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Topological insulator (TI) is a new class of quantum material with inverted band structure caused by strong spin-orbit coupling (SOC), resulting an insulating bulk and topologically protected surface states. By introducing magnetism to break the time-reversal symmetry, it can host emerging topological quantum phases such as quantum anomalous Hall (QAH) effect, axion insulator quantum phase, and can host chiral Majorana fermion when coupled to superconductors. The goal of this dissertation is to study these quantum phases by material growth and transport measurements.First, we studied the growth condition by molecular beam epitaxy (MBE) and achieved high quality magnetically doped topological insulator (MTI) film growth that can host QAH effect. To understand the different origins of zero Hall conductance plateau in QAH insulators and axion insulators, we carried out the thickness dependent study on MTI sandwiched structures and observed a dimension crossover between 2D QAH and 3D axion insulators by minor loops measurements and scaling analysis. Then, we investigated the QAH insulator and antiferromagnetic heterostructures which offer an additional degree of freedom to manipulate the QAH state in MTI. By proximity coupling the QAH insulator to antiferromagnetic insulator Al-Cr2O3, we observed an exchange biased QAH effect, and the exchange bias can be effectively controlled by a field training process. In addition, chiral Majorana edge modes are reported to exist in QAH insulator and superconductors heterostructures. Aiming to understand the discrepancy of recent experimental reports, we fabricated QAH insulator with superconductor and normal metals hybrid devices, and we found the details of material characteristics, interface conditions play important roles on the experiment observations. Finally, two collaborative works closely related to the main scope of this dissertation are introduced. To probe the size limit and to understand the inter-channel scattering of QAH effect, we fabricated mesoscopic scale sub-micron size QAH insulator devices and carried out size dependent studies. Enabled by the successful growth of QAH film on insulating 2D van-der-Waals substrate MICA, we were able to fabricate dual-gate QAH device by exfoliation and transfer techniques. By applying a vertical electric field, we observe a topological phase transition from QAH to a trivial insulator state. This research will greatly improve the understanding of emerging topological quantum physics, and lead to the new revolution of quantum electronic devices.

Quantum computers have the potential to solve certain problems in minutes that would otherwise take classical computers thousands of years due to the exponential speed-up certain quantum algorithms have over classical algorithms. In order to leverage such quantum algorithms, it is necessary for them to run on quantum devices. Examples of such devices include, but are not limited to, semiconductor and superconducting qubits, and semiconductor single and entangled photon emitters. The conventional method of constructing a semiconductor qubit is to apply gates on a semiconductor surface to localize electrons, where the electronic spin states are mapped to a qubit basis. Examples of this include the spin qubit where the spin-1/2 states of a single electron is the qubit basis and the gated singlet-triplet qubit where the states of two coupled electrons are mapped to a qubit basis. In general, gated semiconductor spin qubits are subject to decoherence from the environment which alters the electronic wavefunction by entanglement with the nuclear spins and phonons in the lattice compromising the stability of the qubit. Semiconductor nanostructures can also be designed as photon emitters. Self-assembled quantum dots are an example of such nanostructures and have been shown to emit single photons through exciton recombination and entangled photons through biexciton-exciton cascade. The difficulty in designing photon sources using self-assembled quantum dots is that the size and shape varies from dot to dot, implying that the electronic and magnetic properties also vary. In this thesis, I present the design of a single photon emitter using an InAsP quantum dot embedded in an InP nanowire and the design of a singlet-triplet qubit that is topologically protected from decoherence using an array of such quantum dots embedded in an InP nanowire. The advantage of using quantum dot nanowires over self-assembled quantum dots as photon emitters is that the quantum dot thickness, radius and composition can be controlled deterministically using a technique known as vapour-liquid-solid epitaxy which allows the emission spectrum to be engineered. Using a microscopic model, I simulated an InAsP quantum dot embedded in a nanowire with upwards of millions of atoms and showed that the emission spectrum came in agreement with the actual InAsP/InP quantum dot nanowires that were fabricated at the National Research Council of Canada. Moreover, I showed that altering the distribution of As atoms in the quantum dot can cause dramatic change in the emission spectrum. For the design of the topologically protected singlet-triplet qubit, I demonstrated that the ground state of an array of such quantum dots embedded in an InP nanowire, with four electrons in each dot, is four-fold degenerate and is topologically protected from higher energy states, making the ground state robust against perturbations. This state is known as the Haldane phase and can be understood in terms of two spin-1/2 quasiparticles at each edge of the array. Though the spectral gap in my simulation was of the order of 1 meV, this work provides insight into the potential design of a room temperature operating Haldane qubit where the spectral gap is of the order of room temperature.

