Electronic Topological Insulators Research Articles

Coupled Electronic and Magnonic Topological States in Two-Dimensional Ferromagnets.

Magnetic materials offer a fertile playground for fundamental physics discovery, with not only electronic but also magnonic topological states intensively explored. However, one natural material with both electronic and magnonic nontrivial topologies is still unknown. Here, we demonstrate the coexistence of first-order topological magnon insulators (TMIs) and electronic second-order topological insulators (SOTIs) in 2D honeycomb ferromagnets, giving rise to the nontrivial corner states being connected by the charge-free magnonic edge states. We show that, with symmetry, the phase factor ± ϕ caused by the next nearest-neighbor Dzyaloshinskii-Moriya interaction breaks the pseudo-spin time-reversal symmetry , which leads to the split of magnon bands, i.e., the emergence of TMIs with a nonzero Chern number of , in experimentally feasible candidates of MoI3, CrSiTe3, and CrGeTe3 monolayers. Moreover, protected by the symmetry, the electronic SOTIs characterized by nontrivial corner states are obtained, bridging the topological aspect of fermions and bosons with a high possibility of innovative applications in spintronics devices.

Topological acoustic tweezer and pseudo-spin states of acoustic topological insulators

Topological protection wave engineering in artificially structured media is at the forefront of metamaterials research. Acoustic analogs of electronic topological insulators have brought a lot of new opportunities for manipulating sound propagation and have attracted the attention of many scholars. A variety of artificial acoustic systems hosting topological edge states have been proposed. However, the pseudo-spin edge states at a boundary have not been clearly and intuitively characterized. In this article, we provide experimental verification of pseudo-spin states by the method of acoustic particle manipulation by using the rotation of the particle to describe the pseudo-spin sound field characteristics at the boundary of the acoustic topological insulator in detail. It indicates the existence of pseudo-spin–orbit coupling effects and pseudo-spin-related acoustic unidirectional transmission even if the defect exists. Furthermore, the pseudo-spin sound field can be used to control the rotation of multiple particles and droplets. This kind of topological acoustic tweezer with defect immunity has great application potential in the fields of biomedicine and materials science.

Kekulé Lattice in Graphdiyne: Coexistence of Phononic and Electronic Second-Order Topological Insulator.

Topological physics has been extensively studied in different kinds of bosonic and Fermionic systems, but the coexistence of topological phonons and electrons in one single material has seldom been reported. Recently, graphdiyne has been proposed as a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, we found that graphdiyne is equivalent to Kekulé lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap and are tunable by the local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in the electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.

In-Plane Magnetization-Induced Corner States in Bismuthene

We theoretically demonstrate that the electronic second-order topological insulator with robust corner states, having a buckled honeycomb lattice, can be realized in bismuthene by inducing in-plane magnetization. Based on the sp 3 Slater–Koster tight-binding model with parameters extracted from first-principles results, we show that spin-helical edge states along zigzag boundaries are gapped out by the in-plane magnetization whereas four robust in-gap electronic corner states at the intersection between two zigzag boundaries arise. By regulating the orientation of in-plane magnetization, we show different position distribution of four corner states with different energies. Nevertheless, it respects some spatial symmetries and thus can protect the higher-order topological phase. Combined with the Kane–Mele model, we discuss the influence of the magnetization orientation on the position distribution of corner states.

Transfer-matrix method of circular polarization light in an axionic photonic insulator

The photonic analog of an axioniclike system (or electronic topological insulator) is called an axionic photonic crystal. These materials are classified by three physical properties: permittivity $\ensuremath{\epsilon}$, permeability $\ensuremath{\mu}$, and the topological parameter $\ensuremath{\theta}$. As a particular case, crystals with periodic $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$ are the so-called photonic crystals. In this paper, we employ a transfer-matrix treatment to study the propagation of light waves in an axionic photonic crystal composed of alternating building layers $A$ and $B$. We present numerical results for the photonic band structure as a function of the ratio between permittivities $R={\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{A}$, layer thicknesses $X={d}_{B}/{d}_{A}$, and topological parameters $\ensuremath{\delta}={\ensuremath{\pi}}^{2}{({\ensuremath{\theta}}_{A}\ensuremath{-}{\ensuremath{\theta}}_{B})}^{2}/{\ensuremath{\alpha}}^{2}$. Our numerical results reveal that the band-gap features (width, center position, upper and lower frequencies) depend on the three parameters $\ensuremath{\epsilon}$, $\ensuremath{\mu}$, and $\ensuremath{\theta}$, but with the dependence on $\ensuremath{\theta}$ being stronger. In particular, as far as the band-gap width is concerned, we find that $X$ and $R$ work against each other; that is, as $X$ increases, $R$ must decreases for a wide band-gap emergence and vice versa. More interesting, however, are the results for the topological parameter $\ensuremath{\theta}$. We show that the presence of $\ensuremath{\theta}$ produces a photonic band gap (PBG) which depends only on the $\ensuremath{\delta}$ term. The widening of this PBG is slightly asymmetrical and monotonic as a function of $\ensuremath{\delta}$. It was also found that $\ensuremath{\delta}$ has no influence on the center position of the PBG. Our results open possibilities for technological applications of axionic photonic crystals with regard to the controlling and confinement of the propagation of light.

