Topological Phase Research Articles

Quantum anomalous Hall effect in a nonmagnetic bismuth monolayer with a high Chern number.

The quantum anomalous Hall effect (QAHE) with a high Chern number hosts multiple dissipationless chiral edge channels, which is of fundamental interest and promising for applications in spintronics. However, QAHE is currently limited in two-dimensional (2D) ferromagnets with Chern number . Using a tight-binding model, we put forward that Floquet engineering offers a strategy to achieve QAHE in 2D nonmagnets, and, in contrast to generally reported QAHE in 2D ferromagnets, a high-Chern-number is obtained accompanied by the emergence of two chiral edge states. Moreover, based on the first-principles calculations, we identify tetragonal bismuth as an experimentally feasible candidate of the proposed light-induced QAHE, where remarkably a topological phase transition from the 2D 2 topological insulator to QAHE occurs. Our results open new opportunities to realize exotic QAH physics that increases the feasibility of experimental realization and applications in spintronics devices.

Noncollinear Magnetic Configurations in Frustrated Magnets.

The exploration of materials with nanoscale noncollinear configurations has been continuously attracting attention due to the prospective applications in high-performance magnetic devices. Compared to ferromagnetic materials, noncollinear structures in frustrated magnets hold greater research value due to their smaller sizes and unique properties. However, an effective description of the nanoscale noncollinear domain structures in frustrated magnets is lacking. Here, we propose an approach based on a phase-field model to predict magnetic configurations in frustrated magnets within a square lattice system. The metastable domain structures have been determined under the competition between the nearest-neighbor ferromagnetic interaction and the third-neighbor antiferromagnetic exchange interaction. The conditions required for the stable existence of noncollinear phases have been theoretically derived. Additionally, we investigate the spin response to external fields for different J1 - J3 values, and we also examine the spin response to external fields for various values of J1 - J3, focusing on the emerging topological soliton states. Our research results not only hold crucial significance in facilitating an understanding of the complex characteristics of frustrated magnets but also offer theoretical guidance for further exploring the application potentials of these systems in diverse aspects such as emerging inductor devices and storage devices.

Fano resonance-boosted topological sensor for next-generation sensing

The rapidly developing field of topological photonics has the potential to revolutionize the design and operation of optical systems. This study presents a novel approach for constructing a resilient sensor based on topological resonance. The coupling of the photonic crystal waveguide (PCW) with the topological corner state (TCS) within the structure forms the proposed sensor. The PCW provides a well-defined propagating mode, while the TCS is a localized mode that is topologically protected against perturbations. The coupling between the two modes contributes growth to a Fano resonance and results in a sharp and narrow spectral feature sensitive to the refractive index variation of the surrounding medium. The proposed sensor possesses a high sensitivity of ∼461.96 nm/RIU with a high Q-factor {10}^{6})$$\\end{document}]]>, high figure of merit {10}^{6}\\:{\ ext{R}\ ext{I}\ ext{U}}^{-1})$$\\end{document}]]>, and has an ideal detection limit value of. The present study gives a new platform for a more productive way of creating highly efficient topological Fano resonance sensors. The proposed sensor is resistant, sensitive, and highly versatile, making it beneficial for different applications.

Atomistic Insights into Elemental Two-Dimensional Materials and Their Heterostructures.

Inspired by the success of graphene, two-dimensional (2D) materials have been at the forefront of advanced (opto-)nanoelectronics and energy-related fields owing to their exotic properties like sizable bandgaps, Dirac fermions, quantum spin Hall states, topological edge states, and ballistic charge carrier transport, which hold promise for various electronic device applications. Emerging main group elemental 2D materials, beyond graphene, are of particular interest due to their unique structural characteristics, ease of synthetic exploration, and superior property tunability. In this review, we present recent advances in atomic-scale studies of elemental 2D materials with an emphasis on synthetic strategies and structural properties. We also discuss the challenges and perspectives regarding the integration of elemental 2D materials into various heterostructures.

Double-sided van der Waals epitaxy of topological insulators across an atomically thin membrane.

