Topological Phase Research Articles

Tuning chiral edge state and spin-filtering in irradiated silicene nanoribbons based on side potentials

Topological edge states are critical for developing low-loss devices, making it essential to understand their properties. This study examines the influence of side potentials on the topological edge states in irradiated zigzag silicene nanoribbons. The potentials consist of three external fields, which collectively facilitate the emergence of modified chiral edge modes and spin-valley-related chiral edge states. The mechanism involves shifting the spin-polarized edge states outside the range of the Fermi level with the side potentials, thereby inducing intriguing topological edge states. Additionally, we propose a quasi-bulk state characterized by exponential decay that differs from conventional bulk modes. Based on these modified edge states, a tunable spin filter utilizing side potentials is proposed. We believe that these findings are essential for future developments in spintronic device design.

Prediction of dual quantum spin Hall insulator in NbIrTe4 monolayer

Abstract Dual quantum spin Hall insulator (QSHI) is a newly discovered topological state in the 2D material TaIrTe4, exhibiting both a traditional Z 2 band gap at the charge neutrality point and a Van Hove singularity (VHS) induced correlated Z 2 band gap with weak doping. Inspired by the recent progress in theoretical understanding and experimental measurements, we predicted a promising dual QSHI in the counterpart material of the NbIrTe4 monolayer by first-principles calculations. In addition to the well-known band inversion at the charge neutrality point, two new band inversions were found after a CDW phase transition when the chemical potential is near the VHS, one direct and one indirect Z 2 band gap. The VHS-induced non-trivial band gap is around 10 meV, much larger than that from TaIrTe4. Furthermore, since the new generated band gap is mainly dominated by the 4d orbitals of Nb, electronic correlation effects should be relatively stronger in NbIrTe4 as compared to TaIrTe4. Therefore, the dual QSHI state in the NbIrTe4 monolayer is expected to be a good platform for investigating the interplay between topology and correlation effects.

Optical manifestations and bounds of topological Euler class

We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined optical weights of the Euler bands at different dopings and further restrict the size of the adjacent band gaps. In this process, we also consider the associated interband contributions to dc conductivities in the flat-band limit. We physically validate these results by recasting the bound in terms of transition rates associated with the optical absorption of light, and demonstrate how the Euler connections and curvatures can be determined through the use of momentum and frequency-resolved optical measurements, allowing for a direct measurement of this multiband invariant. Additionally, we prove that the bound holds beyond the degenerate limit of Euler bands, resulting in nodal topology captured by the patch Euler class. In this context, we deduce optical manifestations of Euler topology within k·p models, which include quantized optical conductivity, and third-order jerk photoconductivities. We showcase our findings with numerical validation in lattice-regularized models that benchmark effective theories for real materials and are realizable in metamaterials and optical lattices. Published by the American Physical Society 2025

Single-particle spectral function of fractional quantum anomalous Hall states

Fractional quantum Hall states are the most prominent example of states with topological order, hosting excitations with fractionalized charge. Recent experiments in twisted MoTe2 and graphene-based heterostructures provided evidence of fractional quantum anomalous Hall (FQAH) states, which spontaneously break time-reversal symmetry and persist even without an external magnetic field. Understanding the unique properties of these states requires the characterization of their low-energy excitations. To that end, we construct a parton theory for the energy- and momentum-resolved single-particle spectral function of FQAH states. We explicitly consider several experimentally observed filling fractions as well as a composite Fermi liquid in the half-filled Chern band. Charge fractionalization manifests itself in nearly momentum-independent spectra with a characteristic series of peaks determined from the filling fraction. The parton description qualitatively captures our numerical exact diagonalization results. Additionally, we discuss how the finite bandwidth of the Chern band and the nonideal quantum geometry affect the fractionalized excitations. Our work demonstrates that the energy- and momentum-resolved electronic single-particle spectral function provides a valuable tool to characterize fractionalized excitations of FQAH states in moiré lattices. Published by the American Physical Society 2025

Polar topology in self-assembled PbTiO3 ferroelectric nano-islands.

The topological domains in ferroelectrics have garnered significant attention for their potential applications in nanoelectronics. However, current research is predominantly limited to rhombohedral BiFeO3 materials. To validate the universality of topological domains in non-rhombohedral ferroelectrics, it is crucial to explore the existence and characteristics of topological states in alternative material systems. In this work we successfully construct topological polar structures in PbTiO3 nano-islands with a tetragonal structure. Furthermore, the topological structures can be well manipulated by electric field and mechanical stress, making them switchable between center-divergent structure and center-converging types. Phase-field simulations revealed that the aggregation and redistribution of free charges play a decisive role in the formation and manipulation of topological states. These findings not only verify the feasibility of constructing topological domains in universal ferroelectrics, but also validate the multiple manipulability of these topological domains, displaying their significant potential in high-density nonvolatile memory devices.

