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We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are potentially useful as either analytical or computational tools for understanding the corresponding higher-order equation. We perform a systematic analysis of a family of linear model equations and show that for each member of this family there is a stable hyperbolic approximation whose solution converges to that of the model equation in a certain limit. We then show through several examples that this approach can be applied successfully to a very wide range of nonlinear PDEs of practical interest.

Hexagonal boron nitride (h-BN) is brittle, however, its atomic-scale structural engineering can lead to unprecedented physical properties. Here we report the bulk synthesis of high-density crystalline h-BN solids by using high-temperature spark plasma sintering (SPS) of micron size h-BN powders. In addition to the high mechanical strength and ductile response of such materials, we have obtained anomalous values of dielectric constant beyond theoretical limits, high thermal conductivity, and exceptional neutron radiation shielding capability. Through exhaustive characterizations we reveal that SPS induces non-basal plane crystallinity, twisting of layers, and facilitates inter-grain fusion with a high degree of in-plane alignment across macroscale dimensions, resulting in near-theoretical density and anomalous properties. Our findings highlight the importance of material design, via new approaches such as twisting and interconnections between atomically thin layers, to create novel ceramics with properties that could go beyond their intrinsic theoretical predictions., Comment: Authors revised version, 46 pages, 4 figures

Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high-order convergence for linear problems; we refer to these conditions as weak stage order conditions. We prove a general relationship between the method's order, weak stage order, and number of stages. We derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear problems.

The nonlinear Schr\"{o}dinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate long-time simulations, particularly for multi-soliton solutions. We propose an essentially explicit discretization that conserves one or two of these conserved quantities by combining higher-order Implicit-Explicit (ImEx) Runge-Kutta time integrators with the relaxation technique and adaptive step size control. We show through numerical tests that our mass-conserving method is much more efficient and accurate than the widely-used 2nd-order time-splitting pseudospectral approach. Compared to higher-order operator splitting, it gives similar results in general and significantly better results near the semi-classical limit. Furthermore, for some problems adaptive time stepping provides a dramatic reduction in cost without sacrificing accuracy. We also propose a full discretization that conserves both mass and energy by using a conservative finite element spatial discretization and multiple relaxation in time. Our results suggest that this method provides a qualitative improvement in long-time error growth for multi-soliton solutions.

Heterostructures based on ultrawide-bandgap (UWBG) semiconductors (bandgap >4.0 eV), boron nitride (BN) and diamond are important for next-generation high-power electronics. However, in-situ hetero-epitaxy of BN/diamond or vice-versa remains extremely challenging, due to their non-trivial growth kinetics. Here, we have grown BN thin film on (100) single crystal diamond by pulsed laser deposition and investigated its structural and magnetic properties, optical refractive index, and thermal conductivity. Structural characterizations confirm the mixed (stable hexagonal and metastable cubic) phase growth. Film shows diamagnetic behavior at room temperature. It displays anisotropic refractive index within the visible-to-near-infrared wavelength range. The room temperature cross-plane thermal conductivity of BN is ~1.53 W/(mK), and the thermal conductance of the BN/diamond interface is ~20 MW/(m2K). Our findings are useful for various device related applications based on UWBG BN/diamond heterostructures., Comment: 16 pages, 4 figures

Understanding the emergent electronic structure in twisted atomically thin layers has led to the exciting field of twistronics. However, practical applications of such systems are challenging since the specific angular correlations between the layers must be precisely controlled and the layers have to be single crystalline with uniform atomic ordering. Here, we suggest an alternative, simple and scalable approach where nanocrystalline two-dimensional (2D) film on three-dimensional (3D) substrates yield twisted-interface-dependent properties. Ultrawide-bandgap hexagonal boron nitride (h-BN) thin films are directly grown on high in-plane lattice mismatched wide-bandgap silicon carbide (4H-SiC) substrates to explore the twist-dependent structure-property correlations. Concurrently, nanocrystalline h-BN thin film shows strong non-linear second-harmonic generation and ultra-low cross-plane thermal conductivity at room temperature, which are attributed to the twisted domain edges between van der Waals stacked nanocrystals with random in-plane orientations. First-principles calculations based on time-dependent density functional theory manifest strong even-order optical nonlinearity in twisted h-BN layers. Our work unveils that directly deposited 2D nanocrystalline thin film on 3D substrates could provide easily accessible twist-interfaces, therefore enabling a simple and scalable approach to utilize the 2D-twistronics integrated in 3D material devices for next-generation nanotechnology., Comment: 33 pages, 4 figures