The Berry curvature (BC) - a quantity encoding the geometric properties of the electronic wavefunctions in a solid - is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations of BC are generally linked to single-particle wavefunctions that are a quantum superposition of electron and hole excitations. BC-mediated effects are consequently observed in two-dimensional systems with pairs of massive Dirac cones and three-dimensional bulk crystals with quartets of Weyl cones. Here, we demonstrate that in materials equipped with orbital degrees of freedom local BC concentrations can arise even in the complete absence of hole excitations. In these solids, the crystals fields appearing in very low-symmetric structures trigger BCs characterized by hot-spots and singular pinch points. These characteristics naturally yield giant BC dipoles and large non-linear transport responses in time-reversal symmetric conditions., 11 pages, 4 figure and supplemental material (6 pages, figures)

We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw–Rebbi (JR) models. We show that time-reversal (T), charge-conjugation (C), parity (P), and discrete internal field rotation ($$Z_n$$ Z n ) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the $$Z_2$$ Z 2 rotation symmetry, whereas it shows chiral solitons with the broken $$Z_2$$ Z 2 rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only $$Z_2$$ Z 2 rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced $$Z_4$$ Z 4 rotation symmetry. Moreover, we find that the nonchiral solitons have C, P symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that T, C, P symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.

Recently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals., Comment: 26 + 14 pages, 8 + 2 figures

Skyrmion and antiskyrmion spin textures are axisymmetric inhomogeneous localized objects with distinct chirality in magnetic systems. These spin textures are potential candidates for the next generation energy-efficient spintronic applications due to their unique topological properties. Controlled and effective creation of the spin textures is required to use in conventional and neuromorphic computing applications. Here we show by micromagnetic simulations creating an isolated skyrmion, skyrmion lattice and antiskyrmion lattice through the magnetization reversal in Co/Pd multilayer nanostructure using spin-polarized current. The spin textures' stability depends on the spin-polarized current density, current pulse width, and Dzyaloshinskii–Moriya interaction (DMI). Antiskyrmions are evolved during the formation of a single skyrmion and skyrmion lattice. Skyrmion and antiskyrmion lattices together are observed for lower pulse width, 0.05 ns. Our micromagnetic studies suggest that the two distinct lattice phases' evolution could help to design the topological spin textures-based devices.

We theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

International audience; Strain is ubiquitous in solid-state materials, but despite its fundamental importance and technological relevance, leveraging externally applied strain to gain control over material properties is still in its infancy. In particular, strain control over the diverse phase transitions and topological states in two-dimensional transition metal dichalcogenides remains an open challenge. Here, we exploit uniaxial strain to stabilize the long-debated structural ground state of the 2D topological semimetal IrTe2, which is hidden in unstrained samples. Combined angle-resolved photoemission spectroscopy and scanning tunneling microscopy data reveal the strain-stabilized phase has a 6 × 1 periodicity and undergoes a Lifshitz transition, granting unprecedented spectroscopic access to previously inaccessible type-II topological Dirac states that dominate the modified inter-layer hopping. Supported by density functional theory calculations, we show that strain induces an Ir to Te charge transfer resulting in strongly weakened inter-layer Te bonds and a reshaped energetic landscape favoring the 6×1 phase. Our results highlight the potential to exploit strain-engineered properties in layered materials, particularly in the context of tuning inter-layer behavior.

