Second-order Topological Insulator Research Articles

Stacking model of a three-dimensional second-order topological insulator manifesting quantum anomalous Hall effect

Stacking model of a three-dimensional second-order topological insulator manifesting quantum anomalous Hall effect

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 nano-switches in higher-order topological insulators

We consider multi-terminal transport through a flake of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field. This system has been shown to be a second-order topological insulator, thus exhibiting corner states at its boundaries. The position of the corner states and their decay length can be controlled by the direction of the magnetic field. In the leads we assume that the magnetic field is absent and therefore we have helical one-dimensional propagating states characteristic of the spin-Hall effect. Using a low-energy effective Hamiltonian we show analytically that, in a two-terminal setup, transport can be turned on and off by a rotation of the in-plane magnetic field. Similarly, in a three terminal configuration, the in-plane magnetic field can be used to turn on and off the transmission between neighbouring contacts, thus realising a directional switch. Analytical calculations are supplemented by a numerical finite-difference method. For small values of the Fermi energy and field strength, the analytical results agree exceptionally well with the numerics. The effect of disorder is also addressed in the numerical approach. We find that the switching functionality is remarkably robust to the presence of strong disorder stemming from the topological nature of the states contributing to the electron transport.

Pseudospin-dependent acoustic topological edge and corner states in silica aerogel metamaterialsa).

Fueled by the concepts of topological insulators, analogous topological acoustics offer an alternative approach to manipulate sound. Theoretical proposals for subwavelength acoustic topological insulators are considered to be ideal effective parameters or utilizeing artificial coiling-space metamaterials. However, the corresponding realization using realistic soft metamaterials remains challenging. In this study, we present the design of an acoustic subwavelength second-order topological insulator using nanoscale porous solid material, silica aerogel, which supports pseudospin-dependent topological edge and corner states simultaneously. Through simulations and experiments, we demonstrate that silica aerogel can function as a soft acoustic metamaterial at the subwavelength scale. By embedding silica aerogel in an air matrix to construct a honeycomb lattice, a double Dirac cone is obtained. A topological phase transition is induced by expanding or contracting the supercell, resulting in band inversion. Additionally, we propose topologically robust acoustic transmission along the one-dimensional edge. Furthermore, we discover that the proposed sonic crystal sustains zero-dimensional corner states, which can efficiently confine energy at subwavelength corners. These findings offer potential for the realization of subwavelength topological acoustic devices using realistic soft metamaterials.

Two-dimensional Weyl metal and second-order topological insulator phases in the modified Kane-Mele model

Two-dimensional Weyl metal and second-order topological insulator phases in the modified Kane-Mele model

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets.

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Second‐Order Topological Insulator in Ferromagnetic Monolayer and Antiferromagnetic Bilayer CrSBr

Second‐order topological insulators (SOTIs) in 2D materials have attracted significant research interest. Recent theoretical predictions suggest that SOTIs can be achievable in 2D magnetic systems, especially within ferromagnetic (FM) materials. Yet, the quest for suitable 2D antiferromagnetic (AFM) materials capable of hosting magnetic SOTIs remains a challenge. Herein, utilizing first‐principles calculations and theoretical analysis, 2D CrSBr is proposed, including monolayer and bilayer forms, as a promising candidate for a magnetic high‐order topological insulator. The monolayer exhibits a FM ground state and features quantized fractional corner charge in its spin‐up channel in the absence of spin–orbital coupling (SOC), yielding fully spin‐polarized corner states. Intriguingly, the bilayer form adopts an AFM ground state while retaining the SOTI properties, with quantized corner charge in both spin channels. Remarkably, the SOTI properties in both monolayer and bilayer structures remain robust against the influence of SOC and symmetry‐breaking perturbations. The work not only identifies a tangible material for realizing 2D magnetic SOTIs, encompassing both FM and AFM phases, but also offers a path to explore the distinctive characteristics of SOTIs merged with magnetism.

Multifrequency corner states in acoustic second-order topological insulators

Multifrequency corner states in acoustic second-order topological insulators

Corner states and particle trapping in waterborne acoustic crystals

Higher-order topological insulators exhibit intriguing capacity to confine energy on lower-dimensional boundaries owing to the unique bulk-boundary correspondence. Many potential practical applications of the higher-order states in classical wave systems have been proposed and achieved. In this work, we implement a second-order topological insulator in a waterborne acoustic crystal by drilling and grooving a copper plate based on a two-dimensional Su–Schrieffer–Heeger lattice with different intracell and intercell couplings. The far-field transmission spectrum and near-field pressure field distributions verify the existence of the one-dimensional edge states and zero-dimensional corner states in the bulk bandgap. Due to the highly localized edge and corner states, the polystyrene particles are trapped at the edges and corners by the acoustic gradient force. Our findings provide a good platform to manipulate underwater acoustic wave and may inspire topological acoustic applications.

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks.

Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.

