Topological Insulator Research Articles

Corner and edge states in topological Sierpinski Carpet systems

Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel ways. Here we present a theoretical study on localized corner and edge states, emerging from topological phases in Sierpinski Carpet within a $\pi$-flux regime. A topological phase diagram is presented correlating the quadrupole moment with different hopping parameters. Particular localized states are identified following spatial signatures in distinct fractal generations. The specific geometry and scaling properties of the fractal systems can guide the supported topological states types and their associated functionalities. A conductive device is proposed by coupling identical Sierpinski Carpet units providing transport response through projected edge states which carry on the details of the system's topology. Our findings suggest that fractal lattices may also work as alternative routes to tune energy channels in different devices.

Tutorial: From Topology to Hall Effects—Implications of Berry Phase Physics

AbstractThe Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the essential mathematical framework required to grasp its significance. We explore the intrinsic link between the emergence of a non-trivial Berry phase and the presence of topological characteristics in quantum systems, showing the connection between the Berry phase and the band structure as well as the phase’s gauge-invariant nature during cyclic evolutions. The tutorial delves into various topological effects arising from the Berry phase, such as the quantum, anomalous, and spin Hall effects, which exemplify how these quantum phases manifest in observable phenomena. We then extend our discussion to cover the transport properties of topological insulators, elucidating their unique behaviour rooted in the Berry phase physics. This tutorial aims at equipping its readers with a robust understanding of the basic theory underlying the Berry phase and of its pivotal role in the realm of topological quantum phenomena.

FIB-fabrication of superconducting devices based on Bi2Se3 junctions

Recent advances in quantum technologies are highly influencing the current technological scenario. Hybrid devices combining superconductors and topological insulators represent an excellent opportunity to study the topological superconducting phase, which offers interesting features that might have significant implications in the development of quantum sensing and quantum computing. Furthermore, focused ion beam techniques, whose versatility enables to create sophisticated devices with high degree of customization, can enhance the creation of complex devices. Here, we develop a novel approach for creating single-crystal devices that is applied to the fabrication of superconducting devices based on topological insulator Bi2Se3 in a geometry characteristic of a superconducting quantum interference device. Characterization of these devices reveals that superconductivity is induced in our crystal and the supercurrent is modulated by applying an external magnetic field. These results open the way to tailoring the response of hybrid devices that combine superconductors and topological insulators by focused ion beam techniques.

Longitudinal one-dimensional mechanical topological insulator

Abstract We present a study of a longitudinal one-dimensional mechanical topological insulator based on a slinky spring in the Su–Schrieffer–Heeger (SSH) configuration. The system demonstrates key characteristics of topological insulators, including the existence of edge states in the bandgap, exponential decay of amplitude, and a winding number of 1 for topological phases. By manipulating the stiffness of the spring through the placement of masses, we transition between trivial, metallic, and topological phases. Our findings also show that the edge states are robust against perturbations, and we observe a critical phase transition where the coherence length follows a critical exponent of -1, as predicted by theory. This simple mechanical system provides an accessible platform for studying the special properties of topological insulators and opens up new possibilities for exploring topological phenomena in classical systems.

Effects of self-consistent extended Hubbard interactions and spin-orbit couplings on energy bands of semiconductors and topological insulators

Effects of self-consistent extended Hubbard interactions and spin-orbit couplings on energy bands of semiconductors and topological insulators

