Topological Band Structure Research Articles

Influence of Magnetic and Electric Fields on Universal Conductance Fluctuations in Thin Films of the Dirac Semimetal Cd3As2.

Time-reversal invariance (TRS) and inversion symmetry (IS) are responsible for the topological band structure in Dirac semimetals (DSMs). These symmetries can be broken by applying an external magnetic or electric field, resulting in fundamental changes to the ground state Hamiltonian and a topological phase transition. We probe these changes using universal conductance fluctuations (UCF) in the prototypical DSM, Cd3As2. With increasing magnetic field, the magnitude of the UCF decreases by a factor of , in agreement with numerical calculations of the effect of broken TRS. In contrast, the magnitude of the UCF increases monotonically when the chemical potential is gated away from the charge neutrality point. We attribute this to Fermi surface anisotropy rather than broken IS. The concurrence between experimental data and theory provides unequivocal evidence that UCF are the dominant source of fluctuations and offers a general methodology for probing broken-symmetry effects in topological quantum materials.

A symmetry-protected exceptional ring in a photonic crystal with negative index media

Abstract Non-Hermitian topological band structures such as symmetry-protected exceptional rings (SPERs) can emerge for systems described by the generalized eigenvalue problem (GEVP) with Hermitian matrices. In this paper, we numerically analyze a photonic crystal with negative index media, which is described by the GEVP with Hermitian matrices. Our analysis using COMSOL Multiphysics® demonstrates that a SPER emerges for photonic crystals composed of split-ring resonators and metal-wire structures. We expect that the above SPER can be observed in experiments as it emerges at a finite frequency.

Identifying and Constructing Complex Magnon Band Topology.

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Moiré modulation of lattice strains in PdTe2 quantum Films

We report the epitaxial growth of PdTe2 ultrathin films on a topological insulator Bi2Se3. A prominent moiré pattern was observed in scanning tunneling microscope measurements. The moiré periodicity increases as film thickness decreases, indicating a lattice expansion of epitaxial PdTe2 thin films at lower thicknesses. In addition, our simulations based on a multilayer relaxation technique reveal uniaxial lattice strains at the edge of PdTe2 domains, and anisotropic strain distributions throughout the moiré supercell with a net change in lattice strain up to ∼2.9%. Our density functional theory calculations show that this strain effect leads to a narrowing of the band gap at Γ point near the Fermi level. Under a strain of ∼2.8%, the band gap at Γ closes completely. Further increasing the lattice strain makes the band gap reopen and the order of conduction band and valence bands inverted in energy. The experimental and theoretical results shed light on a method for constructing quantum grids of topological band structure under the modulation of moiré potentials.

Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence

We predict and examine various topological states on a two-dimensional (2D) triangular kagome lattice (TKL) using the tight-binding (TB) models and theory of topological quantum chemistry (TQC). Firstly, on the basis of TQC, we diagnose band structures with fragile topology and calculate Wilson-loop spectra and Hofstadter butterfly spectra to confirm their non-trivial nature. Secondly, we examine the bulk-boundary correspondence and find that an obstructed-atomic-limit (OAL) insulator hosts fractional corner states without being accompanied by fragile topological band structures, which implies that the presence of OALs and corner states is not a sufficient condition to fragile topology. Last but not least, we predict a topological phase transition from a second-order topological phase to a first-order topological phase that can be realized in the TKL under the action of a magnetic field.

Bulk and surface electronic structure of NiBi3

We present a high-resolution, angle-resolved photoemission spectroscopy study of the normal electronic state of the superconducting ${\mathrm{NiBi}}_{3}$. Our experimental results show a complex Fermi surface structure with many sheets along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ and $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}Y$ directions of the Brillouin zone. The band structure presents a topological surface state (TSS) at the high symmetry $\mathrm{\ensuremath{\Gamma}}$ point with a surface Dirac point at the energy $\ensuremath{-}0.185$ eV. The Dirac-like cone presents a linear dispersion along ${\mathrm{k}}_{x}$ while it presents saddle-like states along ${\mathrm{k}}_{y}$ located in the vicinity of the surface Dirac point. Our results are in good agreement with results of density functional theory band structure calculations. We also discuss the topological band structure of the ${\mathrm{NiBi}}_{3}$ compound.