Boron nitride (BN) is an exceptional material and among its polymorphs, two-dimensional (2D) hexagonal and three-dimensional (3D) cubic BN (h-BN and c-BN) phases are most common. The phase stability regimes of these BN phases are still under debate and phase transformations of h-BN/c-BN remain a topic of interest. Here, we investigate the phase stability of 2D/3D h-BN/c-BN nanocomposites and show that the co-existence of two phases can lead to strong non-linear optical properties and low thermal conductivity at room temperature. Furthermore, spark-plasma sintering of the nanocomposite shows complete phase transformation to 2D h-BN with improved crystalline quality, where 3D c-BN grain sizes governs the nucleation and growth kinetics. Our demonstration might be insightful in phase engineering of BN polymorphs based nanocomposites with desirable properties for optoelectronics and thermal energy management applications., Comment: 29 pages, 5 figures

We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined by multiple time stepping algorithms. Similar to the directional projection method of Calvo et. al., we use embedded Runge-Kutta methods to facilitate this in a computationally efficient manner. Proof of the accuracy of the modified RK methods and the existence of valid relaxation parameters are given, under some restrictions. Among other examples, we apply this technique to Implicit-Explicit Runge-Kutta time integration for the Korteweg-de Vries equation and investigate the feasibility and effect of conserving multiple invariants for multi-soliton solutions.

Wide and ultrawide-bandgap semiconductors lie at the heart of next-generation high-power, high-frequency electronics. Here, we report the growth of ultrawide-bandgap boron nitride (BN) thin films on wide-bandgap gallium nitride (GaN) by pulsed laser deposition. Comprehensive spectroscopic (core level and valence band XPS, FTIR, Raman) and microscopic (AFM and STEM) characterizations confirm the growth of BN thin films on GaN. Optically, we observed that BN/GaN heterostructure is second-harmonic generation active. Moreover, we fabricated the BN/GaN heterostructure-based Schottky diode that demonstrates rectifying characteristics, lower turn-on voltage, and an improved breakdown capability (234 V) as compared to GaN (168 V), owing to the higher breakdown electrical field of BN. Our approach is an early step towards bridging the gap between wide and ultrawide-bandgap materials for potential optoelectronics as well as next-generation high-power electronics., Comment: 5 Figures, Published in Applied Physics Letters

Two-dimensional van der Waals (2D-vdW) layered hexagonal boron nitride (h-BN) has gained tremendous research interest over recent years due to its unconventional domain growth morphology, fascinating properties and application potentials as an excellent dielectric layer for 2D-based nano-electronics. However, the unidirectional domain growth of h-BN thin films directly on insulating substrates remains significantly challenging because of high-bonding anisotropicity and complex growth kinetics than the conventional thin films growth, thus resulting in the formation of randomly oriented domains morphology, and hindering its usefulness in integrated nano-devices. Here, ultra-wide bandgap h-BN thin films are grown directly on low-miscut atomically smooth highly insulating c-plane sapphire substrates (without using any metal catalytic layer) by pulsed laser deposition, showing remarkable unidirectional triangular-shape domains morphology. This unidirectional domain growth is attributed to the step-edge guided nucleation caused by reducing the film-substrate interfacial symmetry and energy, thereby breaking the degeneracy of nucleation sites of random domains, as revealed by the density functional theory (DFT) calculations. Through extensive characterizations, we further demonstrate the excellent single crystal-like functional properties of films. Our findings might pave the way for feasible large-area direct growth of electronic-quality h-BN thin films on insulating substrates for high-performance 2D-electronics, and in addition would be beneficial for hetero engineering of 2D-vdW materials with emergent phenomena., Comment: 39 pages, 7 figures, Revised accepted version of the article