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails., 23 pages (including appendices), 13 figures. Recently revised version with modified figures, additional references and discussions

Topological order is important in many aspects of condensed matter physics, and has been extended to bosonic systems. In this Letter we report on the nontrivial topology of the magnon bands in two distinct quantum skyrmion crystals appearing in zero external magnetic field. This is revealed by nonzero Chern numbers for some of the bands. As a bosonic analog of the quantum anomalous Hall effect, we show that topological magnons can appear in skyrmion crystals without explicitly breaking time-reversal symmetry with an external magnetic field. By tuning the value of the easy-axis anisotropy at zero temperature, we find eight quantum topological phase transitions signaled by discontinuous jumps in certain Chern numbers. We connect these quantum topological phase transitions to gaps closing and reopening between magnon bands., 6+17 pages, 2+3 figures, includes supplemental material, accepted in Physical Review Research

With the help of quantum mechanics, digital quantum hardware may be able to tackle some of the problems that are too difficult for ordinary computers. But despite these expectations and the ongoing effort of the research community, reliable quantum computers are not yet realized in a lab setting. The optimal strategies for early applications of such special hardware are not settled either. The present thesis addresses these issues of implementing and harnessing quantum computers.Firstly, several strategies are introduced to implement and characterize digital quantum hardware using the technique called braiding. Two realizations are considered: the edge modes of topological superconductors and the parafermionic modes in Fractional Quantum Hall materials.Secondly, this work explores applying quantum computers to prepare simulated ground states (lowest-energy configurations) of complex quantum systems. To this end, several new techniques are presented in the context of variational quantum algorithms, simulated cooling, and quantum control theory.

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Magnetic skyrmion is a topologically protected particle-like object in magnetic materials, appearing as a nanometric swirling spin texture. The size and shape of skyrmion particles can be flexibly controlled by external stimuli, which suggests unique features of their crystallization and lattice transformation process. Here, we investigated the detailed mechanism of structural transition of skyrmion lattice (SkL) in a prototype chiral cubic magnet Cu2OSeO3, by combining resonant soft X-ray scattering (RSXS) experiment and micromagnetic simulation. This compound is found to undergo a triangular-to-square lattice transformation of metastable skyrmions by sweeping magnetic field (B). Our simulation suggests that the symmetry change of metastable SkL is mainly triggered by the B-induced modification of skyrmion core diameter and associated energy cost at the skyrmion-skyrmion interface region. Such internal deformation of skyrmion particle has further been confirmed by probing the higher harmonics in the RSXS pattern. These results demonstrate that the size/shape degree of freedom of skyrmion particle is an important factor to determine their stable lattice form, revealing the exotic manner of phase transition process for topological soliton ensembles in the non-equilibrium condition., Skyrmions are topological spin textures and are of great interest due to their impressive stability. Here, by sweeping an applied magnetic field, the authors observe a change in the skyrmion lattice structure, shedding light on the relation between skyrmion size and stability.

Spin angular momentum enables fundamental insights for topological matters, and practical implications for information devices. Exploiting the spin of carriers and waves is critical to achieving more controllable degrees of freedom and robust transport processes. Yet, due to the curl-free nature of longitudinal waves distinct from transverse electromagnetic waves, spin angular momenta of acoustic waves in solids and fluids have never been unveiled only until recently. Here, we demonstrate a metasurface waveguide for sound carrying non-zero acoustic spin with tight spin-momentum coupling, which can assist the suppression of backscattering when scatters fail to flip the acoustic spin. This is achieved by imposing a soft boundary of the π reflection phase, realized by comb-like metasurfaces. With the special-boundary-defined spin texture, the acoustic spin transports are experimentally manifested, such as the suppression of acoustic corner-scattering, the spin-selected acoustic router with spin-Hall-like effect, and the phase modulator with rotated acoustic spin., Spin angular momenta play a crucial role in topological phases of matter, in acoustic waves they have been demonstrated recently. Here, the authors present a symmetry-breaking metasurface waveguide that assists backscattering suppression of acoustic waves, because of tight spin-momentum coupling.