Narrowband, Angle-Tunable, Helicity-Dependent Terahertz Emission from Nanowires of the Topological Dirac Semimetal Cd3As2.

All-optical control of terahertz pulses is essential for the development of optoelectronic devices for next-generation quantum technologies. Despite substantial research in THz generation methods, polarization control remains difficult. Here, we demonstrate that by exploiting band structure topology, both helicity-dependent and helicity-independent THz emission can be generated from nanowires of the topological Dirac semimetal Cd3As2. We show that narrowband THz pulses can be generated at oblique incidence by driving the system with optical (1.55 eV) pulses with circular polarization. Varying the incident angle also provides control of the peak emission frequency, with peak frequencies spanning 0.21-1.40 THz as the angle is tuned from 15 to 45°. We therefore present Cd3As2 nanowires as a promising novel material platform for controllable terahertz emission.

Rigorous index theory for one-dimensional interacting topological insulators

We present a rigorous but elementary index theory for a class of one-dimensional systems of interacting (and possibly disordered) fermions with U(1)⋊Z2 symmetry defined on the infinite chain. The class includes the Su–Schrieffer–Heeger (SSH) model [Su et al., “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698 (1979); Su et al., “Soliton excitations in polyacetylene,” Phys. Rev. B 22, 2099 (1983); and Asbóth et al., A Short Course on Topological Insulators: Band-Structure Topology and Edge States in One and Two Dimensions, Lecture Notes in Physics (Springer, 2016)] as a special case. For any locally unique gapped (fixed-charge) ground state of a model in the class, we define a Z2 index in terms of the sign of the expectation value of the local twist operator. We prove that the index is topological in the sense that it is invariant under continuous modification of models in the class with a locally unique (fixed-charge) gapped ground state. This establishes that any path of models in the class that connects the two extreme cases of the SSH model must go through a phase transition. Our rigorous Z2 classification is believed to be optimal for the class of models considered here. We also show an interesting duality of the index and prove that any topologically nontrivial model in the class has a gapless edge excitation above the ground state when defined on the half-infinite chain. The results extend to other classes of models, including the extended Hubbard model. Our strategy to focus on the expectation value of local unitary operators makes the theory intuitive and conceptually simple. This paper also contains a careful discussion about the notion of unique gapped ground states of a particle system on the infinite chain. (There are two lecture videos in which the main results of this paper are discussed [H. Tasaki, “Rigorous index theory for one-dimensional interacting topological insulators: A brief introduction,” online lecture (21:41), November, 2021, seehttps://www.gakushuin.ac.jp/~881791/OL/#Index1DTI2021S and https://youtu.be/ypGVb3eYrpg and H. Tasaki, “Rigorous index theory for one-dimensional interacting topological insulators: With a pedagogical introduction to the topological phase transition in the SSH model,” online lecture (49:07), November, 2021, see https://www.gakushuin.ac.jp/~881791/OL/#Index1DTI2021L and https://youtu.be/yxZYOevV2Y].

Edge and corner superconductivity in a two-dimensional topological model

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a nontrivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0\ensuremath{\le}r\ensuremath{\le}1$, the inhomogeneous superconducting phases induced by an attractive-$U$ Hubbard interaction are studied using mean-field theory. We show, analytically and by numerical diagonalization, that in lattices with open boundaries, phases with enhanced superconducting order on the corners or the edges can appear, depending on the filling. For finite samples at half filling, the corner site superconducting transition temperature can be much larger than that of the bulk. A novel proximity effect thus arises for ${T}_{c,\mathrm{bulk}}<T<{T}_{c,\mathrm{corner}}$, in which the corner site creates a nonzero tail of the superconducting order in the bulk. We show that such tails should be observable for a range of $r$ and $U$ values.