Room temperature growth of two-dimensional van der Waals (2D-vdW) materials is indispensable for state-of-the-art nanotechnology. The low temperature growth supersedes the requirement of elevated growth temperature accompanied with high thermal budgets. Moreover, for electronic applications, low or room temperature growth reduces the possibility of intrinsic film-substrate interfacial thermal diffusion related deterioration of functional properties and consequent device performance. Here, we demonstrated the growth of ultrawide-bandgap boron nitride (BN) at room temperature by using the pulsed laser deposition (PLD) process and demonstrated various functionalities for potential applications. Comprehensive chemical, spectroscopic and microscopic characterization confirms the growth of ordered nanosheet-like hexagonal BN. Functionally, nanosheets show hydrophobicity, high lubricity (low coefficient of friction), low refractive index within the visible to near-infrared wavelength range, and room temperature single-photon quantum emission. Our work unveils an important step that brings a plethora of applications potential for room temperature grown h-BN nanosheets as it can be feasible on any given substrate, thus creating a scenario for h-BN on demand at frugal thermal budget., Comment: 27 pages, 4 figures, Authors version of the article

Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order, DIRK (diagonally implicit Runge-Kutta) schemes are practically important due to their structural simplicity; however, these cannot possess high stage order. The concept of weak stage order (WSO) can also overcome order reduction, and it is compatible with the DIRK structure. DIRK schemes of WSO up to 3 have been proposed in the past, however, based on a simplified framework that cannot be extended beyond WSO 3. In this work a general theory of WSO is employed to overcome the prior WSO barrier and to construct practically useful high-order DIRK schemes with WSO 4 and above. The resulting DIRK schemes are stiffly accurate, L-stable, have optimized error coefficients, and are demonstrated to perform well on a portfolio of relevant ODE and PDE test problems.

Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the method satisfies certain weak stage order (WSO) conditions, which are less restrictive than traditional stage order conditions. This paper outlines the first algebraic theory of WSO, and establishes general order barriers that relate the WSO of a RK scheme to its order and number of stages for both fully-implicit and DIRK schemes. It is shown in several scenarios that the constructed bounds are sharp. The theory characterizes WSO in terms of orthogonal invariant subspaces and associated minimal polynomials. The resulting necessary conditions on the structure of RK methods with WSO are then shown to be of practical use for the construction of such schemes.

Layered nanolaminate ternary carbides, nitrides and carbonitrides with general formula Mn+1AXn or MAX (n = 1, 2, or 3, M is an early transition metal, A is mostly group 13 or 14 element, and X is C and/or N) has revolutionized the world of nanomaterials, due to the coexistence of both ceramic and metallic nature, giving rise to exceptional mechanical, thermal, electrical, chemical properties and wide range of applications. Although several solid-state bulk synthesis methods have been developed to produce a variety of MAX phases, however, for certain applications, the growth of MAX phases, especially in its high-quality epitaxial thin films form is of increasing interest. Here, we summarize the progress made thus far in epitaxial growth and property evaluation of MAX phase thin films grown by various deposition techniques. We also address the important future research directions to be made in terms of thin-film growth. Overall, in the future, high-quality single-phase epitaxial thin film growth and engineering of chemically diverse MAX phases may open up interesting new avenues for next-generation technology., Comment: Review Article, 27 Pages, 4 Figures

