thick) slabs also improve up to 10.6% and 10.8%/11% as compared to unstrained ones for −5% compressive strain, respectively. Hence, the present work yields deep observations into the combined effect of crystal cell thickness and strain on the ferroelectricity of KNO, which provides a possible way to tune the P to enhance its potential realization in the oxide industry.

Linear Stability of Double-sided Symmetric Thin Liquid Film by Integral-theory

The Integral Theory approach is used to explore the stability and dynamics of a free double-sided symmetric thin liquid film. For a Newtonian liquid with non-variable density and moving viscosity, the flowing in a thinning liquid layer is analyzed in two dimensions. To construct an equation that governs such flow, the Navier and Stokes formulas are utilized with proper boundary conditions of zero shear stress conjointly of normal stress on the bounding free surfaces with dimensionless variables. After that, the equations that are a non-linear evolution structure of layer thickness, local stream rate, and the unknown functions can be solved by using straight stability investigation, and the normal mode strategy can moreover be connected to these conditions to reveal the critical condition. The characteristic equation for the growth rate and wave number can be analyzed by using MATLAM programming to show the region of stable and unstable films. As a result of our research, we are able to demonstrate that the effect of a thin, free, double-sided liquid layer is an unstable component.

Multilayered Cu/NiFe thin films for electromagnetic interference shielding at high frequency

Cu/NiFe multilayers with different structures were fabricated by electroplating for electromagnetic wave interference shielding in the high-frequency region. The electromagnetic wave interference shielding effectiveness of the symmetric, asymmetric, and thickness-gradient multilayer films was evaluated to optimize these structures. The thickness of the NiFe layer, which acts as an interlayer between Cu layers, is an important factor. The five-layered thin film (S9), with a thickness gradient that continues to increase toward the lower layer, shows an electromagnetic interference shielding effectiveness of − 74 dB in the wideband region, even though the total thickness of the multilayer is 1 µm. Focused ion beam, scanning electron microscopy, vector network, X-ray diffraction, four-point probe, and inductively coupled plasma–optical emission spectroscopy analyses were performed to characterize the multilayered Cu/NiFe thin films. • A Cu/NiFe multilayer was fabricated via electroplating. • The electrical conductivity and shielding effectiveness were investigated. • The electromagnetic interference shielding mechanism of the multilayer was studied.

Symmetric Thin Films Based on Silicon Materials for Angle‐Insensitive Full‐Color Structural Colors

AbstractHere, reflective full‐color structural colors with symmetrical thin film structures made from all silicon‐based materials are demonstrated. Considering practical application scenarios, the five‐layer reflection enhancement unit located in the core of the device is composed of amorphous silicon (a‐Si) and SiO2. Because of the large refractive index difference, the high reflection efficiency can be achieved, and the highest peak reflectivity of the sample can reach 89%. On both sides of the device, the same anti‐reflection (AR) unit composed of SiOx and SiO2 is deposited, which can significantly reduce the reflection of non‐target wavelength and enhance the color purity of the device. Meanwhile, the thin thickness of the absorbing materials provides the better angular insensitivity and the device shows a stable color appearance in the range of 0–60°. Based on the idea of symmetrical structure, a variety of angular insensitive structural colors can be realized. The scheme is simple in structure and material, which provides the feasibility for mass production. Particularly, the symmetry of the structure makes structural colors have unique advantages and the potential to be widely applied in the color paint fields of printing, decoration, and counterfeit detection.

Carbon molecular sieve hollow fiber composite membrane derived from PMDA-ODA polyimide for gas separation

Carbon molecular sieve (CMS) membranes have excellent gas separation property over conventional polymeric membranes and superior anti-swelling property. PMDA-ODA polyimide has high thermal stability and good mechanical property. It has been extensively adopted as the precursor of CMS membrane. However, due to the insoluble nature, PMDA-ODA CMS membranes are limited to configurations like dense symmetric films or composite membranes using porous inorganic or metal substrates. In this work, CMS hollow fiber composite membranes based on an asymmetric PMDA-ODA hollow fiber were successfully prepared for the first time. The neat PMDA-ODA hollow fiber membrane was crosslinked by polyethyleneimine to alleviate pore collapsing during carbonization and then dip-coated by a PMDA-ODA PAA solution to seal the surface defects. The PDMA-ODA CMS composite hollow fiber membranes showed gas permeances of 93.4 GPU, 19.6 GPU, 6.5 GPU, and 4.7 GPU for CO2, O2, N2, and CH4, respectively, with an ideal selectivity of 14.4, 3.0, and 19.8 for CO2/N2, O2/N2, and CO2/CH4 gas pairs, respectively. The attractive gas separation property shows a great potential for industrial application.

MnBi2Se4-Based Magnetic Modulated Heterostructures

Thin films of magnetic topological insulators (TIs) are expected to exhibit a quantized anomalous Hall effect when the magnetizations on the top and bottom surfaces are parallel and a quantized topological magnetoelectric effect when the magnetizations have opposite orientations. Progress in the observation of these quantum effects was achieved earlier in the films with modulated magnetic doping. On the other hand, the molecular-beam-epitaxy technique allowing the growth of stoichiometric magnetic van der Waals blocks in combination with blocks of topological insulator was developed. This approach should allow the construction of modulated heterostructures with the desired architecture. In the present paper, based on the first-principles calculations, we study the electronic structure of symmetric thin film heterostructures composed of magnetic MnBi2Se4 blocks (septuple layers, SLs) and blocks of Bi2Se3 TI (quintuple layers, QLs) in dependence on the depth of the magnetic SLs relative to the film surface and the TI spacer between them. Among considered heterostructures we have revealed those characterized by nontrivial band topology.

A pedagogical extension of the one-dimensional Schrödinger’s equation to symmetric proximity effect system film sandwiches

This study sought to use Schrödigner’s equation to model superconducting proximity effect systems of symmetric forms. As Werthamer noted [Phys. Rev. 132(6), 2440–2445 (1963)], one to one analogies between the standard superconducting proximity effect equation and the one-dimensional, time-independent Schrödinger’s equation can be made, thus allowing one to model the behavior of proximity effect systems of metallic film sandwiches by solving Schrödinger’s equation. In this project, film systems were modeled by infinite square wells with simple potentials. Schrödinger’s equation was solved for sandwiches of the form S(NS)M and N(SN)M, where S and N represent superconducting and nonsuperconducting metal films, respectively, and M is the number of repeated bilayers, or the period. A comparison of Neumann and Dirichlet boundary conditions was carried out in order to explore their effects. The Dirichlet type produced eigenvalues for S(NS)M and N(SN)M sandwiches that converged for increasing M, but the Neumann type produced eigenvalues for the same structures that approached two different limits as M increased. This last behavior is unexpected as it implies a dependence on the type of the film end layer.