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

Prediction of topological phases in metastable ferromagnetic MPX3 monolayers

Density functional theory calculations are carried out to study the electronic and topological properties of $M$P$X_3$ ($M$ = Mn, Fe, Co, Ni, and $X$ = S, Se) monolayers in the ferromagnetic (FM) metastable magnetic state. We find that FM MnPSe$_3$ monolayers host topological semimetal signatures that are gapped out when spin-orbit coupling (SOC) is included. These findings are supported by explicit calculations of the Berry curvature and the Chern number. The choice of the Hubbard-$U$ parameter to describe the $d$-electrons is thoroughly discussed, as well as the influence of using a hybrid-functional approach. The presence of band inversions and the associated topological features are found to be formalism-dependent. Nevertheless, routes to achieve the topological phase via the application of external biaxial strain are demonstrated. Within the hybrid-functional picture, topological band structures are recovered under a pressure of 15% (17 GPa). The present work provides a potential avenue for uncovering new topological phases in metastable ferromagnetic phases.

Relationship between two-particle topology and fractional Chern insulator

Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\ensuremath{\nu}=1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

Many-body Aharonov-Bohm caging in a lattice of rings

We study a system of a few ultracold bosons loaded into the states with orbital angular momentum $l=1$ of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers $+l$ and $-l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\phi$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\pi$-flux through the plaquettes. We find non-trivial topological band structures and many-body Aharonov-Bohm caging in the $N$-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\phi$ is introduced at an arbitrary lattice periodicity $\Gamma$. For $\Gamma>2$, the $\pi$-flux becomes non-uniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.

Polaritonic Chern Insulators in Monolayer Semiconductors.

Systems with strong light-matter interaction open up new avenues for studying topological phases of matter. Examples include exciton polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave approximation. Here we identify polaritonic Chern insulators by coupling valley excitons in transition metal dichalcogenides to photonic Bloch modes in a dielectric photonic crystal slab. We show that polaritonic Dirac points, which are markers for topological phase transition points, can be constructed from the collective coupling between valley excitons and photonic Dirac cones in the presence of both time-reversal and inversion symmetries. Lifting exciton valley degeneracy by breaking time-reversal symmetry leads to gapped polaritonic bands with nonzero Chern numbers. Through numerical simulations, we predict polaritonic chiral edge states residing inside the topological gaps. Our Letter paves the way for the further study of strong exciton-photon interaction in nanophotonic structures and for exploring polaritonic topological phases and their practical applications in polaritonic devices.

Scaling analysis of anomalous Hall resistivity and magnetoresistance in the quasi-two-dimensional ferromagnet Fe3GeTe2

${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ is a two-dimensional van der Waals bonded layered compound that shows high-temperature itinerant ferromagnetism. We study aspects of the scattering mechanism in the single crystal of high-${T}_{\text{C}}\phantom{\rule{4pt}{0ex}}{\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ via resistivity, magnetotransport, and Hall effect measurements. The quadratic temperature dependence of electrical resistivity below the ${T}_{\text{C}}$ (210 K) points towards the dominance of electron-magnon scattering. A nonsaturating positive magnetoresistance (MR) is observed at low temperatures when the magnetic field is applied parallel to the sample plane. The linear negative MR at high fields for $T<{T}_{\text{C}}$ corroborates to the suppression in the magnon population due to the damping of spin waves. In the high-temperature regime ($T>{T}_{\text{C}}$), MR can be described by the scattering from spin fluctuations using the Khosla and Fischer model. Isothermal Hall resistivity curves unveil the presence of anomalous Hall resistivity. The correlation between magnetoresistance and side jump mechanism further reveals that the electron-magnon scattering is responsible for the side jump contribution to the anomalous Hall effect. Our results provide a clear understanding of the role of electron-magnon scattering on the temperature-driven evolution of the anomalous Hall effect that rules out its origin to be the topological band structure.