High-performance non-volatile resistive random access memories (ReRAM) and their small stimuli control are of immense interest for high-speed computation and big-data processing in the emergent Internet of Things (IOT) arena. Here, we examine the resistive switching (RS) behavior in growth controlled HfO2/La0.67Sr0.33MnO3 heterostructures and their tunability under low magnetic field. It is demonstrated that oxygen-deficient HfO2 films show bipolar switching with high on/off ratio, stable retention, as well as good endurance owing to the orthorhombic-rich phase constitution and charge (de)-trapping-enabled Schottky-type conduction. Most importantly, we have demonstrated that, the RS can be tuned by a very low externally applied magnetic field (0-30 mT). Remarkably, application of a magnetic field of 30 mT causes the RS to be fully quenched and frozen in the high resistance state (HRS) even after the removal of magnetic field. However, the quenched state could be resurrected by applying higher bias voltage than the one for initial switching. This is argued to be a consequence of the electronically and ionically active nature of the HfO2-x/LSMO interface on both sides, and its susceptibility to the electric and low magnetic field effects. This result could pave the way for new designs of interface engineered high-performance oxitronic ReRAM devices., Comment: 45 pages, 5 main figures

This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building blocks for long-time accurate solutions in more complex advection-dominated problems. After establishing a new notion of convergence in an infinite time limit of numerical methods, we first show that linear methods cannot meet this convergence criterion. Then we present a new numerical methodology, based on a nonlinear jet scheme framework. We show that these methods do satisfy the new convergence criterion, thus establishing that numerical methods exist that converge on an infinite time horizon, and demonstrate the long-time accuracy gains incurred by this property., Comment: 21 pages, 10 figures

Recently, nanolaminated ternary carbides have attracted immense interest due to the concomitant presence of both ceramic and metallic properties. Here, we grow nanolaminate Ti3AlC2 thin films by pulsed laser deposition on c-axis-oriented sapphire substrates and, surprisingly, the films are found to be highly oriented along the (103) axis normal to the film plane, rather than the (000l) orientation. Multiple characterization techniques are employed to explore the structural and chemical quality of these films, the electrical and optical properties, and the device functionalities. The 80-nm thick Ti3AlC2 film is highly conducting at room temperature (resistivity of 50 micro ohm-cm), and a very-low-temperature coefficient of resistivity. The ultrathin (2 nm) Ti3AlC2 film has fairly good optical transparency and high conductivity at room temperature (sheet resistance of 735 ohm). Scanning tunneling microscopy reveals the metallic characteristics (with finite density of states at the Fermi level) at room temperature. The metal-semiconductor junction of the p-type Ti3AlC2 film and n-Si show the expected rectification (diode) characteristics, in contrast to the ohmic contact behavior in the case of Ti3AlC2 on p-Si. A triboelectric-nanogenerator-based touch-sensing device, comprising of the Ti3AlC2 film, shows a very impressive peak-to-peak open-circuit output voltage of 80 V. These observations reveal that pulsed laser deposited Ti3AlC2 thin films have excellent potential for applications in multiple domains, such as bottom electrodes, resistors for high-precision measurements, Schottky diodes, ohmic contacts, fairly transparent ultrathin conductors, and next-generation biomechanical touch sensors for energy harvesting., Comment: 41 pages, 8 main figures, Published in Physical Review Applied

For generation of sustainable, clean and highly efficient energy, the electrocatalytic oxygen evolution reaction represents an attractive platform, thus inviting immense research activities in recent years. However, designing the catalyst with enhanced electrocatalytic activity remains one of the major challenges. Here, we examined the oxygen evolution reaction activities of geometrically designed (with and without step-textured morphology) thin films of an electrocatalytically active correlated metallic SrRuO3 perovskite grown on c- and r-plane sapphire substrates. On c-plane sapphire, as compared to the uniform surface, the step-textured films endowed with active Ru-sites show remarkable decrease in the overpotential (25 mV). Interestingly, the behavior is opposite for the r-plane case, highlighting the significance of the active sites, in addition with the polar surface termination of selective crystal facets. Density functional theory calculation confirms the favorable energy reaction pathway for the active site dependent enhancement in OER. Our strategy might pave the way towards designing the surfaces of various oxide thin films for high performance energy conversion based devices., Comment: 18 pages. 5 figures, Published in Applied Surface Science