Atomically thin van der Waals (vdW) films provide a material platform for the epitaxial growth of quantum heterostructures. However, unlike the remote epitaxial growth of three-dimensional bulk crystals, the growth of two-dimensional material heterostructures across atomic layers has been limited due to the weak vdW interaction. Here we report the double-sided epitaxy of vdW layered materials through atomic membranes. We grow vdW topological insulators Sb2Te3 and Bi2Se3 by molecular-beam epitaxy on both surfaces of atomically thin graphene or hexagonal boron nitride, which serve as suspended two-dimensional vdW substrate layers. Both homo- and hetero-double-sided vdW topological insulator tunnel junctions are fabricated, with the atomically thin hexagonal boron nitride acting as a crystal-momentum-conserving tunnelling barrier with abrupt and epitaxial interfaces. By performing field-angle-dependent magneto-tunnelling spectroscopy on these devices, we reveal the energy-momentum-spin resonance of massless Dirac electrons tunnelling between helical Landau levels developed in the topological surface states at the interfaces.

Extended quantum anomalous Hall states in graphene/hBN moiré superlattices.

Electrons in topological flat bands can form new topological states driven by correlation effects. The pentalayer rhombohedral graphene/hexagonal boron nitride (hBN) moiré superlattice was shown to host fractional quantum anomalous Hall effect (FQAHE) at approximately 400 mK (ref. 1), triggering discussions around the underlying mechanism and role of moiré effects2-6. In particular, new electron crystal states with non-trivial topology have been proposed3,4,7-15. Here we report electrical transport measurements in rhombohedral pentalayer and tetralayer graphene/hBN moiré superlattices at electronic temperatures down to below 40 mK. We observed two more fractional quantum anomalous Hall (FQAH) states and smaller Rxx values in pentalayer devices than those previously reported. In the new tetralayer device, we observed FQAHE at moiré filling factors v = 3/5 and 2/3. With a small current at the base temperature, we observed a new extended quantum anomalous Hall (EQAH) state and magnetic hysteresis, where Rxy = h/e2 and vanishing Rxx spans a wide range of v from 0.5 to 1.3. At increased temperature or current, EQAH states disappear and partially transition into the FQAH liquid16-18. Furthermore, we observed displacement field-induced quantum phase transitions from the EQAH states to the Fermi liquid, FQAH liquid and the likely composite Fermi liquid. Our observations established a new topological phase of electrons with quantized Hall resistance at zero magnetic field and enriched the emergent quantum phenomena in materials with topological flat bands.

Synthesis of a semimetallic Weyl ferromagnet with point Fermi surface.

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moiré quantum matter and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall (QAH) effect1-3. By contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions4-6. Nearly all known Weyl materials are overwhelmingly metallic and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)2Te3. In transport, we find a record bulk anomalous Hall angle of greater than 0.5 along with non-metallic conductivity, a regime that is strongly distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation of more than 75% of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal-synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue towards new correlated states and nonlinear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices.

ℤ-Classified Topological Phases and Bound States in the Continuum Induced by Multiple Orbitals.

ℤ-classified higher-order topological insulators (HOTIs) with chiral-symmetric higher-order topological phases protected by multipole chiral numbers (MCNs) have attracted extensive interest recently. However, how to design artificial ℤ-classified HOTIs with multiple topological phases remains an unresolved issue. Here, multiorbital degrees of freedom are introduced to acoustic crystals and the various methods of topological phase transitions are achieved for the orbital ℤ-classified HOTIs. Experimental results demonstrate the realization the coexistence of corner modes with distinct mechanisms within one single model. This provides a pathway for finding ℤ-classified with large MCNs independent of long-range coupling. Additionally, a universal approach is introduced here to fabricate topological bound states in the continuum derived from the discrepant onsite energy of degenerate p-orbitals. These findings provide new insights into the study of topological wave physics using orbital degrees of freedom and may pave the way for designing innovative orbital topological devices for sensing and computing.

Emergent p-Wave Superconductivity in a Dual Topological Insulator BiSe via Superconducting Proximity Effect.