Topological magnons on the triangular kagome lattice

We present the topology of magnons on the triangular kagome lattice (TKL) by calculating its Berry curvature, Chern number, and edge states. In addition to the ferromagnetic state, the TKL hosts ferrimagnetic ground state as its two sublattices can couple with each other either ferromagnetically or antiferromagnetically. Using Holstein-Primakoff (HP) boson theory and Green's function approach, we find that the TKL has a rich topological band structure with added high Chern numbers compared with the kagome and honeycomb lattices. The magnon edge current allows a convenient calculation of thermal Hall coefficients and the orbital angular momentum gives correlation to the Einstein--de Haas effect. We apply the calculations to the TKL and derive the topological gyromagnetic ratio showing a nonzero Einstein--de Haas effect in the zero-temperature limit. Our results render the TKL as a potential platform for quantum magnonics applications including high-precision mechanical sensors and information transmission.

Research progress of novel quantum states and charge-spin interconversion in transition metal oxides

For efficient storage and processing of massive data in the information technology era, spintronic device attracts tremendous attention due to its low power consumption and non-volatile feature. Spin source material, which can efficiently generates spin current, is an important constituent of novel spin-orbit torque device. The efficiency of spin current generation in spin source material directly determines the performances of various spintronic devices. In the past two decades, great progress has been made in exploring high-efficient spin source material systems and understanding the relevant physical mechanisms. A wide variety of materials are explored, ranging from traditional heavy metals and semiconductors to topological insulators and two-dimensional (2D) materials. Recently, the material family of transition metal oxides attracts tremendous attention due to its efficient and highly tunable charge-spin conversion intimately related to its emerging novel quantum states and electronic structure. The mechanism of charge-spin conversion generally has two contributions: the bulk spin Hall effect and the spin-momentum locked interface with inversion symmetry breaking. Novel electronic structures such as topological band structures and spin-momentum locked surface states can realize efficient charge-spin conversion. For example, the Weyl points in SrRuO<sub>3</sub> and the topological Dirac nodal line in SrIrO<sub>3</sub> are predicted to give rise to a large Berry curvature and corresponding spin Hall conductance; the topological surface states can generate spin accumulation due to spin-momentum locking; the Rashba states at the oxide interface such as the 2D electron gas in SrTiO<sub>3</sub> and KTaO<sub>3</sub> can generate spin current by Rashba-Edelstein effect. Furthermore, the entanglement of various degrees of freedom, including spin, charge, lattice and orbit in transition metal oxides lead to the electronic structure being highly tunable by various methods including gate voltage, substrate constraint, thickness, interface engineering, etc. Therefore, charge-spin conversion in transition metal oxides is of great significance for both modulating of novel electronic structure in fundamental research and exploring its promising potential in future spintronic devices. In this review, we focus on introducing aspects of exotic electronic structures, spin transport mechanism, charge-spin interconversion characterization, efficiency and manipulation in transition metal oxides, and giving a prospect on the future development trend.

