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The interplay of topology, magnetism, and correlations gives rise to intriguing phases of matter. In this study, through state-of-the-art angle-resolved photoemission spectroscopy, density functional theory and dynamical mean-field theory calculations, we visualize a fourfold degenerate Dirac nodal line at the boundary of the bulk Brillouin zone in the antiferromagnet YMn2Ge2. We further demonstrate that this gapless, antiferromagnetic Dirac nodal line is enforced by the combination of magnetism, space-time inversion symmetry and nonsymmorphic lattice symmetry. The corresponding drumhead surface states traverse the whole surface Brillouin zone. YMn2Ge2 thus serves as a platform to exhibit the interplay of multiple degenerate nodal physics and antiferromagnetism. Interestingly, the magnetic nodal line displays a d-orbital dependent renormalization along its trajectory in momentum space, thereby manifesting Hund coupling. Our findings offer insights into the effect of electronic correlations on magnetic Dirac nodal lines, leading to an antiferromagnetic Hund nodal line.

The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields [1-3]. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding [4-6], resulting in the conduction electrons exhibiting the topological Hall effect (THE) [7]. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated [8,9]. The resulting emergent electrodynamics dictate the magnitude of the THE via the relative motion of SkL and conduction electrons. Here, we report the emergent electrodynamics induced by SkL motion in Gd$_2$PdSi$_3$, facilitated by its giant THE [10,11]. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, where the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE can be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity-current profile, which reveals the inertial-like motion of the SkL in the creep regime, appearing as current-hysteretic behavior of the skyrmion velocity.

Engineering heterostructures with various types of quantum materials can provide an intriguing playground for studying exotic physics induced by the proximity effect. Here, we report the successful synthesis of iron-based superconductor FeSe$_{x}$Te$_{1-x}$ (FST) thin films across the entire composition range of $0 \leq x \leq 1$ and its heterostructure with a magnetic topological insulator by using molecular beam epitaxy. Superconductivity is observed in the FST films with an optimal superconducting transition temperature $T_c$ $\sim$ 12 K at around x = 0.1. We found that superconductivity survives in the very Te-rich films ($x \leq 0.05$), showing stark contrast to bulk crystals with suppression of superconductivity due to an appearance of bicollinear antiferromagnetism accompanied by a monoclinic structural transition. By examining thickness $t$ dependence of magnetic susceptibility and electrical transport properties, we observed a trend where anomalies associated with the first order structural transition broaden in films with below $t \sim$ 100 nm. We infer this observation suggests a suppression of the structural instability near substrates. Furthermore, we fabricated an all chalcogenide-based heterointerface between FST and a magnetic topological insulator (Cr,Bi,Sb)$_{2}$Te$_{3}$ for the first time, observing both superconductivity and a large anomalous Hall conductivity. The anomalous Hall conductivity increases with decreasing temperature, approaching the quantized value of $e^2/h$ down to the measurable minimum temperature at $T_c$. The result suggests coexistence of magnetic and superconducting gaps at low temperatures opening at the top and bottom surfaces, respectively. Our novel magnetic topological insulator/superconductor heterostructure could be an ideal platform to explore chiral Majorana edge mode.

The interplay between Kondo screening and magnetic interactions is central to comprehending the intricate phases in heavy-fermion compounds. However, the role of the itinerant magnetic order, which is driven by the conducting (c) electrons, has been largely uncharted in the context of heavy-fermion systems due to the scarcity of material candidates. Here we demonstrate the coexistence of the coherent Kondo screening and d-orbital ferromagnetism in material system La$_{1-x}$Ce$_x$Co$_2$As$_2$, through comprehensive thermodynamic and electrical transport measurements. Additionally, using angle-resolved photoemission spectroscopy (ARPES), we further observe the f-orbit-dominated bands near the Fermi level ($E_f$) and signatures of the f-c hybridization below the magnetic transition temperature, providing strong evidence of Kondo lattice state in the presence of ferromagnetic order. Remarkably, by changing the ratio of Ce/La, we observe a substantial enhancement of the anomalous Hall effect (AHE) in the Kondo lattice regime. The value of the Hall conductivity quantitatively matches with the first-principle calculation that optimized with our ARPES results and can be attributed to the large Berry curvature (BC) density engendered by the topological nodal rings composed of the Ce-4f and Co-3d orbitals at $E_f$. Our findings point to the realization of a new platform for exploring correlation-driven topological responses in a novel Kondo lattice environment., Comment: 4 Figs and 22 pages. This is the submitted version and the work will be presented in March meeting (section T19). All comments are welcome!