Synthetic crystal lattices provide ideal environments for simulating and exploring the band structure of solid-state materials in clean and controlled experimental settings. Physical realisations have, so far, dominantly focused on implementing irreversible patterning of the system, or interference techniques such as optical lattices of cold atoms. Here, we realise reprogrammable synthetic band-structure engineering in an all optical exciton-polariton lattice. We demonstrate polariton condensation into excited states of linear one-dimensional lattices, periodic rings, dimerised non-trivial topological phases, and defect modes utilising malleable optically imprinted non-Hermitian potential landscapes. The stable excited nature of the condensate lattice with strong interactions between sites results in an actively tuneable non-Hermitian analogue of the Su-Schrieffer-Heeger system., To simulate band structures of solid state materials synthetic lattices are usually generated by optical lattices or by irreversible patterning the system. Here, the authors present reconfigurable synthetic band-structures in optical exciton-polariton lattices and generate non-Hermitian topological phases.

Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively studied in band theory and have been experimentally discovered, the classification and diagnosis of their strongly interacting counterparts are relatively less well understood. Here we present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space "building blocks" and "connectors". Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are "glue" that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the "no-open-edge condition" and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology., 17+44 pages, 7+1 figures, 0+2 tables. The content is the same as the published version, but arranged differently

Knots and links have been conjectured to play a fundamental role in a wide range of scientific fields. Recently, tying isolated vortex knots in the complex optical field has been realized. However, how to construct the acoustic vortex knot is still an unknown problem. Here we propose theoretically and demonstrate experimentally the creation of acoustic vortex knots using metamaterials, with decoupled modulation of transmitted phase and amplitude. Based on the numerical simulation, we find that the knot function can be embedded into the acoustic field by designed metamaterials with only 24 × 24 pixels. Furthermore, using the optimized metamaterials, the acoustic fields with Hopf link and trefoil knot vortex lines have been observed experimentally., Although knots in complex optical fields have been realized experimentally, the realization of acoustic vortex knots is still problematic. Here, the authors have demonstrated the creation of acoustic vortex knots by embedding the knot function into a propagating acoustic field using a metasurface hologram.

The prediction of non-trivial topological electronic states hosted by half-Heusler compounds makes them prime candidates for discovering new physics and devices as they harbor a variety of electronic ground states including superconductivity, magnetism, and heavy fermion behavior. Here we report normal state electronic properties of a superconducting half-Heusler compound YPtBi using angle-resolved photoemission spectroscopy (ARPES). Our data reveal the presence of a Dirac state at the zone center of the Brillouin zone at 500 meV below the chemical potential. We observe the presence of multiple Fermi surface pockets including two concentric hexagonal and six half oval shaped pockets at the gamma and K points of the Brillouin zone, respectively. Furthermore, our measurements show Rashba-split bands and multiple surface states crossing the chemical potential which are supported by the first-principles calculations. Our finding of a Dirac state in YPtBi plays a significant role in establishing half-Heusler compounds as a new potential platform for novel topological phases and explore their connection with superconductivity., 6 pages, 4 figures

We have investigated the valley Chern number and gapless edge states in wide-gap semiconductor SiC and BN monolayers by using the density functional theory calculations. We found that while SiC monolayer has a non-quantized valley Chern number due to a partial mixing of the Berry curvature peaks pertaining to the opposite valleys, there exist topologically protected gapless edge states within the bulk gap, leading to a quantum valley Hall effect. Doping of the opposite charge carriers causes a backscattering-free valley current flowing on the opposite edge, which can be used for experimental confirmation and application at room temperature. BN monolayer, on the other hand, was found to have gapped edge states due to the too large staggered AB-sublattice potentials.

