Topological Insulator Magnetic Tunnel Junctions: Quantum Hall Effect and Fractional Charge via Folding

We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized fractional charge, also taking into account interaction effects for the 2D case. We show that the effects of tunneling are topologically equivalent to a certain deformation or folding of the sample geometry. Our key advance is the realization that the quantum Hall or fractional charge physics can appear in the presence of only a \emph{single} magnet unlike previous proposals which involve magnetic domain walls on the surface or edges of topological insulators respectively. We give illustrative topological folding arguments to prove our results and show that for the 2D case our results are robust even in the presence of interactions.Comment: 5 pages, 2 figure

Fractional Spin Josephson Effect and Electrically Controlled Magnetization in Quantum Spin Hall Edges

We explore a spin Josephson effect in a system of two ferromagnets coupled by a tunnel junction formed of 2D time-reversal invariant topological insulators. In analogy with the more commonly studied instance of the Josephson effect for charge in superconductors, we investigate properties of the phase-coherent {\it spin} current resulting from the misalignment of the in-plane magnetization angles of the two ferromagnets. We show that the topological insulating barrier offers the exciting prospect of hosting a {\it fractional} spin Josephson effect mediated by bound states at the ferromagnet-topological insulator interface. We provide multiple perspectives to understand the $4\pi$ periodic nature of this effect. We discuss several measurable consequences, such as, the generation of a transverse voltage signal which allows for purely electrical measurements, an inverse of this effect where an applied voltage gives rise to a transverse spin-current, and a fractional AC spin-Josephson effect.Comment: 5 pages, 2 figures (v2:fixed typo, added reference

Adaptive Backstepping Control for Air-Breathing Hypersonic Vehicles with Input Nonlinearities

This paper addresses the control problem of air-breathing hypersonic vehicles subject to input nonlinearities, aerodynamic uncertainties and flexible modes. An adaptive backstepping controller and a dynamic inverse controller are developed for the altitude subsystem and the velocity subsystem, respectively, where the former eliminates the problem of “explosion of terms” inherent in backstepping control. Moreover, a modified smooth inverse of the dead-zone is proposed to compensate for the dead-zone effects and reduce the computational burden. Based on this smooth inverse, an input nonlinear pre-compensator is designed to handle input saturation and dead-zone nonlinearities, which leads to a simpler control design for the altitude subsystem subject to these two input nonlinearities. It is proved that the proposed controllers can guarantee that all closed-loop signals are bounded and the tracking errors converge to an arbitrarily small residual set. Simulation results are carried out to demonstrate the effectiveness of the proposed control scheme

A high-density theta burst paradigm enhances the aftereffects of transcranial magnetic stimulation: Evidence from focal stimulation of rat motor cortex

Background: Theta burst stimulation (TBS) is an efficient noninvasive neuromodulation paradigm that has been widely adopted, clinically. However, the efficacy of TBS treatment remains similarly modest as conventional 10 Hz repetitive transcranial magnetic stimulation (rTMS). Objective/hypothesis: To develop a new TBS paradigm that enhances the effects of TMS administration while maintaining high time-efficiency. Methods: We describe here a new TMS paradigm, named High-Density Theta Burst Stimulation (hdTBS). This paradigm delivers up to 6 pulses per burst, as opposed to only 3 in conventional TBS, while maintaining the inter-burst interval of 200 ms (or 5 Hz) - a critical parameter in inducing long-term potentiation. This paradigm was implemented on a TMS stimulator developed in-house; its physiological effects were assessed in the motor cortex of awake rats using a rodent specific focal TMS coil. Microwire electrodes were implanted into each rat\u27s limb muscles to longitudinally record motor-evoked potential (MEP). Four different TBS paradigms (3, 4, 5 or 6 pulses per burst, 200 s per session) were tested; MEP signals were recorded immediately before (baseline) and up to 35 min post each TBS session. Results: We developed a stimulator based on a printed-circuit board strategy. The stimulator was able to deliver stable outputs of up to 6 pulses per burst. Animal experiments (n = 15) revealed significantly different aftereffects induced by the four TBS paradigms (Friedman test, p = 0.018). Post hoc analysis further revealed that, in comparison to conventional 3-pulse TBS, 5- and 6-pulse TBS enhanced the aftereffects of MEP signals by 56% and 92%, respectively, while maintaining identical time efficiency. Conclusion(s): A new stimulation paradigm is proposed, implemented and tested in the motor cortex of awake rats using a focal TMS coil developed in the lab.We observed enhanced aftereffects as assessed by MEP, with no obvious adverse effects, suggesting the translational potentials of this paradigm

Exploring the interplay between topological order, magnetism and superconductivity

