Design of wideband vibration-based electromagnetic generator by means of dual-resonator

This paper describes the design of a wideband electromagnetic energy harvester that utilizes a novel dual-resonator method to improve the operational frequency range of the vibration-based generator. The device consists of two separate resonator systems (coil and magnet), which each comply with their respective resonance frequencies. This is because both resonators are designed in such a way that both magnet and coil components will oscillate at an additive phase angle, and hence create greater relative motion between the two dominating resonance frequencies, which realizes the wideband generator. Each resonator system consists of a distinctive cantilever beam, one attached with four magnets and steel keepers, the other attached with a copper coil and stainless steel holder as the free end mass. Both cantilevers are clamped and fitted to a common base that is subjected to a vibration source. Basic analytical models are derived and a numerical model is implemented in MATLAB-Simulink. Electromagnetic, structural modal and static mechanical analysis for the design of the prototype are completed using ANSYS finite element tools. For a 0.8 m s−2 acceleration, the open-loop voltage obtained from the experiment shows a good correlation with those from the simulation. Peak induced voltage is measured to be 259.5Vrms as compared to 240.9Vrms from the simulator at 21.3 Hz, which implies an error range of 7.7%. The results also indicate that there is a maximum of 58.22% improvement in the induced voltage within the intermediate region which occurs at the intersection point between the output response plots of two single resonator generators

Tri-Dirac Surface Modes in Topological Superconductors

We propose a new type of topological surface modes having cubic dispersion in three-dimensional topological superconductors. Lower order dispersions are prohibited by the threefold rotational symmetry and time-reversal symmetry. Cooper pairing in the bulk changes sign under improper rotations, akin to$^{3}$He-B. The surface manifestations are a divergent surface density of states at the Fermi level and isospins that rotate three times as they circle the origin in momentum space. We propose that Heusler alloys with band inversion are candidate materials to harbor the novel topological superconductivity.Comment: Five-page main text plus five-page supplementary materials; three figure

Entanglement Spectrum Classification of CnC_n-invariant Noninteracting Topological Insulators in Two Dimensions

We study the single particle entanglement spectrum in 2D topological insulators which possess $n$-fold rotation symmetry. By defining a series of special choices of subsystems on which the entanglement is calculated, or real space cuts, we find that the number of protected in-gap states for each type of these real space cuts is a quantum number indexing (if any) non-trivial topology in these insulators. We explicitly show the number of protected in-gap states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the number of occupied states that transform according to $m$-th one-dimensional representation of the $C_n$ point group. We find that the entanglement spectrum contains in-gap states pinned in an interval of entanglement eigenvalues $[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show that in a homogeneous system, the $Z^n$ index can be determined through an evaluation of the eigenvalues of point group symmetry operators at all high-symmetry points in the Brillouin zone. When disordered $n$-fold rotationally symmetric systems are considered, we find that the number of protected in-gap states is identical to that in the clean limit as long as the disorder preserves the underlying point group symmetry and does not close the bulk insulating gap.Comment: 14.2 pages for main text, 4.8 pages for Appendices, four figures and two table

Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$, where integer $C$ is called the Chern number, and represents the number of gapless edge modes. Recent experiments demonstrated that chromium doped thin-film (Bi,Sb)$_2$Te$_3$ is a QAH insulator with Chern number $C=\pm1$. Here we theoretically predict that thin-film topological crystalline insulators (TCI) can host various QAH phases, when doped by ferromagnetically ordered dopants. Any Chern number between $\pm4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through proximity effect and (c) the thickness of the thin film. The tunable Chern numbers found in TCI possess significant potential for ultra-low power information processing applications.Comment: References update

New class of topological superconductors protected by magnetic group symmetries

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor In$_x$Sn$_{1-x}$Te.Comment: Accepted version to appear in PRL: 4-page text plus 4-page supplementary materials, two figure

Spinless Topological Insulators without Time-Reversal Symmetry

We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n =3,4 and 6 of the C_{nv} groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups, i.e., not needing time-reversal symmetry. To describe these C_{nv} systems, we introduce the notions of (a) a halved mirror chirality: an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number: the traditional TKNN invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities

Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry

We perform a complete classification of two-band \bk\cdot\mathbf{p} theories at band crossing points in 3D semimetals with $n$-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by $C_{4,6}$-protected double-Weyl nodes with quadratic in-plane (along $k_{x,y}$) dispersion or $C_6$-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr$_2$Se$_4$ and confirm it is a double-Weyl metal protected by $C_4$ symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001]- to the [111]-axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group $S_6$ of that phase. Finally, we discuss experimentally relevant effects including splitting of multi-Weyl nodes by applying $C_n$ breaking strain and the surface Fermi arcs in these new semimetals.Comment: 4+ pages, 2 figures, 1 tabl

Analytical and finite-element study of optimal strain distribution in various beam shapes for energy harvesting applications

Due to the increasing demand for harvesting energy from environmental vibration, for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted great interest from various parties and become one of the most common approaches to convert redundant mechanical energy into electrical energy. As the output voltage produces from a piezoelectric material depends greatly on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beams that have been overseen in most of the prior literature. Both analytical and finite element models are derived and the resultant strain distributions in the beam are computed based on MATLAB solver and ANSYS finite element analysis tools. An optimum geometry for a vibration-based energy harvester system is verified. Lastly, experimental results comparing the power density for a triangular and rectangular piezoelectric beams are also presented to validate the finding of the study and the claim as suggested in the literature is verified

Modular Anomalies in (2+1) and (3+1)-D Edge Theories

The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an anomalous phase arising in the edge theory of a D-dimensional system under modular transformation, or modular anomaly, signals the presence of a (D+1)-D non-trivial bulk. In this work, we discuss the modular transformations of conformal field theories along a (2+1)-D and a (3+1)-D edge. Using both analytical and numerical methods, we show that chiral complex free fermions in (2+1)-D and (3+1)-D are modular invariant. However, we show in (3+1)-D that when the edge theory is coupled to a background U(1) gauge field this results in the presence of a modular anomaly that is the manifestation of a quantum Hall effect in a (4+1)-D bulk. Using the modular anomaly, we find that the edge theory of (4+1)-D insulator with spacetime inversion symmetry(P*T) and fermion number parity symmetry for each spin becomes modular invariant when 8 copies of the edges exist