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This dissertation comprises two parts, each of which details an investigation within topological matter.In the first part, we investigate the real space localization properties of static topological insulators in two dimensions. We develop three numerical procedures each of which removes an extensive fraction of the local degrees of freedom. We probe the real space properties of the residual projection operator, showing that the maximally localized length scale ξ supported in the residual Hilbert space diverges as the fraction of states remaining approaches 0. The power-law exponent ν = 1/2 characterizing the singular behavior of ξ appears universal across class A insulators with non-zero Chern number.In the second part, we explore a class of Floquet topological phases in three dimensions. These phases have translational invariance but no other symmetry, and exhibit anomalous transport at a boundary surface. We show that the boundary behavior of such phases falls into equivalence classes up to local 2D unitary evolution. This provides a classification of the 3D bulk, which we conjecture to be complete. We demonstrate that such phases may be generated by exactly solvable “exchange drives” in the bulk. The edge behavior of a general exchange drive in two or three dimensions is shown to derive from the geometric properties of its action in the bulk, a form of bulk-boundary correspondence.

Topology has manifestations in physics ranging from the field of condensed matter to photonics. This dissertation provides a two-fold study on the impact of topology in Hermitian and non-Hermitian band structures. Salient examples include the notion of topological invariants and knots, which are both used to describe characteristics of eigenvalue intersections. The first part focuses on Hermitian topological phases of matter, where general methods predicting transport properties in both gapped and gapless phases are presented. The second part turns to non-Hermitian phases and revolves around the topological properties of their exceptional eigenvalue degeneracies. Through a generic construction originating in knot theory, it is shown that such degeneracies take the form of knots, which furthermore bound open Fermi surfaces coinciding with the respective Seifert surfaces. This construction is then extended and applied in a similar fashion to parity-time-symmetric systems, where the exceptional points form surfaces and curves of any topology, as well as points. These theoretical descriptions constitute a fruitful platform to study dissipative systems—in particular in optics where parity-time symmetry implies a balance between gain and loss in photonic crystals—but also give rise to interesting connections to gravity in the context of analogue black holes.

Quantum computing promises to solve problems, which are impossible for classical computers. Among the different schemes of how to design a quantum computer, one particularly exotic version has raised a lot of attention lately. Although so-called topological quantum computing is a rather young concept, it promises to reduce the required overhead of physical quantum bits per logical quantum bit by a factor of 100–1000, due to an intrinsic protection against certain quantum errors. Once the fundamental mechanism – braiding of Majorana zero modes – is demonstrated, the topological scheme could become the most promising in terms of scalability. This article offers a short introduction to the topological concept and also aims to review the latest developments and efforts in this rapidly evolving field. In addition to this, it discusses different platforms for experimental realization of topologically protected devices. One particularly promising platform might evolve when in-situ fabrication techniques are applied to magnetically doped topological insulators. As a result, it should become possible to fabricate high fidelity Majorana devices for quantum computational tasks in a scalable fashion.

Topological materials promise new functionalities, which are revealed with the help of angle resolved photoemission. Herein, the search for the magnetic bandgap at the Dirac point as a precondition for the quantum anomalous Hall effect is reviewed and its opening for the topological insulator heterostructure MnBi2Te4 Bi2Te3 is demonstrated. Essential preconditions are explained and the reasons why nonmagnetic gaps occur when Se replaces Te. Angle resolved photoelectron spectroscopy ARPES probes the quantum mechanical final state, and this allows investigation of spin manipulation by light using spin resolved ARPES and the dependence of the charge carrier lifetime on the peculiar spin texture of topological states. It is shown that ARPES data do not support SmB6 as the first strongly correlated topological insulator and an alternative, trivial explanation for the results of ARPES and electrical transport experiments is formulated. Epitaxially grown topological crystalline insulators are, due to their dependence on crystal symmetries, more versatile in the control of individual bulk band inversions. It is shown that this leads to topological quantum phase transitions and associated novel functionalities. Finally, the surface and bulk band connectivity of a type II 3D Weyl semimetal is investigated and an outlook is given for the scientific field