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below Tc~4.5K. Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc.These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling., Comment: accepted by PRL

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of the charge ordering and the associated structural distortion remains elusive. We discuss the structural and electronic properties of FeGe. Our proposed ground state phase accurately captures atomic topographies acquired by scanning tunneling microscopy. We show that the 2$\times$2$\times$1 CDW likely results from the Fermi surface nesting of hexagonal-prism-shaped kagome states. FeGe is found to exhibit distortions in the positions of the Ge atoms instead of the Fe atoms in the kagome layers. Using in-depth first-principles calculations and analytical modeling, we demonstrate that this unconventional distortion is driven by the intertwining of magnetic exchange coupling and CDW interactions in this kagome material. Movement of Ge atoms from their pristine positions also enhances the magnetic moment of the Fe kagome layers. Our study indicates that magnetic kagome lattices provide a material candidate for exploring the effects of strong electronic correlations on the ground state and their implications for transport, magnetic, and optical responses in materials.

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena. Here, utilizing angle-resolved photoemission spectroscopy, we demonstrate Weyl lines with strong out-of-plane dispersion in an A-A stacked kagome magnet TbxGd1-xMn6Sn6. On the Gd rich side, the Weyl line remains nearly spin-orbit-gapless due to a remarkable cooperative interplay between Kane-Mele spin-orbit-coupling, low site symmetry and in-plane magnetic order. Under Tb substitution, the kagome Weyl line gaps due to a magnetic reorientation to out-of-plane order. Our results illustrate the magnetic moment direction as an efficient tuning knob for realizing distinct three-dimensional topological phases., Comment: 12 pages, 4 figures. Comments are welcome!

Layered transition metal dichalcogenides have rich phase diagram and they feature two dimensionality on numerous physical properties. Co1/3NbS2 is one of the newest members of this family where Co atoms are intercalated into the Van der Waals gaps between NbS2 layers. We study the three-dimensional electronic band structure of Co1/3NbS2 using both surface and bulk sensitive angle-resolved photoemission spectroscopy. We show that the electronic bands do not fit into the rigid-band-shift picture after the Co intercalation. Instead, Co1/3NbS2 displays a different orbital character near the Fermi level compared to the pristine NbS2 compound and has a clear band dispersion in kz direction despite its layered structure. Our photoemission study demonstrates the out-of-plane electronic correlations introduced by the Co intercalation, thus offering a new perspective on this compound. Finally, we propose how Fermi level tuning could lead to exotic phases such as spin density wave instability., Comment: Accepted by Physical Review B

The intersections of topology, geometry and strong correlations offer many opportunities for exotic quantum phases to emerge in condensed matter systems. Weyl fermions, in particular, provide an ideal platform for exploring the dynamical instabilities of single-particle physics under interactions. Despite its fundamental role in relativistic field theory, the concept of causality and the associated spacetime light cone and event horizon has not been considered in connection with interacting Weyl fermionic excitations in quantum matter. Here, by using charge-density wave (CDW) as an example, we unveil the behavior of interacting Weyl fermions and show that a Weyl fermion in a system can open a band gap by interacting only with other Weyl fermions that lie within its energy-momentum dispersion cone. In this sense, causal connections or interactions are only possible within overlapping dispersion cones and each dispersion cone thus constitutes a solid-state analogue of the more conventional `event horizon' of high-energy physics. Our study provides a universal framework for considering interacting relativistic quasiparticles in condensed matter by separating them into energy-like and momentum-like relationships in analogy with the time-like and space-like events in high-energy physics. Finally, we consider two different candidate materials for hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study greatly enriches the phenomenology and unveils new connections between condensed matter and high-energy physics.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids, magnets, the quantum Hall effect, topological insulators, Weyl semimetals and other phenomena. Here we report a remarkable linking number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's bulk Brillouin zone three-torus, $\mathbb{T}^3$. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits linking number $(2,2,2)$, providing a direct determination of the invariant structure from the experimental data. On the surface of our samples, we further predict and observe Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of exotic properties of quantum matter., Comment: See popular summary at https://research.princeton.edu/news/electrons-crystal-exhibit-linked-and-knotted-quantum-twists

Van Hove singularity are electronic instabilities that lead to many fascinating interactions, such as superconductivity and charge-density waves. And despite much interest, the nexus of emergent correlation effects from van Hove singularities and topological states of matter remains little explored in experiments. By utilizing synchrotron-based angle-resolved photoemission spectroscopy and Density Functional Theory, here we provide the first discovery of the helicoid quantum nature of topological Fermi arcs inducing van Hove singularities. In particular, in topological chiral conductors RhSi and CoSi we directly observed multiple types of inter- and intra-helicoid-arc mediated singularities, which includes the type-I and type-II van Hove singularity. We further demonstrate that the energy of the helicoid-arc singularities are easily tuned by chemical engineering. Taken together, our work provides a promising route to engineering new electronic instabilities in topological quantum materials.

