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Skyrmions were originally introduced in Particle Physics as a possible mechanism to explain the stability of particles. Lately the concept has been applied in Condensed Matter Physics to describe the newly discovered topologically protected magnetic configurations called the magnetic Skyrmions. Here, we introduce the concept at a level suitable for beginning students of Physics.
Here we report the design and observation of an ideal weak topological insulator in a quasi-one-dimensional bismuth halide, Bi 4 I 1.2 Br 2.8 . Via angle-resolved photoemission spectroscopy, we identify that Bi 4 I 1.2 Br 2.8 hosts topological surface states on the (100)′ side surface in the form of two anisotropic π-offset Dirac cones while topologically dark on the (001) top surface. The results fully determine a unique side-surface Hamiltonian and thereby identify two pairs of nondegenerate helical saddle points. The fact that both the surface Dirac and helical saddle points are in the global bulk band gap of 195 meV suggests the potential of this system to be a fertile ground for topological many-body physics.
Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.
Recently discovered alongside its sister compounds KV 3 Sb 5 and RbV 3 Sb 5 , CsV 3 Sb 5 crystallizes with an ideal kagome network of vanadium and antimonene layers separated by alkali metal ions. This work presents the electronic properties of CsV 3 Sb 5 , demonstrating bulk superconductivity in single crystals with a T c = 2.5 K. The normal state electronic structure is studied via angle-resolved photoemission spectroscopy and density-functional theory, which categorize CsV 3 Sb 5 as a Z 2 topological metal. Multiple protected Dirac crossings are predicted in close proximity to the Fermi level (E F ), and signatures of normal state correlation effects are also suggested by a high-temperature charge density wavelike instability. Finally, the implications for the formation of unconventional superconductivity in this material are discussed.
The fault modes, protection, and fault-tolerant topologies of voltage source inverters have been investigated for decades. However, issues and solutions related to the fault modes of current source inverters are less well understood. This paper summarizes some of the key topics relevant to a fault in current source inverters, including types of fault modes and their ramifications, post-fault protection methods, and fault- tolerant current source inverter topologies that have been presented in the literature.
Atomic monolayers on semiconductor surfaces represent an emerging class of functional quantum materials in the two-dimensional limit — ranging from superconductors and Mott insulators to ferroelectrics and quantum spin Hall insulators. Indenene, a triangular monolayer of indium with a gap of ~ 120 meV is a quantum spin Hall insulator whose micron-scale epitaxial growth on SiC(0001) makes it technologically relevant. However, its suitability for room-temperature spintronics is challenged by the instability of its topological character in air. It is imperative to develop a strategy to protect the topological nature of indenene during ex situ processing and device fabrication. Here we show that intercalation of indenene into epitaxial graphene provides effective protection from the oxidising environment, while preserving an intact topological character. Our approach opens a rich realm of ex situ experimental opportunities, priming monolayer quantum spin Hall insulators for realistic device fabrication and access to topologically protected edge channels.
Antiferromagnetically (AFM) coupled skyrmions offer potential advantages for spintronic devices, including reduced dipolar fields that may enable smaller skyrmion sizes and a reduction of the skyrmion Hall effect. However, the topological stability of AFM-coupled skyrmions subjected to dramatic spin deformation through low-temperature cycling has not been investigated. We report the discovery of a topological spin memory effect for AFM-coupled skyrmion pairs in [Co/Gd/Pt](10) multilayered films. Photoemission electron microscopy imaging shows that bubble skyrmions in the multilayer that are stable at room temperature evolve into complex in-plane spin textures as the temperature is lowered and reform completely when the sample is warmed back up. Simulations demonstrate that Dzyaloshinskii-Moriya interactions play a key role in this spin memory effect, and furthermore reveal that the topological charge is preserved throughout the dramatic spin texture rearrangement and recovery. These results highlight a key aspect of topological protection-the preservation of the topological properties under continuous deformation-and also provide a promising avenue for information encryption and recovery.
Understanding and manipulating emergent phases, which are themes at the forefront of quantum-materials research, rely on identifying their underlying symmetries. This general principle has been particularly prominent in materials with coupled electronic and magnetic degrees of freedom, in which magnetic order influences the electronic band structure and can lead to exotic topological effects. However, identifying symmetry of a magnetically ordered phase can pose a challenge, particularly in the presence of small domains. Here we introduce a multimodal approach for determining magnetic structures, which combines symmetry-sensitive optical probes, scattering, and group-theoretical analysis. We apply it to EuIn 2 As 2 , a material that has received attention as a candidate axion insulator. While first-principles calculations predict this state on the assumption of a simple collinear antiferromagnetic structure, subsequent neutron-scattering measurements reveal a much more intricate magnetic ground state characterized by two coexisting magnetic wave vectors reached by successive thermal phase transitions. The proposed high- and low-temperature phases are a spin helix and a state with interpenetrating helical and Néel antiferromagnetic order termed a “broken helix,” respectively. Employing a multimodal approach, we identify the magnetic structure associated with these two phases of EuIn 2 As 2 . We find that the higher-temperature phase is characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower-temperature structure is similar to the broken helix, with one important difference: Because of local strain, the relative orientation of the magnetic structure and the lattice is not fixed. Consequently, the symmetry required to protect the axion phase is not generically protected in EuIn 2 As 2 , but we show that it can be restored if the magnetic structure is tuned with uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions that account for the complex magnetic order in EuIn 2 As 2 . Our work highlights the importance of a multimodal approach in determining the symmetry of complex order parameters.