The quest for anisotropic superconductors has been a long-standing pursuit due to their potential applications in quantum computing. In this regard, experimentally, d-wave and anisotropic s-wave superconducting order parameters are predominantly observed, while p-wave superconductors remain largely elusive. Achieving p-wave superconductivity in topological phases is highly desirable, as it is considered suitable for creating topologically protected qubits. To achieve topological superconductivity in the dual topological insulator BiSe, we place an s-wave superconductor NbSe2 in its close proximity employing the van der Waals epitaxy technique. Low-temperature differential conductance measurements performed at the heterojunction exhibit a dual-dip feature with a V-shaped inner dip, a characteristic of p-wave superconductivity. This observation is corroborated by the multiband 2D Blonder-Tinkham-Klapwijk (BTK) fitting, where the inner and outer gaps exhibit p-wave and s-wave character, respectively. Furthermore, the BTK analysis reveals that the two superconducting gaps experience distinct effective critical fields and transition temperatures.

Anomalous and large topological Hall effects in β-Mn chiral compound Co6.5Ru1.5Zn8Mn4: electron electron interaction facilitated quantum interference effect

β-Mn-type chiral cubic CoxZnyMnz(x+y+z= 20) alloys present a intriguing platform for exploring topological magnetic orderings with promising spintronic potential. This study examines the magnetotransport properties of Co6.5Ru1.5Zn8Mn4, a skyrmion-hostingβ-Mn-type chiral compound. The longitudinal resistivity (ρxx) exhibits field-insensitive low-temperature minima due to quantum interference effects, driven byT1/2-dependent electron-electron interactions. We observe a substantial intrinsic anomalous Hall conductivity, unaffected by quantum interference. Additionally, a pronounced topological Hall effect is observed at the metastable skyrmionic state, persisting up toTCand achieving notable magnitudes for stoichiometric compounds. These results position the CoxZnyMnzfamily favourably to leverage the rich pallete of emergent magnetotransport properties for spintronic applications.

Toward a Classification of Mixed-State Topological Orders in Two Dimensions

Toward a Classification of Mixed-State Topological Orders in Two Dimensions

Intrinsic Mixed-State Topological Order

Intrinsic Mixed-State Topological Order

Higher-order topological fermion phase and Weyl phonon phase in Li-intercalated graphene layers

Higher-order topological fermion phase and Weyl phonon phase in Li-intercalated graphene layers

Gapless topological behaviors in a long-range quantum spin chain

Topology is a fascinating phenomena in condensed-matter physics typically associated with a bulk gap. However, recent research shifts focus to quantum critical points or phases that exhibit nontrivial topological properties. Here we explore a cluster-Ising chain with long-range antiferromagnetic interactions that decay as a power law with distance. Using large-scale density matrix renormalization group simulations, we demonstrate that the nontrivial topology at the critical point remains stable against long-range interactions, resulting in a topologically nontrivial critical line. Moreover, even within the gapped region, the interplay between topology and long-range interaction can give rise to a topological phase featuring algebraically decaying correlations and edge modes, similar to gapless topological phases. We refer to this phase as the algebraic topological phase, which exhibits nontrivial gapless topological behaviors and arises solely from long-range interactions without short-range counterparts. The findings pave the way for more studies on topological states in long-range systems.

Engineering Floquet Moiré Patterns for Scalable Photocurrents.

While intense laser irradiation and moiré engineering have independently proven powerful for tuning material properties on demand in condensed matter physics, their combination remains unexplored. Here we exploit tilted laser illumination to create spatially modulated light-matter interactions, leading to two striking phenomena in graphene. First, using two lasers tilted along the same axis, we create a quasi-1D supercell hosting a network of Floquet topological states that generate controllable and scalable photocurrents spanning the entire irradiated region. Second, by tilting lasers along orthogonal axes, we establish a 2D polarization moiré pattern giving rise to closed orbital propagation of Floquet states, reminiscent of bulk Landau states. These features, imprinted in the bulk of the irradiated region and controlled through laser wavelength and tilt angles, establish a new way for engineering quantum states through spatially modulated light-matter coupling.