Physics of graphene and physics of superfluid phases of 3He have many common features. Both systems are topological materials where quasiparticles behave as relativistic massless (Weyl, Majorana or Dirac) fermions. We formulate the points where these features are overlapping. This will allow us to use graphene for study the properties of superfluid 3He, to use superfluid 3He for study the properties of graphene, and to use the combination to study the physics of topological quantum vacuum. We suggest also some particular experiments with superfluid 3He using graphene as an atomically thin membrane impenetrable for He atoms but allowing for spin, momentum and energy transfer.

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. In gapless topological media, the bulk-surface and bulk-vortex correspondence produce topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and this property may give rise in particular to surface superconductivity which in principle could exist even at room temperature., 4 pages, 3 figures, version accepted for proceedings of the 4th International Conference "Fundamental Problems of High-Temperature Superconductivity" (FPS'11), Zvenigorod, October 2011

Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n−1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n−1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant., Materials with topologically nontrivial band structures possess exotic electronic transport properties however they are naturally constrained below three dimensions. Here, the authors demonstrate how analogous systems with n−1 dimensions may be constructed from Josephson junctions of n-terminals.

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice., 5 pages, 3 figures and a supplementary material (3 pages)

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance is that of {\em holographic symmetry}. It reflects situations wherein global symmetries become, under a duality mapping, symmetries that act solely on the system's boundary. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by systematically deriving generalized order parameters for pure and matter-coupled Abelian gauge theories, and for some models of topological matter., Comment: v2, 10 pages, 3 figures. Accepted for publication in Physical Review B Rapid Communications

Motivated by the prospect of attaining Majorana modes at the ends of nanowires, we analyze interacting Majorana systems on general networks and lattices in an arbitrary number of dimensions, and derive various universal spin duals. Such general complex Majorana architectures (other than those of simple square or other crystalline arrangements) might be of empirical relevance. As these systems display low-dimensional symmetries, they are candidates for realizing topological quantum order. We prove that (a) these Majorana systems, (b) quantum Ising gauge theories, and (c) transverse-field Ising models with annealed bimodal disorder are all dual to one another on general graphs. As any Dirac fermion (including electronic) operator can be expressed as a linear combination of two Majorana fermion operators, our results further lead to dualities between interacting Dirac fermionic systems. The spin duals allow us to predict the feasibility of various standard transitions as well as spin-glass type behavior in {\it interacting} Majorana fermion or electronic systems. Several new systems that can be simulated by arrays of Majorana wires are further introduced and investigated: (1) the {\it XXZ honeycomb compass} model (intermediate between the classical Ising model on the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice realization of the model of Xu and Moore for superconducting $(p+ip)$ arrays, and a (3) compass type two-flavor Hubbard model with both pairing and hopping terms. By the use of dualities, we show that all of these systems lie in the 3D Ising universality class. We discuss how the existence of topological orders and bounds on autocorrelation times can be inferred by the use of symmetries and also propose to engineer {\it quantum simulators} out of these Majorana networks., Comment: v3,19 pages, 18 figures, submitted to Physical Review B. 11 new figures, new section on simulating the Hubbard model with nanowire systems, and two new appendices

We have synthesized new topoogical ring-shaped and figure-8 crystals of NbSe3 grown from chemical vapor transportation. We confirm that the ring-NbSe3 is a single-phase crystal from X-ray diffraction, and that a charge-density wave (CDW) transition takes place near 140 K by observing satellites of electron diffraction peaks. The non-linear conduction due to the CDW sliding is also observed in the ring crystals. We also observed an interference effect of CDW in the sliding regime, caused by having the obvious ring-topology.

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.

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)

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.

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.

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.

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.

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.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\nu }}={{0}},\pm {{1}}$$\end{document}ν=0,±1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields., The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

Nature materials 20, 30 - 37 (2021). doi:10.1038/s41563-020-00807-1, Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states., Published by Nature Publishing Group, Basingstoke

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.