Refraction of flexural wave in the valley topological interface

Abstract The transport behavior of valley kink states has attracted significant research interest due to its potential prospects in energy harvesting vibration mitigation and elastic wave imaging In this work we extensively investigate the topological refraction in valley elastic topological insulators (TIs) when the topological edge states (TES) transport from the interface termination into the bare plate We show that the refraction pattern (negative or positive refraction) depends on the type of valleys from which the edge state is projected and the refraction angles can be tuned by the Dirac frequency Thus we can realize the conversion of the refracted wave into the evanescent wave resulting in no refraction beams in the bare plate which provides a new perspective for vibration isolation and mitigation We then construct a new layered TI by alternately arranging two unit cells with opposite topological phases The dispersion relation of the layered TI shows a negative band and a positive band in the bulk band gap corresponding to two different edge modes In the edge states the wave energy would transfer toward the negative (positive) direction of the wave vector along the interface when an incident wave couples to this TI resulting in a negative (positive) shift parallel to the interface We selectively achieve negative (positive) refraction by exciting only one desired edge mode In particular the presence of the impedance mismatch between the layered TIs and the bare plate leads to the relatively low energy amplitude of the refracted beam Our research results provide new insights into manipulating the refraction wave in plates and facilitate potential applications in vibration mitigation beam splitting and negative refraction images

Investigation of square-root higher-order topological insulator based on honeycomb-Kagome lattice of graphene plasmonic crystals

Abstract In this paper, a composite lattice of graphene plasmonic crystals consisting of breathing Kagome lattice and honeycomb lattice is constructed. The band structure of the proposed lattice is obtained by tight binding model, where the Hamiltonian demonstrate the square-root nature, and optical first principle calculation. The results from both methods agree well with each other. The square-root higher-order topological insulator in graphene plasmonic crystal is realized by constructing a sandwich structure, where two sets of corner states are observed. The proposed plasmonic structure might provide a new perspective for integrated plasmonic circuits and nano-topological lasers.

Supervised learning of an interacting two-dimensional hardcore boson model of a weak topological insulator using correlation functions

Supervised learning of an interacting two-dimensional hardcore boson model of a weak topological insulator using correlation functions

Robust Majorana bound state in pseudospin domain wall of a two-dimensional topological insulator

Robust Majorana bound state in pseudospin domain wall of a two-dimensional topological insulator

Lithium niobate waveguide-integrated Bi2Te3/graphene heterojunction photodetector.

We demonstrate an on-chip photodetector by integrating a graphene and topological insulator Bi2Te3 heterostructure on a thin-film lithium niobate waveguide. Lithium niobate on insulator (LNOI) waveguides are fabricated by the photolithography-assisted chemical mechanical etching method. The bismuth telluride (Bi2Te3) and graphene heterostructure design provides enhanced photocurrent due to the effective photocarrier generation. The lithium niobate waveguide-integrated Bi2Te3/graphene heterojunction presents a high absorption coefficient of 2.1 dB/µm. The Bi2Te3/graphene heterojunction photodetector exhibits a responsivity of 2.54 mA/W without external bias at a 1.55 µm wavelength, which is enhancement of sevenfold as compared to the pure graphene-based photodetector. The photodetector has a 3 dB bandwidth of over 4.7 GHz. This work provides a potentially viable method for a self-powered, high responsivity, and fast response of the photodetector integrated with the LNOI photonic platform.

Second harmonic generation induced by gate voltage oscillation in few layer MnBi2Te4

Nonlinear charge transport, such as nonreciprocal longitudinal resistance and nonlinear Hall effect, has attracted considerable interest in probing the symmetries and topological properties of new materials. Recent research has revealed significant nonreciprocal longitudinal resistance and nonlinear Hall effect in MnBi2Te4, an intrinsic magnetic topological insulator, induced by the quantum metric dipole. However, the inconsistent response with charge density and conflicting C3z symmetry requirement necessitate a thorough understanding of factors affecting the nonlinear transport measurement. This study uncovers an experimental factor leading to significant nonlinear transport signals in MnBi2Te4, attributed to gate voltage oscillation from the application of large alternating current. Additionally, a methodology is proposed to suppress this effect by individually grounding the voltage electrodes during second-harmonic measurements. The investigation underscores the critical importance of assessing gate voltage oscillation’s impact before determining the intrinsic nature of nonlinear transport in 2D material devices with an electrically connected operative gate electrode.