Engineering flux-controlled flat bands and topological states in a Stagome lattice

Abstract We present the Stagome lattice, a variant of the Kagome lattice, where one can make any of the bands completely flat by tuning an externally controllable magnetic flux. This systematically allows the energy of the flat band to coincide with the Fermi level. We have analytically calculated the compact localized states associated to each of these flat bands appearing at different values of the magnetic flux. We also show that, this model features nontrivial topological properties with distinct integer values of the Chern numbers as a function of the magnetic flux. We argue that this mechanism for making any of the bands exactly flat could be of interest to address the flat-band superconductivity in such a system. Additionally, we show that our results are robust even in the presence of a small amount of disorder. Furthermore, we believe that the phenomenon of photonic flat band localization could be studied in the Stagome lattice structure, designed for instance using femtosecond laser induced single-mode waveguide arrays.

Reconfigurable group delay with tunable topological edge state based on phase transitions material Ge2Sb2Te5 in dual-band

Reconfigurable group delay with tunable topological edge state based on phase transitions material Ge2Sb2Te5 in dual-band

Coalescence of multiple topological orders in quasi-one-dimensional bismuth halide chains

Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications for future quantum devices, can be driven by topological phase transition through modulating intrinsic or extrinsic ordering parameters. The conjoined topology, however, is still elusive in experiments due to the lack of suitable material platforms. Here we use scanning tunneling microscopy, angle-resolved photoemission spectroscopy, and theoretical calculations to investigate the doping-driven band structure evolution of a quasi-one-dimensional material system, bismuth halide, which contains rare multiple band inversions in two time-reversal-invariant momenta. According to the unique bulk-boundary correspondence in topological matter, we unveil a composite topological phase, the coexistence of a strong topological phase and a high-order topological phase, evoked by the band inversion associated with topological phase transition in this system. Moreover, we reveal multiple-stage topological phase transitions by varying the halide element ratio: from high-order topology to weak topology, the unusual dual topology, and trivial/weak topology subsequently. Our results not only realize an ideal material platform with composite topology, but also provide an insightful pathway to establish abundant topological phases in the framework of band inversion theory.

Fermi arcs of topological surface states and Lifshitz transitions in multi-Weyl semimetals

Fermi arcs of topological surface states and Lifshitz transitions in multi-Weyl semimetals

Scaling theory for non-Hermitian topological transitions

Understanding the critical properties is essential for determining the physical behavior of topological systems. In this context, scaling theories based on the curvature function in momentum space, the renormalization group (RG) method, and the universality of critical exponents have proven effective. In this work, we develop a scaling theory for non-Hermitian topological states of matter. We utilize the curvature function renormalization group (CRG) method, incorporating biorthonormal vectors for a one dimensional2×2non-Hermitian Dirac model. This approach allows us to analyze the Wannier state correlation function (WCF) and determine the corresponding localization critical exponent. The CRG method successfully identifies topological phase transitions and locates stable and unstable fixed points. To account for non-Hermitian effects, we construct the curvature function in the generalized Brillouin zone using non-Bloch wave functions, enabling a comprehensive WCF and CRG analysis.

Web of 4D dualities, supersymmetric partition functions and SymTFT

We study ℤN one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed ’t Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

Synthesizing spin–orbit couplings and symmetry-protected topological phase in acoustic metamaterials

Spin–orbit couplings (SOCs) underlie several key concepts of topological matter. However, acoustic waves lack intrinsic spin and SOCs, which makes some topological phases impossible. We develop in the present work a realistic scheme to synthesize simultaneously the intrinsic and Rashba–Dresselhaus SOCs in acoustic systems and explore the symmetry-protected topological phase induced by the SOCs. To be precise, we construct a two-leg ladder composed of acoustic resonators and linking tubes. Utilizing the concept of pseudospin, the spin-1/2 is encoded by the leg degree of freedom of the ladder, and meanwhile, the SOCs are achieved by engineering the couplings between resonators. We further highlight the emergence of the symmetry-protected topological phase respecting the chiral unitary (AIII) symmetry in such acoustic SOC lattices. This scheme is confirmed by the full-wave simulations. Our acoustic structure is within immediate experimental reach and enables the direct visualization of symmetry-protected topological boundary states, not yet been observed experimentally. Our results represent a route to synthesize the SOCs and will benefit an in-depth study of the spin–orbit physics in acoustics.

Crystalline-symmetry-protected Majorana modes in coupled quantum dots

We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site artificial Kitaev chains in a similar setup. We find that introducing a π-phase domain wall in the Kitaev chain leads to a pair of mirror-protected Majorana zero modes located at or near the junction. Joining two π junctions into a closed loop, we can simulate two distinct classes of two-dimensional higher-order topological superconducting phases, both carrying symmetry-protected Majorana modes around the sample corners. As an extension of the π junction, we further consider a general vertex structure where n Kitaev chains meet, i.e., a Kitaev n vertex. We prove that such an n vertex, if respecting a dihedral symmetry group Dn, necessarily carries n vertex-bound Majorana modes protected by the Dn symmetry. Resilience of the junction and vertex Majorana bound states against disorder and correlation effects is also discussed. Our architecture paves the way for designing, constructing, and exploring a wide variety of artificial topological crystalline phases in quantum-dot experiments. Published by the American Physical Society 2025