Magnonic topological insulator realized in 2D magnetic skyrmion crystals

With the concept of topological order of electronic states in crystals being proposed, the pursuit of topological phases in various systems has become an important subject of modern physical science. The existence of antisymmetric Dzyaloshinskii–Moriya interaction caused by spin–orbit coupling in magnetic systems leads to the non-reciprocal propagation of magnons, which is a key factor to realize the magnonic analog of an electronic topological insulator (TI). Here, a two-dimensional magnetic skyrmion crystal (SkX) is introduced as a platform for realizing magnonic TI. It is numerically demonstrated that nonchiral and chiral edge states could exist in different magnonic bandgaps. The nonchiral edge magnons can propagate to both directions simultaneously along the boundary of the SkX with different wavelengths and group velocities. By contrast, chiral edge magnons are topologically protected, resulting in the unidirectional propagation along the boundaries and the robustness against defects or disorders. Furthermore, the chirality and the presence of edge magnons can be manipulated by the polarity of skyrmions and the width of the second magnonic bandgap via the magnetic field. Our findings could provide a skyrmionic paradigm for investigating topological magnonics and even quantum magnonics.

Berry bands and pseudo-spin of topological photonic phases

Realising photonic analogues of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionise the performance of photonic devices. Here we show that new symmetry protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The "Berry bands" span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in $\mathrm{C}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known case of Wu & Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently discovered fragilely topological crystal, and show that both crystals belong to the same $\mathrm{C}_2\mathcal{T}$-protected $\mathbb{Z}_2$ topological phase. This work helps unite theory and numerics, and is useful in defining and identifying new symmetry-protected phases in photonics and electronics.

PHELIX – A new soft X-ray spectroscopy beamline at SOLARIS synchrotron

PHELIX is a new beamline at National Synchrotron Radiation Centre SOLARIS in Kraków using soft X-rays. The source of radiation is an Elliptically Polarizing Undulator APPLE II type with permanent magnets producing a variable polarization of light. The maximum size of the excited area on the sample will be smaller than 100 µm × 100 µm with the resolving power (RP) of at least 10000 over the entire energy range (available range 50–1500 eV) and for all polarizations. The PHELIX end-station enables a wide range of spectroscopic methods including angle integrated and angle resolved photoemission, spin resolved photoemission and x-ray absorption studies under UHV conditions. The VLEED spin detector allows to determine all three components of photoelectron spin. The beamline is perfectly suited for investigations of new electronic materials, topological insulators, thin films and multilayers systems, surface of bulk compounds, surface magnetism, spin polarized surface states, biomaterials, etc.

Probing bulk topological invariants using leaky photonic lattices

Topological invariants characterizing filled Bloch bands underpin electronic topological insulators and analogous artificial lattices for Bose–Einstein condensates, photonics and acoustic waves. In bosonic systems, there is no Fermi exclusion principle to enforce uniform band filling, which makes measuring their bulk topological invariants challenging. Here we show how to achieve the controllable filling of bosonic bands using leaky photonic lattices. Leaky photonic lattices host transitions between bound and radiative modes at a critical energy, which plays a role analogous to the electronic Fermi level. Tuning this effective Fermi level into a bandgap results in the disorder-robust dynamical quantization of bulk topological invariants such as the Chern number. Our findings establish leaky lattices as a highly flexible platform for exploring topological and non-Hermitian wave physics. Topological materials are characterized by the topological invariants of filled bands, which cannot be used for bosonic systems. Instead, their topological invariants can be found via the transition from bound to leaky modes in photonic lattices.