Interface Dependent Coexistence of Two‐Dimensional Electron and Hole Gases in Mn‐doped InAs/GaSb

AbstractThe interface of common III‐V semiconductors InAs and GaSb can be utilized to realize a two‐dimensional (2D) topological insulator state. The 2D electronic gas at this interface can yield Hall quantization from coexisting electrons and holes. This anomaly is a determining factor in the fundamental origin of the topological state in InAs/GaSb. Here, the coexistence of electrons and holes in InAs/GaSb is tied to the chemical sharpness of the interface. Magnetotransport, in samples of Mn‐doped InAs/GaSb cleaved from wafers grown at a spatially inhomogeneous substrate temperature, is studied. It is reported that the observation of quantum oscillations and a quantized Hall effect whose behavior, exhibiting coexisting electrons and holes, is tuned by this spatial nonuniformity. Through transmission electron microscopy measurements, it is additionally found that samples that host this co‐existence exhibit a chemical intermixing between group III and group V atoms that extends over a larger thickness about the interface. The issue of intermixing at the interface is systematically overlooked in electronic transport studies of topological InAs/GaSb. These findings address this gap in knowledge and shed important light on the origin of the anomalous behavior of quantum oscillations seen in this 2D topological insulator.

Topological phase transitions and flat bands on a square-octagon lattice

We construct a square-octagon lattice model by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-nearest-neighbor (NNN) hoppings, where zero-Chern-number topological insulator (ZCNTI) phases emerge. At 1/4 filling, by tuning the staggered fluxes and NNN hopping potential, this model supports the phase transition from a Chern insulator (CI) with Chern number C = 2 to a ZCNTI phase. At half filling, we observe that staggered magnetic fluxes can induce a higher-order topological insulator (HOTI) state. Interestingly, the ZCNTI appears at 3/4 filling when considering the NN and NNN hoppings in the absence of staggered fluxes, which has been rarely reported in previous work. Contrary to conventional HOTIs, this ZCNTI phase hosts both robust corner states and gapless edge states which can be identified based on the quantized dipole and quadrupole moments. Additionally, a topological flat band (TFB) with flatness ratio about 24 appears. We further investigate ν = 1/2 fractional Chern insulator (FCI) state when hard-core bosons fill into this TFB model.

The incorporation of armchair and zigzag boron nitride nanoribbons in graphene monolayers: An examination of the structural, electronic, and magnetic properties

The opening of an energy gap and generating magnetism in graphene are certainly the most significant and urgent topics in your current research. The majority of proposed applications for it require the ability to modify its electronic structure and induce magnetism in it. Here, using first-principles calculations utilizing the PBE and HSE06 functionals, we examine the structural, energetic, electronic, magnetic, and phonon transport characteristics of armchair graphene and boron nitride nanoribbons (aGNRs and aBNNRs), and zigzag graphene and boron nitride nanoribbons (zGNRs and zBNNRs) with varying widths. We shall emphasize the impact of incorporating aBNNRs and zBNNRs of varying widths into graphene monolayers (GMLs). The findings suggest that zBNNRs are easier to insert into GMLs than aBNNRs. A study of the average formation energies of graphene and boron nitride nanoribbons reveals that BNNRs have a formation energy that is at least twenty times greater than GNRs. We have observed energy gaps that can be classified into three distinct families in aGNRs, aBNNRs, and aBNNRs inserted into GML. In the zGNRs and zBNNRs inserted in GML, depending on the width, different magnetic orderings (antiferromagnetic, ferrimagnetic, and ferromagnetic), and electronic behaviors are observed (metallic, semimetallic, semiconductor, and topological insulator).