Lasing behavior of optically active planar topological Weyl semimetal (TWS) is investigated in view of the Kerr and Faraday rotations. Robust topological character of TWS is revealed by the presence of Weyl nodes and relevant surface conductivities. We focus our attention on the surfaces where no Fermi arcs are formed, and thus Maxwell equations contain topological terms. We explicitly demonstrate that two distinct lasing modes arise because of the presence of effective refractive indices which lead to the birefringence phenomena. Transfer matrix is constructed in such a way that reflection and transmission amplitudes involve $2\times2$ matrix-valued components describing the bimodal character of the TWS laser. We provide associated parameters of the topological laser system yielding the optimal impacts. We reveal that gain values corresponding to the lasing threshold display a quantized behavior, which occurs due to topological character of the system. Our proposal is supported by the corresponding graphical demonstrations. Our observations and predictions suggest a concrete way of forming TWS laser and coherent perfect absorber; and are awaited to be confirmed by an experimental realization based on our computations., Comment: 17 pages, 9 figures, 3 tables

SmB6 has drawn much attention in recent times due to the discovery of anomalies in its ground state properties as well as prediction of topologically protected gapless surface states. Varied theories have been proposed to capture the ground state anomalies. Here, we studied the electronic structure of SmB6 employing density functional theory using different exchange correlation potentials, spin-orbit coupling and electron correlation strength. We discover that a suitable choice of interaction parameters such as spin-orbit coupling, electron correlation strength and exchange interaction within the generalized gradient approximation provides a good description of the spectral functions observed in the angle-resolved photoemission spectroscopy (ARPES) studies. The Fermi surface plots exhibit electron pockets around X-point and hole pockets around ΓX line having dominant Sm 4f character. These observations corroborate well with the recent experimental results involving quantum oscillation measurements, ARPES, etc. In addition to primarily Sm 4f contributions observed at the Fermi level, the results exhibit significantly large contribution from B 2p states compared to weak Sm 5d contributions. This suggests important role of B 2p - Sm 4f hybridization in the exotic physics of this system.

Quantitative 2D neutron dark-field-imaging with neutron grating interferometry has been used to characterize structures in the size range below the imaging resolution. We present the first 3D quantitative neutron dark-field imaging experiment. We characterize sub-pixel structure sizes below the imaging resolution in tomography by quantitatively analyzing the change in dark-field contrast with varying neutron wavelength. This proof of principle experiment uses a dedicated reference sample with four different solutions of microspheres, each with a different diameter. The result is a 3D tomogram featuring a real space scattering function in each voxel. The presented experiment is expected to mark the path for future material science research through the individual quantification of small-angle scattering structures in each voxel of a volume of a bulk inhomogeneous sample material.

Interplay of magnetism and electronic band topology in unconventional magnets enables the creation and fine control of novel electronic phenomena. In this work, we use scanning tunneling microscopy and spectroscopy to study thin films of a prototypical kagome magnet Fe3Sn2. Our experiments reveal an unusually large number of densely-spaced spectroscopic features straddling the Fermi level. These are consistent with signatures of low-energy Weyl fermions and associated topological Fermi arc surface states predicted by theory. By measuring their response as a function of magnetic field, we discover a pronounced evolution in energy tied to the magnetization direction. Electron scattering and interference imaging further demonstrates the tunable nature of a subset of related electronic states. Our experiments provide a direct visualization of how in-situ spin reorientation drives changes in the electronic density of states of the Weyl fermion band structure. Combined with previous reports of massive Dirac fermions, flat bands, and electronic nematicity, our work establishes Fe3Sn2 as an interesting platform that harbors an extraordinarily wide array of topological and correlated electron phenomena.