We report a very high precision interferometric sensor with resolution up to ~{\lambda}/1024, exploiting hollow photonic bandgap waveguide-based geometry for the first time. Here sensing has been measured by a complete switching in the direction of the outgoing beam, owing to transverse momentum oscillation phenomena. Using a 1.32 {\mu}m source and core-width of 7.25 {\mu}m, a complete switching cycle is obtained even due to a small change of ~1 nm in the core-width. Using hollow-core photonic bandgap waveguide, Talbot effect, revivals of the initial phase, oscillation in the transverse momentum along with multi-mode interference served as the backbone of the design. The ultra-sensitive multi-mode interferometric sensor based on photonic crystals will certainly open up a paradigm shift in interferometer-based sensing technologies toward device-level applications in photonic sensing/switching and related precision measurement systems., Comment: 5 pages; 4 figures

One of the most intriguing topological features of open systems is exhibiting exceptional point (EP) singularities. Apart from the widely explored second-order EPs (EP2s), the explorations of higher-order EPs in any system requires more complex topology, which is still a challenge. Here, we encounter a third-order EP (EP3) for the first time in a simple fabrication feasible gain-loss assisted optical microcavity. Using scattering-matrix formalism, we study the simultaneous interactions between three successive coupled states around two EP2s, which yield an EP3. Following an adiabatic parametric variation around the identified EP3, we present a robust successive-state-conversion mechanism among three coupled states. The proposed scheme indeed opens a unique platform to manipulate light in integrated devices., Comment: 6 pages, 4 figures

In view of their immensely intriguing properties, two dimensional materials are being intensely researched in search of novel phenomena and diverse application interests, however, studies on the realization of nanocomposites in the application-worthy thin-film platform are rare. Here we have grown MoS2-hBN composite thin films on different substrates by the pulsed laser deposition technique and made comparative studies with the pristine MoS2 and hBN films. The Raman, XPS and HRTEM confirm the concomitant presence of both the 1T (conducting) and 2H (semiconducting) polymorphs of MoS2 in the composite film. Interestingly, a peculiar reentrant semiconductor-metal-insulator transition is seen in the composite film which is absent in the MoS2 film, and it correlates well with the signatures of phonon softening seen in temperature-dependent Raman spectroscopy. Furthermore, electrostatic force microscopy reveals the presence of three distinct regions (metallic, semiconducting, and insulating) in the composite film with differing contact potentials and enhanced propensity for charge transfer with respect to pristine MoS2. A triboelectric nanogenerator device containing biphasic composite film as an electron acceptor exhibits more than twofold (sixfold) enhancement in peak-to-peak output voltage as compared to the pristine MoS2 (hBN) film. These observations bring out the potential of nanocomposite thin films for unfolding emergent phenomena and technological applications., Comment: 9 Figures, Published in Physical Review Materials

Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and optical systems. Here, exploiting a gain-loss assisted dual-mode optical waveguide that hosts a dynamical EP-encirclement scheme, we have explored enhanced nonreciprocal effect in the dynamics of light with onset of saturable nonlinearity in the optical medium. We propose a prototype waveguide-based isolation scheme with judicious tuning of nonlinearity level where one can pass only a chosen mode in any of the desired directions as per device requirement. The deliberate presence of EP enormously enhances the nonreciprocal transmission contrast even up to 40 dB over the proposed device length with a scope of further scalability. This exclusive topologically robust mode selective all-optical isolation scheme will certainly offer opportunities in integrated photonic circuits for efficient coupling operation from external sources and improve device performances., Comment: 5 pages, 6 figures