The BaAl 4 prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr 2 Si 2 family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA 4 family of materials (M = Sr, Ba, Eu; A = Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. We predict the exemplary compound BaAl 4 to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the k z direction and quadratic dispersion along the k x / k y direction resides on the rotational axis with C 4 v point group symmetry. An extremely large, unsaturating positive magnetoresistance in BaAl 4 despite an uncompensated band structure is revealed, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl 4 as a topological semimetal, casting its prototype status into a role as a building block for a vast array of topological materials.
We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, the current reveals the ground-state degeneracies that distinguish the ordered and disordered phases. In conclusion, we discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions.
Abstract The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin polarization and the breaking of time-reversal symmetry, we demonstrate that random spin-orbit coupling strongly suppresses such dynamical spin polarization, resulting in the persistence of near quantized edge conduction.
The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.
Here, we show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd 3 As 2 is a promising platform for BCL Floquet engineering. Without strain, BCL irradiation induces a transition to a noncentrosymmetric magnetic Weyl semimetal phase with tunable energy separation between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topological crystalline insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2') and can be controlled by light.
The demand for disorder-tolerant quantum logic and spin electronics can be met by generating and controlling dissipationless spin currents protected by topology. Dirac fermions with helical spin-locking surface transport offer a way of achieving such a goal. Yet, surface-bulk coupling can lead to strong Dirac electron scattering with bulk carriers and phonons as well as impurities, assisted by such dissipative channel, which results in “topological breakdown”. Here, we demonstrate that coherent lattice vibrations periodically driven by a single-cycle terahertz (THz) pulse can significantly suppress such dissipative channel in topological insulators. This is achieved by reducing the phase space in the bulk available for Dirac fermion scattering into during coherent lattice oscillations in Bi 2 Se 3 . This light-induced suppression manifests as a remarkable transition exclusively in surface transport, absent for bulk, above the THz electric fields for driving coherent phonons, which prolongs the surface transport lifetime. These results, together with simulations, identify the critical role of spin–orbit coupling for the “phase space contraction” mechanism that suppresses the surface-bulk coupling. Imposing vibrational quantum coherence into topological states of matter may become a universal light control principle for reinforcing the symmetry-protected helical transport.
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be ν = 1.42 ± 0.12. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. Finally, we also quantitatively map our quantum network model to an effective Hamiltonian and we find its low-energy k ∙ p expansion.
The broad goal of this project was to develop new analytical and numerical insights for how important photonic processes can be improved using recently discovered principles in topological and non-Hermitian physics. In particular, there are two recent discoveries that we aimed to harness to achieve this goal. First, it was discovered in condensed matter physics that crystalline symmetries can protect low-dimensional topologically protected states in lattices without the need for breaking time-reversal symmetry. These so-called ‘higher-order’ topological systems represent an important development for photonic systems, where it is very difficult to break time-reversal symmetry, and which had been previously thought necessary to realize topological phenomena. Second, the last decade has seen a significant amount of interest in phenomena which are unique to non-Hermitian systems, i.e., systems which do not conserve energy. For example, spatially patterned gain and loss can be used to realize exceptional points, which are degeneracies in a system’s spectrum where the system becomes defective, while the existence of radiative losses also enables a new route to confinement through bound states in the continuum. For such non-Hermitian phenomena, photonics again represents a critical platform, as photonic systems naturally lose light to their radiative environments, making them generally non-Hermitian, and it is also possible to incorporate additional gain or loss. Based on these broad principles, we pursued a range of projects to harness bound states in the continuum in a variety of different systems and architectures, develop real-space methods for classifying topological systems to yield better photonic design principles, and a novel Brillouin-based fiber laser for sensing strain.
Here we consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dominantly measured, we find area-law entangled phases that protect two topological qubits (on a torus) for a time exponential in system size. This generalizes the recently proposed idea of Floquet codes, where logical qubits are dynamically generated by a time-periodic measurement schedule, to a stochastic setting. When all types of bonds are measured with comparable frequency, we find a critical phase with a logarithmic violation of the area law, which sharply distinguishes it from its Hamiltonian counterpart. The critical phase has the same set of topological qubits, as diagnosed by the tripartite mutual information, but protects them only for a time polynomial in system size. Furthermore, we observe an unusual behavior for the dynamical purification of mixed states, characterized at late times by the dynamical exponent z = $\frac{1}{2}$ a superballistic dynamics made possible by measurements.