Practical realization of chiral nonlinearity for strong topological protection

Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned with the requirements for nonlinearity. Here we explore nonlinear topological protection by determining nonlinear rules and demonstrate their relevance in real-world experiments. We take advantage of chiral symmetry and identify the condition for its continuation in general nonlinear environments. Applying it to one-dimensional topological lattices, we show possible evolution paths for zero-energy edge states that preserve topologically nontrivial phases regardless of the specifics of the chiral nonlinearities. Based on an acoustic prototype design with non-local nonlinearities, we theoretically, numerically, and experimentally implement the nonlinear topological edge states that persist in all nonlinear degrees and directions without any frequency shift. Our findings unveil a broad family of nonlinearities compatible with topological non-triviality, establishing a solid ground for future drilling in the emergent field of nonlinear topology.

Topological edge states of plasmonic dark mode in one-dimensional split-ring nanochains

Topological edge states of plasmonic dark mode in one-dimensional split-ring nanochains

Transfer matrix approach for topological edge states

Transfer matrix approach for topological edge states

Cryogenic in-memory computing using magnetic topological insulators.

Machine learning algorithms have proven to be effective for essential quantum computation tasks such as quantum error correction and quantum control. Efficient hardware implementation of these algorithms at cryogenic temperatures is essential. Here we utilize magnetic topological insulators as memristors (termed magnetic topological memristors) and introduce a cryogenic in-memory computing scheme based on the coexistence of a chiral edge state and a topological surface state. The memristive switching and reading of the giant anomalous Hall effect exhibit high energy efficiency, high stability and low stochasticity. We achieve high accuracy in a proof-of-concept classification task using four magnetic topological memristors. Furthermore, our algorithm-level and circuit-level simulations of large-scale neural networks demonstrate software-level accuracy and lower energy consumption for image recognition and quantum state preparation compared with existing magnetic memristor and complementary metal-oxide-semiconductor technologies. Our results not only showcase a new application of chiral edge states but also may inspire further topological quantum-physics-based novel computing schemes.

Unique Berry phase in one-dimensional topological photonic systems.

A new concept, to the best of our knowledge, of the unique Berry phase (UBP) for identifying the topological nature of one-dimensional (1D) topological photonic systems is presented. The advantage of this concept compared to the typical Zak phase (TZP) is that the origin position can be chosen arbitrarily. Traditionally, there are always two inversion centers for a 1D binary photonic system with inversion symmetry. The TZP is quantized at either 0 or π if one of the inversion centers is selected as the origin. Its value depends on the choice of origin location of the unit cell. However, the dependence of the TZP on the choice of the inversion center leads to ambiguities in the distinguished topology. Moreover, when the origin position is not chosen to be in the center of inversion symmetry, the TZP cannot be quantized by integer multiples. A UBP is proposed to avoid this issue in advance. The quantitative value of the UBP is the same, regardless of which inversion center is selected as the origin. It can efficiently predict a topological phase change in a 1D photonic system called the unique Berry phase.

2.5-dimensional topological superconductivity in twisted superconducting flakes

Multilayer flakes of two-dimensional materials were recently shown to be tunable by twisting monolayers on their surface. This raises the question whether qualitatively new phenomena can occur in such finite-thickness moiré systems. Here we demonstrate the emergence of distinct topological phases and transitions in N-layered flakes of nodal superconductors with a single monolayer twisted on top of it. We show that a c-axis current transforms the whole system into a chiral topological superconductor. Increasing the current drives a sequence of topological transitions between states characterized by a Chern number increasing from ~O(N) up to ~O(N2), well beyond the additive effect of stacking N layers. We predict thickness-independent signatures of these states in the thermal Hall and tunneling microscopy measurements. Twisted superconductor flakes thus provide an example of a “2.5-dimensional” material where the synergy of two-dimensional layers extended in a third dimension realize states inaccessible in either monolayer or bulk materials.

Finite-size topological phases from semimetals

Topological semimetals are some of the topological phases of matter most intensely studied experimentally. The Weyl semimetal phase, in particular, has garnered tremendous, sustained interest given fascinating signatures such as the Fermi arc surface states and the chiral anomaly, as well as the minimal requirements to protect this three-dimensional (3D) topological phase. Here, we show that thin films of Weyl semimetals [which we call quasi-(3−1)-dimensional, or q(3−1)D] generically realize finite-size topological phases distinct from 3D and 2D topological phases of established classification schemes: response signatures of the 3D bulk topology coexist with topologically protected, quasi-(3−2)D Fermi arc states or chiral boundary modes due to a second, previously unidentified bulk-boundary correspondence. We show these finite-size topological semimetal phases are realized by Hamiltonians capturing the Fermiology of few-layer van der Waals material MoTe2 in experiment. Given the broad experimental interest in few-layer van der Waals materials and topological semimetals, our work paves the way for extensive future theoretical and experimental characterization of finite-size topological phases. Published by the American Physical Society 2025