Non-Hermiticity and topological invariants of magnon Bogoliubov–de Gennes systems

Abstract Since the theoretical prediction and experimental observation of the magnon thermal Hall effect, a variety of novel phenomena that may occur in magnonic systems have been proposed. We review recent advances in the study of topological phases of magnon Bogoliubov–de Gennes (BdG) systems. After giving an overview of previous works on electronic topological insulators and the magnon thermal Hall effect, we provide the necessary background for bosonic BdG systems, with particular emphasis on their non-Hermiticity arising from the diagonalization of the BdG Hamiltonian. We then introduce definitions of $$ \mathbb{Z}_2 $$ topological invariants for bosonic systems with pseudo-time-reversal symmetry, which ensures the existence of bosonic counterparts of “Kramers pairs.” Because of the intrinsic non-Hermiticity of bosonic BdG systems, these topological invariants have to be defined in terms of the bosonic Berry connection and curvature. We then introduce theoretical models that can be thought of as magnonic analogs of two- and three-dimensional topological insulators in class AII. We demonstrate analytically and numerically that the $$ \mathbb{Z}_2 $$ topological invariants precisely characterize the presence of gapless edge/surface states. We also predict that bilayer CrI$$_3$$ with a particular stacking would be an ideal candidate for the realization of a two-dimensional magnon system characterized by a nontrivial $$ \mathbb{Z}_2 $$ topological invariant. For three-dimensional topological magnon systems, the magnon thermal Hall effect is expected to occur when a magnetic field is applied to the surface.

Hybridization effect on the x-ray absorption spectra for actinide materials: Application to PuB4

Studying the local moment and 5$f$-electron occupations sheds insight into the electronic behavior in actinide materials. X-ray absorption spectroscopy (XAS) has been a powerful tool to reveal the valence electronic structure when assisted with theoretical calculations. However, the analysis currently taken in the community on the branching ratio of the XAS spectra generally does not account for the hybridization effects between local $f$-orbitals and conduction states. In this paper, we discuss an approach which employs the DFT+Gutzwiller rotationally-invariant slave boson (DFT+GRISB) method to obtain a local Hamiltonian for the single-impurity Anderson model (SIAM), and calculates the XAS spectra by the exact diagonalization (ED) method. A customized numerical routine was implemented for the ED XAS part of the calculation. By applying this technique to the recently discovered 5$f$-electron topological Kondo insulator PuB$_4$, we determined the signature of 5$f$-electronic correlation effects in the theoretical X-ray spectra. We found that the Pu 5$f$-6$d$ hybridization effect provides an extra channel to mix the $j=5/2$ and $7/2$ orbitals in the 5$f$ valence. As a consequence, the resulting electron occupation number and spin-orbit coupling strength deviate from the intermediate coupling regime.

Pseudospin induced topological corner state at intersecting sonic lattices

Inspired by the discoveries of electronic topological phases and topological insulators, topologically protected boundary states in classical wave-based systems have attracted considerable interest in the last decade. Most recently, acoustic higher-order topological insulators and Kekul\'e-distorted sonic lattices have been proposed to support topological corner states and zero-dimensional bound states. Here, we demonstrate a domain wall induced topological corner state that is bound at the crossing point among finite acoustic graphenelike crystals. The approach is based on designing multipolar pseudospin resonances, which give rise to topologically trivial and nontrivial transitions across the domain walls that flank this unusual corner excitation toward the crossing point. By deliberately adding a substantial amount of defects into the cavities of the sonic lattice, we find that the pseudospin induced topological corner state remains entirely unaffected and pinned spectrally to the complete audible band gap. Our findings may thus have the potential to broaden the possibilities for sound confinement and focusing.

Robust Hot Electron and Multiple Topological Insulator States in PtBi2.

A two-dimensional topological insulator features (only) one bulk gap with nontrivial topology, which protects one-dimensional boundary states at the Fermi level. We find a quantum phase of matter beyond this category: a multiple topological insulator. It possesses a ladder of topological gaps; each gap protects a robust edge state. We prove a monolayer of van der Waals material PtBi2 as a two-dimensional multiple topological insulator. By means of scanning tunneling spectroscopy, we directly visualize the one-dimensional hot electron (and hole) channels with nanometer size on the samples. Furthermore, we confirm the topological protection of these channels by directly demonstrating their robustness to variations of crystal orientation, edge geometry, and sample temperature. The discovered topological hot electron materials may be applied as efficient photocatalysts in the future.