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.

We study the stability of multiple conducting edge states in a topological insulator against perturbations allowed by the time-reversal symmetry. A system is modeled as a multi-channel Luttinger liquid, with the number of channels equal to the number of Kramers doublets at the edge. Assuming strong interactions and weak disorder, we first formulate a low-energy effective theory for a clean translation invariant system and then include the disorder terms allowed by the time-reversal symmetry. In a clean system with N Kramers doublets, N − 1 edge states are gapped by Josephson couplings and the single remaining gapless mode describes collective motion of Cooper pairs synchronous across the channels. Disorder perturbation in this regime, allowed by the time reversal symmetry is a simultaneous backscattering of particles in all N channels. Its relevance depends strongly on the parity if the number of channel N is not very large. Our main result is that disorder becomes irrelevant with the increase of the number of edge modes leading to the stability of the edge states superconducting regime even for repulsive interactions.

Driving and controlling single-skyrmion motion promises skyrmion-based spintronic applications. Recently progress has been made in moving skyrmionic bubbles in thin-film heterostructures and low-temperature chiral skyrmions in the FeGe helimagnet by electric current. Here, we report the motion tracking and control of a single skyrmion at room temperature in the chiral-lattice magnet Co9Zn9Mn2 using nanosecond current pulses. We have directly observed that the skyrmion Hall motion reverses its direction upon the reversal of skyrmion topological number using Lorentz transmission electron microscopy. Systematic measurements of the single-skyrmion trace as a function of electric current reveal a dynamic transition from the static pinned state to the linear flow motion via a creep event, in agreement with the theoretical prediction. We have clarified the role of skyrmion pinning and evaluated the intrinsic skyrmion Hall angle and the skyrmion velocity in the course of the dynamic transition. Our results pave a way to skyrmion applications in spintronic devices., Skyrmions, topological spin textures, have attracted interest for use in spin-based information processing. Here, Peng et al analyse the current driven motion of a single skyrmion at room temperature in a chiral-lattice magnet, tracking the motion using Lorentz transmission electron microscopy.

Band inversions are key to stabilising a variety of novel electronic states in solids, from topological surface states in inverted bulk band gaps of topological insulators to the formation of symmetry-protected three-dimensional Dirac and Weyl points and nodal-line semimetals. Here, we create a band inversion not of bulk states, but rather between manifolds of surface states. We realise this by aliovalent substitution of Nb for Zr and Sb for S in the ZrSiS family of nonsymmorphic semimetals. Using angle-resolved photoemission and density-functional theory, we show how two pairs of surface states, known from ZrSiS, are driven to intersect each other in the vicinity of the Fermi level in NbGeSb, as well as to develop pronounced spin-orbit mediated spin splittings. We demonstrate how mirror symmetry leads to protected crossing points in the resulting spin-orbital entangled surface band structure, thereby stabilising surface state analogues of three-dimensional Weyl points. More generally, our observations suggest new opportunities for engineering topologically and symmetry-protected states via band inversions of surface states., In press at Nature Communications. This is the originally submitted manuscript prior to changes during the review process. Contains 20+6 pages, including Supplementary Information

We theoretically study chiral magnetic effect in type-II Weyl semimetals based on a concise formalism for the magnetoconductance in the semiclassical limit. Using the formula, we find that the anomaly-related current is generally dominated by the contribution from the Weyl nodes when the Fermi level is sufficiently close to the nodes. This is related to the fact that the current is proportional to the square of the Berry curvature, which enhances the contribution from the electrons around the Weyl nodes. The increase and the anisotropy of magnetoconductance induced by the tilting is also explained in a comprehensive way.