This thesis presents a theoretical study of topological insulators coupled with superconductor and magnet. We discuss different physics due to these novel couplings and the topological properties. Chapter 2 describes the background of the research projects. We present different Quantum Hall systems, discuss their topological properties. Also we provide some basic formulas in Luttinger liquid theory, which will be used heavily in this thesis. Chapter 3 presents different phases we discovered in 2D topological insulators. We explore the phases exhibited by an interacting quantum spin Hall edge state in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature of the edge state gives rise to orders that are expected to be absent in non-chiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wavevector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. We find that finite spin imbalance favors a finite current carrying groundstate that is not condensed in the absence of interactions and is superconducting for attractive interactions. This state is characterized by FFLO-type oscillations where the Cooper pairs obtain a finite center of mass momentum. Chapter 4 describes the new spin Josephson effect. We explore a spin Josephson effect in a system of two ferromagnets coupled by a tunnel junction formed of 2D time-reversal invariant topological insulators. In analogy with the more commonly studied instance of the Josephson effect for charge in superconductors, we investigate properties of the phase-coherent {\it spin} current resulting from the misalignment of the in-plane magnetization angles of the two ferromagnets. We show that the topological insulating barrier offers the exciting prospect of hosting a {\it fractional} spin Josephson effect mediated by bound states at the ferromagnet-topological insulator interface. We provide multiple perspectives to understand the $4\pi$ periodic nature of this effect. We discuss several measurable consequences, such as, the generation of a transverse voltage signal which allows for purely electrical measurements, an inverse of this effect where an applied voltage gives rise to a transverse spin-current, and a fractional AC spin-Josephson effect. Chapter 5 presents the inverse spin pumping effect. We study the dynamics of a quantum spin Hall edge coupled to a magnet with its own dynamics. Using spin transfer torque principles, we analyze the interplay between spin currents in the edge state and dynamics of the axis of the magnet, and draw parallels with circuit analogies. As a highlighting feature, we show that while coupling to a magnet typically renders the edge state insulating by opening a gap, in the presence of a small potential bias, spin-transfer torque can restore perfect conductance by transferring angular momentum to the magnet. In the presence of interactions within the edge state, we employ a Luttinger liquid treatment to show that the edge, when subject to a small voltage bias, tends to form a unique dynamic rotating spin wave state that naturally couples into the dynamics of the magnet. We briefly discuss realistic physical parameters and constraints for observing this interplay between quantum spin Hall and spin-transfer torque physics. Chapter 6 discusses possible mass terms in 3D topological insulators. We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized fractional charge, also taking into account interaction effects for the 2D case. We show that the effects of tunneling are topologically equivalent to a certain deformation or folding of the sample geometry. Our key advance is the realization that the quantum Hall or fractional charge physics can appear in the presence of only a \emph{single} magnet unlike previous proposals which involve magnetic domain walls on the surface or edges of topological insulators respectively. We give illustrative topological folding arguments to prove our results and show that for the 2D case our results are robust even in the presence of interactions

Pathway-divergent coupling of 1,3-enynes with acrylates through cascade cobalt catalysis

Abstract Catalytic cascade transformations of simple starting materials into highly functionalized molecules bearing a stereochemically defined multisubstituted alkene, which are important in medicinal chemistry, natural product synthesis, and material science, are in high demand for organic synthesis. The development of multiple reaction pathways accurately controlled by catalysts derived from different ligands is a critical goal in the field of catalysis. Here we report a cobalt-catalyzed strategy for the direct coupling of inexpensive 1,3-enynes with two molecules of acrylates to construct a high diversity of functionalized 1,3-dienes containing a trisubstituted or tetrasubstituted olefin. Such cascade reactions can proceed through three different pathways initiated by oxidative cyclization to achieve multiple bond formation in high chemo-, regio- and stereoselectivity precisely controlled by ligands, providing a platform for the development of tandem carbon-carbon bond-forming reactions

Re_Trans: Combined Retrieval and Transformer Model for Source Code Summarization

Source code summarization (SCS) is a natural language description of source code functionality. It can help developers understand programs and maintain software efficiently. Retrieval-based methods generate SCS by reorganizing terms selected from source code or use SCS of similar code snippets. Generative methods generate SCS via attentional encoder–decoder architecture. However, a generative method can generate SCS for any code, but sometimes the accuracy is still far from expectation (due to the lack of numerous high-quality training sets). A retrieval-based method is considered to have a higher accurac, but usually fails to generate SCS for a source code in the absence of a similar candidate in the database. In order to effectively combine the advantages of retrieval-based methods and generative methods, we propose a new method: Re_Trans. For a given code, we first utilize the retrieval-based method to obtain its most similar code with regard to sematic and corresponding SCS (S_RM). Then, we input the given code and similar code into the trained discriminator. If the discriminator outputs onr, we take S_RM as the result; otherwise, we utilize the generate model, transformer, to generate the given code’ SCS. Particularly, we use AST-augmented (AbstractSyntax Tree) and code sequence-augmented information to make the source code semantic extraction more complete. Furthermore, we build a new SCS retrieval library through the public dataset. We evaluate our method on a dataset of 2.1 million Java code-comment pairs, and experimental results show improvement over the state-of-the-art (SOTA) benchmarks, which demonstrates the effectiveness and efficiency of our method

High-Performance Magnetic-core Coils for Targeted Rodent Brain Stimulations

Objective and Impact Statement. There is a need to develop rodent coils capable of targeted brain stimulation for treating neuropsychiatric disorders and understanding brain mechanisms. We describe a novel rodent coil design to improve the focality for targeted stimulations in small rodent brains. Introduction. Transcranial magnetic stimulation (TMS) is becoming increasingly important for treating neuropsychiatric disorders and understanding brain mechanisms. Preclinical studies permit invasive manipulations and are essential for the mechanistic understanding of TMS effects and explorations of therapeutic outcomes in disease models. However, existing TMS tools lack focality for targeted stimulations. Notably, there has been limited fundamental research on developing coils capable of focal stimulation at deep brain regions on small animals like rodents. Methods. In this study, ferromagnetic cores are added to a novel angle-tuned coil design to enhance the coil performance regarding penetration depth and focality. Numerical simulations and experimental electric field measurements were conducted to optimize the coil design. Results. The proposed coil system demonstrated a significantly smaller stimulation spot size and enhanced electric field decay rate in comparison to existing coils. Adding the ferromagnetic core reduces the energy requirements up to 60% for rodent brain stimulation. The simulated results are validated with experimental measurements and demonstration of suprathreshold rodent limb excitation through targeted motor cortex activation. Conclusion. The newly developed coils are suitable tools for focal stimulations of the rodent brain due to their smaller stimulation spot size and improved electric field decay rate