Robust zero-energy modes in an electronic higher-order topological insulator.

Quantum simulators are essential tools for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices have led the field so far, but the basis for electronic quantum simulators is now being developed. Here, we experimentally realize an electronic higher-order topological insulator (HOTI). We create a breathing kagome lattice by manipulating carbon monoxide molecules on a Cu(111) surface using a scanning tunnelling microscope. We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, but is absent in the trivial one. Different from conventional topological insulators, the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our versatile approach to designing artificial lattices holds promise for revealing unexpected quantum phases of matter.

Twist-projected two-dimensional acoustic topological insulators

Acoustic analogs of electronic or photonic topological insulators provide unique approaches to manipulate sound wave propagation. Inspired by twist-induced topological photonic insulators, here we propose a type of two-dimensional acoustic topological insulator (TI) via projecting a section of a three-dimensional twisting structure to a plane, assembling the projected meta-atoms into metamolecules, and arranging the metamolecules into unit cells to form a honeycomb lattice. It follows that in this acoustic TI, topological phases mimic pseudospin-up and pseudospin-down states, and the pseudospin-orbital couplings are tuned via changing the rotation angles of the meta-atoms, which eventually leads to band inversion. By calculating acoustic band structures, pressure field distributions, and spin Chern numbers of bands, we verify that the topological phase transition occurs around the double Dirac cone and present the topological phase diagram as a function of the rotation angle of the meta-atoms. Once the coupling between adjacent metamolecules is sufficiently strong, mode inversion of topological states emerges. Furthermore, we numerically demonstrate the existence of topologically protected edge states. It is shown that robust pseudospin-dependent one-way transmission is immune to defects at the edge of topological distinct regions, which can be applied to acoustic wave transmissions and communications. Our approach in acoustic systems provides a strategy to explore abundant topological states in two-dimensional systems.

Phononic topological insulators based on six-petal holey silicon structures

Since the discovery of the Quantum Spin Hall Effect, electronic and photonic topological insulators have made substantial progress, but phononic topological insulators in solids have received relatively little attention due to challenges in realizing topological states without spin-like degrees of freedom and with transverse phonon polarizations. Here we present a holey silicon-based topological insulator design, in which simple geometric control enables topologically protected in-plane elastic wave propagation up to GHz ranges with a submicron periodicity. By integrating a hexagonal lattice of six small holes with one central large hole and by creating a hexagonal lattice by themselves, our design induces zone folding to form a double Dirac cone. Based on the hole dimensions, breaking the discrete translational symmetry allows the six-petal holey silicon to achieve the topological phase transition, yielding two topologically distinct phononic crystals. Our numerical simulations confirm inverted band structures and demonstrate backscattering-immune elastic wave transmissions through defects including a cavity, a disorder, and sharp bends. Our design also offers robustness against geometric errors and potential fabrication issues, which shows up to 90% transmission of elastic waves even with 6% under-sized or 11% over-sized holes. These findings provide a detailed understanding of the relationship between geometry and topological properties and pave the way for developing future phononic circuits.

Topological Acoustic Delay Line

Acoustic analogues of electronic topological insulators allow a wealth of opportunities for manipulating sound with unconventional acoustic edge modes that are immune to backscattering. However, acoustic devices based on topological edge states still lag, due to a lack of tunability and adaptability to functional needs. This study proposes a path to remote control and structural improvement, to achieve broadband, reconfigurable topological systems. In particular, it takes advantage of reflection-free sound propagation to engineer robust phase-delay detours. This approach could be used in various functions, including signal buffering and pulse processing.

Photoinduced Topological Phase Transitions in Topological Magnon Insulators

Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1–3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.

Topological Phases Protected by Point Group Symmetry

We consider symmetry protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry, and can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, that can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimension. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with $Z_2^P$ (reflection) symmetry, electronic topological crystalline insulators (TCIs) with ${\rm U}(1) \times {Z}_2^P$ symmetry, and bosonic pgSPT phases with $C_{2v}$ symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs we find a $Z_8 \times Z_2$ classification, where the $Z_8$ corresponds to known states obtained from non-interacting electrons, and the $Z_2$ corresponds to a "strongly correlated" TCI that requires strong interactions in the bulk. Our approach may also point the way toward a general theory of symmetry enriched topological (SET) phases with crystalline point group symmetry.