The fermionic self-energy on the surface of a topological insulator proximity coupled to ferro- and antiferromagnetic insulators is studied. An enhanced electron-magnon coupling is achieved by allowing the electrons on the surface of the topological insulator to have a different exchange coupling to the two sublattices of the antiferromagnet. Such a system is therefore seen as superior to a ferromagnetic interface for the realization of magnon-mediated superconductivity. The increased electron-magnon-coupling simultaneously increases the self-energy effects. In this paper we show how the inverse quasiparticle lifetime and energy renormalization on the surface of the topological insulator can be kept low close to the Fermi level by using a magnetic insulator with a sufficient easy-axis anisotropy. We find that the antiferromagnetic case is most interesting from both a theoretical and an experimental standpoint due to the increased electron-magnon coupling, combined with a reduced need for easy-axis anisotropy compared to the ferromagnetic case. We also consider a set of material and instrumental parameters where these self-energies should be measurable in angle-resolved photoemission spectroscopy experiments, paving the way for a measurement of the interfacial exchange coupling strength., 14 pages, 9 figures, accepted in Physical Review B

We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an effective spin model with an anisotropic Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction for a multi-band periodic Anderson model. We find that the anisotropic RKKY interaction gives rise to two distinct SkXs with different skyrmion numbers of one and two depending on a magnetic field. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a field-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd$$_2$$ 2 PdSi$$_3$$ 3 , but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets.

There is tremendous interest in measuring the strong electron–phonon interactions seen in topological Weyl semimetals. The semimetal NbIrTe4 has been proposed to be a Type-II Weyl semimetal with 8 pairs of opposite Chirality Weyl nodes which are very close to the Fermi energy. We show using polarized angular-resolved micro-Raman scattering at two excitation energies that we can extract the phonon mode dependence of the Raman tensor elements from the shape of the scattering efficiency versus angle. This van der Waals semimetal with broken inversion symmetry and 24 atoms per unit cell has 69 possible phonon modes of which we measure 19 modes with frequencies and symmetries consistent with Density Functional Theory calculations. We show that these tensor elements vary substantially in a small energy range which reflects a strong variation of the electron–phonon coupling for these modes.

A tight-binding (TB) Hamiltonian is derived for strained silicene from a multi-orbital basis. The derivation is based on the Slater–Koster coupling parameters between different orbitals across the silicene lattice and takes into account arbitrary distortion of the lattice under strain, as well as the first and second-order spin–orbit interactions (SOI). The breaking of the lattice symmetry reveals additional SOI terms which were previously neglected. As an exemplary application, we apply the linearized low-energy TB Hamiltonian to model the current-induced spin accumulation in strained silicene coupled to an in-plane magnetization. The interplay between symmetry-breaking and the additional SOI terms induces an out-of-plane spin accumulation. This spin accumulation remains unbalanced after summing over the Fermi surfaces of the occupied bands and the two valleys, and can thus be utilized for spin torque switching.

Topologically non-trivial electronic structure is a feature of many rare-earth half-Heusler alloys, which host atoms with high spin-orbit coupling bringing in the non-triviality. In this article, using the first-principles simulations, rare-earth half-Heusler YPdBi, ScPdBi, LaPdBi, LuPdBi, YPtBi and LuPtBi alloys are studied under strain to reveal multiple band inversions associated with topological phase transitions. From our simulations we find that, as a result of first band-inversion, the Brillouin zone of the diamagnetic half-Heusler alloys hosts eight triple points whereas, the second band inversion causes the emergence of sixteen more triple points. These band-inversions are observed to be independent of the spin-orbit coupling and are the reason behind increasing occupation of bismuth 7s orbitals as volume of the unit cell increases. The surface electronic transport in different triple point semi-metallic phases is found to evolve under strain, as the number of Fermi arcs change due to multiple band inversions. Once the second band inversion occurs, further application of tensile strain does not increase the number of triple points and Fermi arcs. However, increasing tensile strain (or decreasing compressive strain) pushes the triple point crossing to higher momenta, making them more effective as source of highly mobile electrons. These observations make a pathway to tune the bulk as well as surface transport through these semi-metals by application of tensile or compressive strain depending on the unstrained relative band-inversion strength of the material.