Progress of Two-Dimensional Magnetic Materials for Spin Orbit Torque

The rapid development of information technology has put forward higher requirements for the performance of information processing and storage devices. At the same time, with the continuous reduction of device size, traditional semiconductor devices based on electron charge properties face the problems and challenges of thermal dissipation and quantum size effect, and semiconductor technology has entered the post-molar era. Unlike traditional charge-based electronic devices, spin-based non-volatile Spintronic devices not only have high integrated density, read and write speed and read and write times, but also can effectively avoid heat dissipation, establishing a new technical platform for the development of information storage, processing and communication. In recent years, two-dimensional materials have attracted a lot of attention due to their unique band structure and rich physical properties. Two-dimensional magnetic materials have shown great research and application potential in the field of Spintronics. Compared to traditional block materials, the atomic thickness, ultra-clean interface and flexible stacking of two-dimensional materials provide great opportunities for exploring novel physical effects and ultra-low-power devices. At the same time, with the rise of topological materials (TMs), their topological protected band structures, diversified crystal structures and symmetries, strong spin-orbit coupling and adjustable electrical conductivity provide an ideal physical research platform for spintronics research. In this paper, we first introduce the common methods of preparing two-dimensional materials, then focus on the research progress of two-dimensional magnetic materials in the field of spin-orbit electronics, and finally look forward to the research challenges in this field. In the future, with continuous in-depth research on the preparation, physical properties and device applications of two-dimensional magnetic materials, two-dimensional magnetic materials will show more extensive research prospects and application value in the field of spintronics. Two-dimensional magnetic materials will provide more material systems for spintronics development.

Research progress of spin orbit torque of two-dimensional magnetic materials

The rapid development of information technology has put forward higher requirements for the performance of information processing and storage devices. At the same time, with the continuous reduction of device size, traditional semiconductor devices based on electron charge properties face the problems and challenges of thermal dissipation and quantum size effect, and semiconductor technology has entered the post-molar era. Unlike traditional charge-based electronic devices, spin-based non-volatile spintronic devices not only have high integrated density, read and write speed and read and write time, but also can effectively avoid heat dissipation, establishing a new technical platform for developing the information storage, processing and communication. In recent years, two-dimensional materials have attracted a lot of attention due to their unique band structures and rich physical properties. Two-dimensional magnetic materials have shown great research and application potential in the field of spintronics. Compared with traditional block materials, the two-dimensional materials can provide great opportunities for exploring novel physical effects and ultra-low-power devices due to their atomic thickness, ultra-clean interface and flexible stacking. At the same time, with the rise of topological materials (TMs), their topological protected band structures, diversified crystal structures and symmetries, strong spin-orbit coupling and adjustable electrical conductivity provide an ideal physical research platform for studying spintronics. In this paper, we first introduce the common methods of preparing two-dimensional materials, then focus on the research progress of two-dimensional magnetic materials in the field of spin-orbit electronics, and finally look forward to the research challenges in this field. In the future, with continuous in-depth research on the preparation, physical properties and device applications of two-dimensional magnetic materials, two-dimensional magnetic materials will show more extensive research prospects and application value in the field of spintronics. Two-dimensional magnetic materials will provide more material systems for spintronics development.

Half-Heusler d0-d gapless semiconductors as strong Z2 topological insulators

The discovery of non-trivial topological materials has attracted a lot of attention in the condensed matter physics. In the following we investigate the mechanical stability, electronic, and topological properties of XAuZ half-Heusler compounds (X=K, Cs; Z=S, Se, Te) using the WIEN2K full-potential electronic structure package, Wannier90, and WannierTools code. It is found that except KAuTe the other compounds are metastable in half-Heusler structure. In addition, the structural phase transition under pressure between stable and metastable phase has been investigated. The band structure without spin–orbit coupling (SOC) indicates a band-inversion and direct gapless semiconducting behavior for all compounds. The SOC effect creates a meaningful band gap in the β-phase compounds KAuS, KAuSe, and CsAuS, thus converting them to topological insulators. The Z2 topological quantum numbers of these compounds are found to be (1; 0 0 0). The Z2 numbers and the surface states spectrum indicate that these compounds are strong topological insulators. The application of modest uniaxial strain is shown to open a gap in γ-phase compounds, and turn CsAuSe and CsAuTe into their topological insulating states. Hence, true metastability together with topology of band structure are promising indicators for potential application of the above compounds as topological spintronic materials, which together with earlier findings of spin-gapless behavior in other d0−d half-Heusler alloys goes to show that these compounds are indeed multifaceted materials for spin-based electronics of the future.