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Nature Communications 13(1), 444 (2022). doi:10.1038/s41467-022-27964-y, Magnetically frustrated systems provide fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles is yet to be found. Using measurements on single crystals of Ho$_2$Ir$_2$O$_7$ combined with dipolar Monte Carlo simulations, we show that the isothermal magnetoresistance is highly sensitive to the monopole density. Moreover, we uncover an unexpected and strong coupling between the monopoles on the holmium sublattice and the antiferromagnetically ordered iridium ions. These results pave the way towards a quantitative experimental measure of monopole density and demonstrate the ability to control antiferromagnetic domain walls using a uniform external magnetic field, a key goal in the design of next-generation spintronic devices., Published by Nature Publishing Group UK, [London]

The magnetic skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phase shifts among the constituent waves. Although such a phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift in the skyrmion crystals leads to a tetra-axial vortex crystal and a meron-antimeron crystal, both of which show a staggered pattern of the scalar spin chirality and give rise to nonreciprocal transport phenomena without the spin-orbit coupling. We demonstrate that such a phase shift can be driven by exchange interactions between the localized spins, thermal fluctuations, and long-range chirality interactions in spin-charge coupled systems. Our results provide a further diversity of topological spin textures and open a new field of emergent electromagnetism by the phase shift engineering., Skyrmions are a type of topological spin texture, which can exist as both an isolated state, and as a skyrmion crystal. Here, Hayami et al present a theoretical study of phase shifts in skyrmion crystals, showing how such phase shifts can lead to other crystalline topological spin textures.

Optical activity, also called circular birefringence, is known for two hundred years, but its applications for topological photonics remain unexplored. Unlike the Faraday effect, the optical activity provokes rotation of the linear polarization of light without magnetic effects, thus preserving the time-reversal symmetry. In this work, we report a direct measurement of the Berry curvature and quantum metric of the photonic modes of a planar cavity, containing a birefringent organic microcrystal (perylene) and exhibiting emergent optical activity. This experiment, performed at room temperature and at visible wavelength, establishes the potential of organic materials for implementing non-magnetic and low-cost topological photonic devices., Most work in topological photonics is performed in periodically structured systems. Here, the authors directly measure the nontrivial Berry curvature of the photonic modes of a birefringent continuous organic system exhibiting emergent optical activity.

A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent $$\nu$$ ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent $$\theta =\nu _{x}/\nu _{z}$$ θ = ν x / ν z . We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for $$\nu$$ ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation $$\nu _{\bar{\alpha }}z_{\bar{\alpha }}=2q$$ ν α ¯ z α ¯ = 2 q and $$\theta =\nu _{x}/\nu _{z}=z_{z}/z_{x}$$ θ = ν x / ν z = z z / z x for $$\nu$$ ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction $$\bar{\alpha }$$ α ¯ . An anisotropic quantum hyperscaling relation is also obtained.

We used the topological insulator (TI) Bi2Te3 and a high-temperature superconductor (HTSC) hybrid device for investigations of proximity-induced superconductivity (PS) in the TI. Application of the superconductor YBa2Cu3O7-δ (YBCO) enabled us to access higher temperature and energy scales for this phenomenon. The HTSC in the hybrid device exhibits emergence of a pseudogap state for T > Tc that converts into a superconducting state with a reduced gap for T c. The conversion process has been reflected in Raman spectra collected from the TI. Complementary charge transport experiments revealed emergence of the proximity-induced superconducting gap in the TI and the reduced superconducting gap in the HTSC, but no signature of the pseudogap. This allowed us to conclude that Raman spectroscopy reveals formation of the pseudogap state but cannot distinguish the proximity-induced superconducting state in the TI from the superconducting state in the HTSC characterised by the reduced gap. Results of our experiments have shown that Raman spectroscopy is a complementary technique to classic charge transport experiments and is a powerful tool for investigation of the proximity-induced superconductivity in the Bi2Te3.