Dual-band topological Bott insulators in Ammann–Beenker-tiling square photonic quasicrystals

Abstract In this work, we study topological states in Ammann-Beenker-tiling photonic quasicrystals made of magneto-optical materials. While conventional topological states in photonic systems with crystalline symmetry are characterized by topological invariants associated with bulk Bloch bands in momentum space, photonic systems in quasicrystal geometries typically lack exact periodicity and translational symmetry. As a result, conventional topological invariants defined in momentum space for photonic crystals, such as Chern number, are not applicable for photonic quasicrystals. Instead, a topological invariant called Bott index defined in real space could be employed for characterizing the topological properties of photonic quasicrystals, which we term as topological Bott insulators. In specific, we investigate the topological properties of photonic quasicrystals made of gyromagnetic dielectric cylinders arranged in a two- dimensional Ammann-Beenker tiling quasicrystalline lattice and find that this system supports dual-band chiral topological edge states, where the topological nature of both bandgaps is unambiguously confirmed by explicit calculations of the Bott index. Our work not only provides new insights on topological states in photonic quasicrystals based on the Ammann-Beenker-tiling, the results may also offer promising potentials for robust multiband photonic devices and applications not constrained by crystalline symmetries.

Coupling between topological edge state and defect mode-based biosensor using phononic crystal

A wealth of details regarding an individual’s state of health, like a person’s respiratory and metabolic functioning, can be studied by analyzing the volatile molecules and atoms in human exhaled breath. Besides, the salinity of seawater is a crucial factor in understanding its characteristics because any variation in the salinity of seawater represents the variations in the hydrological, biological, and chemical distributions. In this paper, a symmetrical one-dimensional phononic structure is theoretically designed using two symmetrical crystals separated with a defective cavity. This structure has been designed to excite a topological edge state coupled with defect mode. The coupled mode achieves high sensitivity to NaCl concentration in an aqueous solution, seven times higher than the defective one. By ranging the NaCl concentration from 0 to 21%, the average sensitivity is 467 and 3160 Hz/% for defect mode and coupled modes, respectively. The bandwidth of the coupled mode of 170 Hz is much narrower than that of the defect mode of 671 Hz for detecting salinity. For detecting the increase in concentration in dry exhaled breath by ranging the concentration from 0 ppm to 100 ppm, the average sensitivity is Hz/ppm for coupled mode. As a result of these enhancements in the sensitivity and bandwidth of the coupled mode, the coupled mode is recommended to be used in different biosensing applications.

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 2 × 2 non-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.

Anomalous Behavior of the Non-Hermitian Topological System with an Asymmetric Coupling Impurity.

A notable feature of systems with non-Hermitian skin effects is the sensitivity to boundary conditions. In this work, we introduce one type of boundary condition provided by a coupling impurity. We consider a system where a two-level system as an impurity couples to a nonreciprocal Su-Schrieffer-Heeger chain under periodic boundary conditions at two points with asymmetric couplings. We first study the spectrum of the system and find that asymmetric couplings lead to topological phase transitions. Meanwhile, a striking feature is that the coupling impurity can act as an effective boundary, and asymmetric couplings can also induce a flexibly adjusted zero mode. It is localized at one of the two effective boundaries or both of them by tuning coupling strengths. Moreover, we uncover three types of localization behaviors of eigenstates for this non-Hermitian impurity system with on-site disorder. These results corroborate the potential for control of a class of non-Hermitian systems with coupling impurities.

Observation of momentum-gap topology of light at temporal interfaces in a time-synthetic lattice

Topological phases have prevailed across diverse disciplines, spanning electronics, photonics, and acoustics. Hitherto, the understanding of these phases has centred on energy (frequency) bandstructures, showcasing topological boundary states at spatial interfaces. Recent strides have uncovered a unique category of bandstructures characterised by gaps in momentum, referred to as momentum bandgaps or k gaps, notably driven by breakthroughs in photonic time crystals. This discovery hints at abundant topological phases defined within momentum bands, alongside a wealth of topological boundary states in the time domain. Here, we report the experimental observation of k-gap topology in a large-scale optical temporal synthetic lattice, manifesting as temporal topological boundary states. These boundary states are uniquely situated at temporal interfaces between two subsystems with distinct k-gap topology. Counterintuitively, despite the exponential amplification of k-gap modes within both subsystems, these topological boundary states exhibit decay in both temporal directions [i.e., with energy growing (decaying) before (after) the temporal interfaces]. Our findings mark a significant pathway for delving into k gaps, temporal topological states, and time-varying physics.