A large non-saturating magnetoresistance has been observed in several nonmagnetic topological Weyl semi-metals with high mobility of charge carriers at the Fermi energy. However, ferromagnetic systems rarely display a large magnetoresistance because of localized electrons in heavy d bands with a low Fermi velocity. Here, we report a large linear non-saturating magnetoresistance and high mobility in ferromagnetic MnBi. MnBi, unlike conventional ferromagnets, exhibits a large linear non-saturating magnetoresistance of 5000% under a pulsed field of 70 T. The electrons and holes’ mobilities are both 5000 cm2V−1s−1 at 2 K, which are one of the highest for ferromagnetic materials. These phenomena are due to the spin-polarised Bi 6p band’s sharp dispersion with a small effective mass. Our study provides an approach to achieve high mobility in ferromagnetic systems with a high Curie temperature, which is advantageous for topological spintronics., Ferromagnetic systems rarely display a large or non-saturating magnetoresistance, due to the low Fermi velocity of the predominant charge carrier. Here, the authors show that MnBi, a ferromagnet, bucks this trend, showing both large and non-saturating magnetoresistance, and high charge carrier motilities.

Topological insulators (TI) have extremely high potential in spintronic applications. Here, a topological insulators thin-film (TITF) spin valve with the use of the segment gate-controlled potential exhibits a huge magnetoresistance (MR) value higher than 1000% at room temperature which is more than 50 times the MR of typical topological insulators (TI) spin-valves. A high spin-polarized current is provided by the band structure generated by the tunable segment potential. The results reveal a very large resistance difference between the parallel and antiparallel configurations. The MR effect is strongly influenced by the thin-film thickness, the gate potential, the gate size, and the distribution. The proposed results will help to not only improve the room-temperature performance of the spin-valves but also enhance the applications of magnetic memories and spintronic devices.

The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the crystallographic orientation of the meeting edges, but also on the growth orientation of the quantum well. Our theoretical results significantly extend the application potential of topological quantum wells based on IV, II-VI and III-V semiconductors with diamond or zinc-blende structures., Comment: The main text and Supplementary Materials

The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 started the research on topological quantum states and laid the foundation of topology in physics. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). Here, we report the experimental discovery of high-Chern-number QHE (C = 2) without Landau levels and C = 1 Chern insulator state displaying a nearly quantized Hall resistance plateau above the Néel temperature in MnBi2Te4 devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures., We report the experimental discovery of high-Chern-number (C = 2) quantum Hall effect without Landau levels and C = 1 Chern insulator state above the Néel temperature in MnBi2Te4 devices.

The magneto-transport, magnetization and theoretical electronic-structure have been investigated on type-II Weyl semimetallic MoTeP. The ferromagnetic ordering is observed in the studied sample and it has been shown that the observed magnetic ordering is due to the defect states. It has also been demonstrated that the presence of ferromagnetic ordering in effect suppresses the magnetoresistance (MR) significantly. Interestingly, a change-over from positive to negative MR is observed at higher temperature which has been attributed to the dominance of spin scattering suppression.

The investigation of transport properties in normal liquid helium-3 and its topological superfluid phases provides insights into related phenomena in electron fluids, topological materials, and putative topological superconductors. It relies on the measurement of mass, heat, and spin currents, due to system neutrality. Of particular interest is transport in strongly confining channels of height approaching the superfluid coherence length, to enhance the relative contribution of surface excitations, and suppress hydrodynamic counterflow. Here we report on the thermal conduction of helium-3 in a 1.1 μm high channel. In the normal state we observe a diffusive thermal conductivity that is approximately temperature independent, consistent with interference of bulk and boundary scattering. In the superfluid, the thermal conductivity is only weakly temperature dependent, requiring detailed theoretical analysis. An anomalous thermal response is detected in the superfluid which we propose arises from the emission of a flux of surface excitations from the channel., Superfluid 3He under confinement can be used as a model system for topological quantum matter, but few related measurements are reported. Here, the authors report on the thermal conduction of helium-3 in a micro-fabricated channel with unanticipated effects in both the normal and superfluid states.