We investigate the astonishing physical aspects of Exceptional Points (EPs) in a 1D planar few-mode optical waveguide. The waveguide hosts four quasi-guided modes. Here interactions between the selected pair of modes are modulated by a spatial distribution of inhomogeneous gain-loss profile. Both the coupled pairs approach two different second-order EPs in parameter plane. Considering a proper parametric loop to encircle the identified EPs simultaneously, we establish a specific topological feature where one round encirclement in parameter space yields the switching between the propagation constants ({\beta}) of the corresponding pairs of couple modes in complex {\beta}-plane. Choosing two different patterns of the parametric loop, we establish the immutable topology in {\beta}- switching phenomena. This robust mode conversion scheme shall provide a platform to realize selective mode switching devices or optical-mode converters., Comment: 6 pages, 4 figures

CubeSats are excellent platforms to rapidly perform simple space experiments. Several hundreds of CubeSats have already been successfully launched in the past few years and the number of announced launches grows every year. These platforms provide an easy access to space for universities and organizations which otherwise could not afford it. However, these spacecraft still rely on RF communications, where the spectrum is already crowded and cannot support the growing demand for data transmission to the ground. Lasercom holds the promise to be the solution to this problem, with a potential improvement of several orders of magnitude in the transmission capacity, while keeping a low size, weight and power. Between 2016 and 2017, The Keck Institute for Space Studies (KISS), a joint institute of the California Institute of Technology and the Jet Propulsion Laboratory, brought together a group of space scientists and lasercom engineers to address the current challenges that this technology faces, in order to enable it to compete with RF and eventually replace it when high-data rate is needed. After two one-week workshops, the working group started developing a report addressing three study cases: low Earth orbit, crosslinks and deep space. This paper presents the main points and conclusions of these KISS workshops., Comment: 7 pages, 5 figures, 2 tables, Official Final Report of KISS (Keck Institute for Space Studies) workshop on "Optical communication on CubeSats" (http://kiss.caltech.edu/workshops/optcomm/optcomm.html)

We report a 1D planar optical waveguide with transverse distribution of inhomogeneous loss profile, which exhibits an exceptional point (EP). The waveguide hosts two leaky resonant modes; where the interaction between them in the vicinity of the EP is controlled by proper adjustment of the inhomogeneity in attenuation profile only. We study the adiabatic dynamics of propagation constants of the coupled modes by quasi-static encirclement of control parameters around the EP. Realizing such an encirclement with the inhomogeneous loss distribution along the direction of light propagation, we report the breakdown of adiabatic evolution of two coupled modes through the waveguide in presence of an EP. Here, during conversion the output mode is irrespective of the choice of input excited mode but depends on the direction of light transportation. This topologically controlled, robust scheme of asymmetric mode conversion in the platform of the proposed all-lossy waveguide structure may open up an extensive way-out for implementation of state-transfer applications in chirality driven waveguide-based devices., Comment: 15 pages, 7 figures

We have grown Au/Ag modulated nanostructured thin films by pulsed laser deposition using metallic targets. The growths performed at room temperature involved deposition of alternate layers of the two metals with larger thickness of Au and much lower thickness of Ag (two cases) on crystalline silicon (100) and quartz substrates. However, the characterization revealed that nanostructured configuration is realized in the film. We characterized the films by x-ray diffraction (XRD), Field emission scanning electron microscopy (FESEM) with energy dispersive analysis of x-rays (EDAX), magnetization (M-T) and resistivity (Rho-T) measurements. The magnetization and resistivity measurements confirm that there is no signature of superconducting transition within the temperature range of 5K to 300K studied in these films., Comment: 7 pages, 4 figures

We explore exceptional points (EP) in a dual-mode symmetric planar optical waveguide with transverse variation of inhomogeneous loss profile; where modal evolution alongside an EP is reported in the context of selective optical mode conversion., Comment: 2 pages 1 figure

Exploiting scattering-matrix in a gain-loss assisted optical-microcavity, interplay between asymmetric-state-conversion and cavity-control parameters around exceptional points is analyzed; where occupying a least area by coupled states during switching, maximum conversion-efficiency with minimal asymmetry is achieved., Comment: 2 pages 1 figure