Robust topological insulating property in C2X-functionalized III-V monolayers

Two-dimensional topological insulators (TIs) show great potential applications in low-power quantum computing and spintronics due to the spin-polarized gapless edge states. However, the small bandgap limits their room-temperature applications. Based on first-principles calculations, a series of C2X (X = H, F, Cl, Br and I) functionalized III-V monolayers are investigated. The nontrivial bandgaps of GaBi-(C2X)2, InBi-(C2X)2, TlBi-(C2X)2and TlSb-(C2X)2are found to between 0.223 and 0.807 eV. For GaBi-(C2X)2and InBi-(C2X)2, the topological insulating properties originate from thes-px,yband inversion induced by the spin-orbital coupling (SOC) effect. While for TlBi-(C2X)2and TlSb-(C2X)2, the topological insulating properties are attributed to the SOC effect-induced band splitting. The robust topological characteristics are further confirmed by topological invariantsZ2and the test under biaxial strain. Finally, two ideal substrates are predicted to promote the applications of these TIs. These findings indicate that GaBi-(C2X)2, InBi-(C2X)2, TlBi-(C2X)2and TlSb-(C2X)2monolayers are good candidates for the fabrication of spintronic devices.

Manipulating Charge-to-Spin conversion via insertion layer control at the interface of topological insulator and ferromagnet

Strong spin–orbit coupling and highly spin-polarized surface states in topological insulators (TIs) are key parameters that explain their extremely high charge-to-spin conversion (CSC) efficiency at interfaces with ferromagnetic materials (FMs). This study focused on the influence of the insertion layer on the proximity effect occurring in a Co4Fe4B2/Bi2Se3 interface. Various insertion layers, including Au, MgO, and Se, were introduced to modulate the proximity effect from TI to FM and vice versa. X-ray photoelectron spectroscopy and transmission electron microscopy revealed that the Se insertion layer effectively suppresses the formation of an additional Bi layer, reducing intermixing against Co4Fe4B2. Electrical transport properties such as RXX and RXY under a vertical magnetic field show that the Se-inserted structure features the lowest anomalous Hall angle and exhibits a pristine topological surface state, indicating its potential for improving CSC efficiency. The Se-inserted structure exhibits the highest spin Hall angle among various heterostructures, according to results obtained from spin-torque ferromagnetic resonance. These findings highlight the importance of selecting an insertion layer and controlling the interface to optimize the spin-transport properties of TI-based spintronic devices and provide insights into the design of future spin devices.

Topological Edge Spectrum Along Curved Interfaces

Abstract We prove that if the boundary of a topological insulator divides the plane into two regions, each containing arbitrarily large balls, then it acts as a conductor. Conversely, we construct a counterexample to show that topological insulators that fit within strips do not need to admit conducting boundary modes. This constitutes a new setup where the bulk-edge correspondence is violated. Our proof relies on a seemingly paradoxical and underappreciated property of the bulk indices of topological insulators: they are global quantities that can be locally computed.

Composite helical edges from Abelian fractional topological insulators

Composite helical edges from Abelian fractional topological insulators

Bose Metals, from Prediction to Realization.

Bose metals are metals made of Cooper pairs, which form at very low temperatures in superconducting films and Josephson junction arrays as an intermediate phase between superconductivity and superinsulation. We predicted the existence of this 2D metallic phase of bosons in the mid 1990s, showing that they arise due to topological quantum effects. The observation of Bose metals in perfectly regular Josephson junction arrays fully confirms our prediction and rules out alternative models based on disorder. Here, we review the basic mechanism leading to Bose metals. The key points are that the relevant vortices in granular superconductors are core-less, mobile XY vortices which can tunnel through the system due to quantum phase slips, that there is no charge-phase commutation relation preventing such vortices from being simultaneously out of condensate with charges, and that out-of-condensate charges and vortices are subject to topological mutual statistics interactions, a quantum effect that dominates at low temperatures. These repulsive mutual statistics interactions are sufficient to increase the energy of the Cooper pairs and lift them out of condensate. The result is a topological ground state in which charge conduction along edges and vortex movement across them organize themselves so as to generate the observed metallic saturation at low temperatures. This state is known today as a bosonic topological insulator.

Structure-driven phase transitions in paracrystalline topological insulators

Structure-driven phase transitions in paracrystalline topological insulators