We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring the diffusive dynamics at the edges. Furthermore, we discover a novel diffusive phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $\pi$ cannot diffuse to the bulk, which is attributed to the complete localization of the edge state., Comment: 9 pages, 7 figures, a reference is added, typos are corrected

The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as α-RuCl3. Currently, two competing scenarios exist for the intermediate field phase of this compound (B = 7 − 10 T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian nature with a fractional quantum number. To discriminate between these scenarios a detailed investigation of excitations over a wide field-temperature phase diagram is essential. Here, we present Raman spectroscopic data revealing low-energy quasiparticles emerging out of a continuum of fractionalized excitations at intermediate fields, which are contrasted by conventional spin-wave excitations. The temperature evolution of these quasiparticles suggests the formation of bound states out of fractionalized excitations., α-RuCl3 has properties consistent with predictions of a phase hosting fractionalized Majorana fermions but that could also be explained by conventional magnetic excitations. Here the authors find evidence for fractionalized quasiparticles by studying magnetic excitations across the field-temperature phase diagram.

The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here we demonstrate that the thermoelectric Hall conductivity $\alpha_{xy}$ in the three-dimensional Dirac semimetal ZrTe$_5$ acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields., Comment: 17+21 pages, 3+14 figures; published version

Weyl semimetals host chiral fermions with distinct chiralities and spin textures. Optical excitations involving those chiral fermions can induce exotic carrier responses, and in turn lead to novel optical phenomena. Here, we discover strong coherent terahertz emission from Weyl semimetal TaAs, which is demonstrated as a unique broadband source of the chiral terahertz wave. The polarization control of the THz emission is achieved by tuning photoexcitation of ultrafast photocurrents via the photogalvanic effect. In the near-infrared regime, the photon-energy dependent nonthermal current due to the predominant circular photogalvanic effect can be attributed to the radical change of the band velocities when the chiral Weyl fermions are excited during selective optical transitions between the tilted anisotropic Weyl cones and the massive bulk bands. Our findings provide a design concept for creating chiral photon sources using quantum materials and open up new opportunities for developing ultrafast opto-electronics using Weyl physics., Here, the authors report photon-energy-dependent terahertz emission and ultrafast photocurrents from the Weyl semimetal, TaAs. The polarization control of the emission is achieved by excitation of the photocurrents whose direction and magnitude depend on the polarization of the femtosecond optical pulses.

We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization towards the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilting the magnetization into the interface plane favors Cooper pairs with center of mass momenta parallel to the magnetization vector, increasing $T_c$ compared to the out-of-plane case. Including the frequency dependence of the magnon propagator, and solving for a low number of Matsubara frequencies, we find that the eigenvectors of the Amperean solutions at the critical temperature are dominantly odd in frequency and even in momentum, thus opening the possibility for odd-frequency Amperean pairing., Comment: 11 pages, 8 figures, updated version

We theoretically address the impact of a random distribution of non-magnetic impurities on the surface states formed at the interface between a trivial and a topological insulator. The interaction of electrons with the impurities is accounted for by a separable pseudo-potential method that allows us to obtain closed expressions for the density of states. Spectral properties of surface states are assessed by means of the Green's function averaged over disorder realizations. For comparison purposes, the configurationally averaged Green's function is calculated by means of two different self-consistent methods, namely the self-consistent Born approximation (SCBA) and the coherent potential approximation (CPA). The latter is often regarded as the best single-site theory for the study of the spectral properties of disordered systems. However, although a large number of works employ the SCBA for the analysis of many-impurity scattering on the surface of a topological insulator, CPA studies of the same problem are scarce in the literature. In this work we find that the SCBA overestimates the impact of the random distribution of impurities on the spectral properties of surface states compared to the CPA predictions. The difference is more pronounced when increasing the magnitude of the disorder., Comment: 16 pages; 6 figures

Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called ‘Weyl points’, carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the experimental observation of ‘type-II’ Weyl points of light at optical frequencies, with the photons having a strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and observing the associated Fermi arc-like surface states. The realization of Weyl points at optical frequencies allows these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version