Engineering a non-Hermitian second-order topological insulator state in quasicrystals

Engineering a non-Hermitian second-order topological insulator state in quasicrystals

Second order topology in a band engineered Chern insulator

Haldane model is a celebrated tight binding toy model of a Chern insulator in a 2D honeycomb lattice that exhibits quantized Hall conductance in the absence of an external magnetic field. In our work, we deform the bands of the Haldane model smoothly by varying one of its three nearest neighbour hopping amplitudes (t1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_1$$\\end{document}), while keeping the other two (t) fixed. This breaks the C3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_3$$\\end{document} symmetry of the Hamiltonian, while the Mx∗T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_x*T$$\\end{document} symmetry is preserved. The symmetry breaking causes the Dirac cones to shift from the K and the K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$'$$\\end{document} points in the Brillouin zone (BZ) to an intermediate M point. This is evident from the Berry curvature plots which show a similar shift in the corresponding values as a function of the deformation parameter, namely t1t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{t_1}{t}$$\\end{document}. We observe two different topological phases of which, one is a topological insulator (TI) and the other is a second order topological insulator (SOTI). The Chern number (C) remains perfectly quantized at a value of C=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=1$$\\end{document} for the TI phase and it goes to zero in the SOTI phase. Furthermore, the evolution of the Wannier charge center (WCC) as the band is smoothly deformed shows a jump in the TI phase indicating the presence of conducting edge modes. We also study the SOTI phase and diagonalize the real space Hamiltonian on a rhombic supercell which shows the presence of in-gap zero energy corner modes. The polarization of the system, namely px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document}, are evaluated, along the x and the y directions, respectively. We see that both px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document} are quantized in the SOTI phase owing to the presence of the inversion symmetry of the system. Finally we establish the SOTI phase as an example of a topological phase with zero Berry curvature and provide an analogy with the two dimensional Su–Schrieffer–Heeger model.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su–Schrieffer–Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

Disorder-induced phase transitions in three-dimensional chiral second-order topological insulator

Disorder-induced phase transitions in three-dimensional chiral second-order topological insulator

Tunable valley polarization effect and second-order topological state in monolayer FeClSH.

In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.

Floquet engineering of the orbital Hall effect and valleytronics in two-dimensional topological magnets.

We show that circularly polarized light is a versatile way to manipulate both the orbital Hall effect and band topology in two-dimensional ferromagnets. Employing the hexagonal lattice, we proposed that interactions between light and matter allow for the modulation of the valley polarization effect, and then band inversions, accompanied by the band gap closing and reopening processes, can be achieved subsequently at two valleys. Remarkably, the distribution of orbital angular momentum can be controlled by the band inversions, leading to the Floquet engineering of the orbital Hall effect, as well as the topological phase transition from a second-order topological insulator to a Chern insulator with in-plane magnetization, and then to a normal insulator. Furthermore, first-principles calculations validate the feasibility with the 2H-ScI2 monolayer as a candidate material, paving a technological avenue to bridge the orbitronics and nontrivial topology using Floquet engineering.

Layer-coupled corner states in two-dimensional topological multiferroics.

The structural diversity and controllability in two-dimensional (2D) materials offers an intriguing platform for exploring a wide range of topological phenomena. The layer degree of freedom, as a novel technique for material manipulation, requires further investigation regarding its association with topological states. Here, using first-principles calculations and a tight-binding model, we propose a novel mechanism that couples the second-order topological corner states with the layer degree of freedom. By analyzing the edge states, topological indices, and spectra of nanoflakes, we identify ferromagnetic H'-Co2XF2 (X = C, N) as 2D second-order topological insulators with intrinsic ferroelectricity. Moreover, the topological corner states strongly couple with the layer degree of freedom, and, remarkably, ferroelectricity provides a nonvolatile handle to manipulate the layer-polarized corner states. These findings open an avenue for the manipulation of second-order topological states and establish a bridge between ferroelectricity and nontrivial topology.

A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta2Pd3Te5

The interplay between topology and interaction always plays an important role in condensed matter physics and induces many exotic quantum phases, while rare transition metal layered material (TMLM) has been proved to possess both. Here we report a TMLM Ta2Pd3Te5 has the two-dimensional second-order topology (also a quadrupole topological insulator) with correlated edge states - Luttinger liquid. It is ascribed to the unconventional nature of the mismatch between charge- and atomic- centers induced by a remarkable double-band inversion. This one-dimensional protected edge state preserves the Luttinger liquid behavior with robustness and universality in scale from micro- to macro- size, leading to a significant anisotropic electrical transport through two-dimensional sides of bulk materials. Moreover, the bulk gap can be modulated by the thickness, resulting in an extensive-range phase diagram for Luttinger liquid. These provide an attractive model to study the interaction and quantum phases in correlated topological systems.

Bulk-boundary-transport correspondence of the second-order topological insulators

Bulk-boundary-transport correspondence of the second-order topological insulators

Higher-order topological Anderson insulator on the Sierpiński lattice

Disorder effects on topological materials in integer dimensions have been extensively explored in recent years. However, its influence on topological systems in fractional dimensions remains unclear. Here, we investigate the disorder effects on a fractal system constructed on the Sierpiński lattice in fractional dimensions. The system supports the second-order topological insulator phase characterized by a quantized quadrupole moment and the normal insulator phase. We find that the second-order topological insulator phase on the Sierpiński lattice is robust against weak disorder but suppressed by strong disorder. Most interestingly, we find that disorder can transform the normal insulator phase to the second-order topological insulator phase with an emergent quantized quadrupole moment. Finally, the disorder-induced phase is further confirmed by calculating the energy spectrum and the corresponding probability distributions.