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co$_3$Sn$_2$S$_2$, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters., Comment: Accepted version. Comments welcome! Early version of this manuscript first submitted in January 2020. See also: arXiv:2005.02400, Co3Sn2S2

Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin-orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk-boundary correspondence giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and of Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss some of the exotic optical and magnetic responses observed in these materials, as well as the progress in developing some of the related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl-line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities., Comment: To appear in Nature Review Materials

Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2x2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2x2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. At impurity-pinning free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral CDW in the frustrated kagome lattice, which can not only lead to large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity., Comment: Orbital magnetism calculation added

Topological phases of matter have established a new paradigm in physics, bringing quantum phenomena to the macroscopic scale and hosting exotic emergent quasiparticles. In this thesis, I theoretically and experimentally demonstrate with my collaborators the first Weyl semimetal, TaAs, using angle-resolved photoemission spectroscopy (ARPES), directly observing its emergent Weyl fermions and topological Fermi arc surface states [Science 349, 6248 (2015); Nat. Commun. 6, 7373 (2015); PRL 116, 066802 (2016)]. Next, I discover high-degeneracy topological chiral fermions in the chiral crystals RhSi and CoSi, with wide topological energy window, maximal separation in momentum space and giant Fermi arcs [Nature 567, 500 (2019); Nat. Mat. 17, 978 (2018)]. I establish a natural relationship between the structural and topological chirality, associated with a robust topological state which we predict supports a four-unit quantized photogalvanic effect [PRL 119, 206401 (2017)]. I also discuss the first quantum topological superlattice, in multilayer heterostructures consisting of alternating topological and trivial insulators [Sci. Adv. 3, e1501692 (2017)]. The Dirac cones at each interface tunnel across layers, forming an emergent atomic chain where the Dirac cones serve as atomic orbitals. I achieve unprecedented control of hopping amplitudes within the superlattice, realizing a topological phase transition. Lastly, I discover a room-temperature topological magnet in Co$_2$MnGa [Science 365, 1278 (2019); PRL 119, 156401 (2017)]. I observe topological Weyl lines and drumhead surface states by ARPES, demonstrating a topological invariant supported by the material's intrinsic magnetic order. I also find that the large anomalous Hall effect in Co$_2$MnGa arises from the Weyl lines. I hope that my discovery of Co$_2$MnGa establishes topological magnetism as a new frontier in condensed matter physics., Comment: Ph.D. Thesis. Based on arXiv:1502.03807, arXiv:1501.00755, arXiv:1703.04537, arXiv:1601.04327, arXiv:1509.07465, arXiv:1604.07079, arXiv:1512.09099, arXiv:1612.05990, arXiv:1610.02013, arXiv:1812.04466, arXiv:1712.09992 and arXiv:2004.00004. Available at http://arks.princeton.edu/ark:/88435/dsp01zs25xc34m

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets., Comment: To appear in Nature Communications (2020), both experiment and theory included. arXiv admin note: text overlap with arXiv:2002.11783

Characterized by the absence of inversion symmetry, non-centrosymmetric materials are of great interest because they exhibit ferroelectricity, second harmonic generation, emergent Weyl fermions, and other fascinating phenomena. It is expected that if time-reversal symmetry is also broken, additional magneto-electric effects can emerge from the interplay between magnetism and electronic order. Here we report topological conducting properties in the non-centrosymmetric magnet PrAlGe. By photoemission spectroscopy, we observe an arc parametrizing surface-localized states---a topological arc. Using the bulk-boundary correspondence, we conclude that these arcs correspond to projected topological charges of $\pm{1}$ in the surface Brillouin zone, demonstrating the presence of magnetic Weyl quasiparticles in bulk. We further observe a large anomalous Hall response, arising from diverging bulk Berry curvature fields associated with the magnetic Weyl band structure. Our results demonstrate a topological phase with robust electronic surface states and anomalous transport in a non-centrosymmetric magnet for the first time, providing a novel material platform to study the interplay between magnetic order, band topology and transport., Comment: To appear in Nature Communications (2020)

The quantum level interplay between geometry, topology, and correlation is at the forefront of fundamental physics. Owing to the unusual lattice geometry and breaking of time-reversal symmetry, kagome magnets are predicted to support intrinsic Chern quantum phases. However, quantum materials hosting ideal spin-orbit coupled kagome lattices with strong out-of-plane magnetization have been lacking. Here we use scanning tunneling microscopy to discover a new topological kagome magnet TbMn6Sn6, which is close to satisfying the above criteria. We visualize its effectively defect-free purely Mn-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state exhibits distinct Landau quantization upon the application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, opening up an avenue for discovering topological quantum phenomena in the RMn6Sn6 (R = rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real and momentum space demonstrates a proof-of-principle method revealing topological magnets., Comment: To appear in Nature (2020)

Three types of fermions have been extensively studied in topological quantum materials: Dirac, Weyl, and Majorana fermions. Beyond the fundamental fermions in high energy physics, exotic fermions are allowed in condensed matter systems residing in three-, six- or eightfold degenerate band crossings. Here, we use angle-resolved photoemission spectroscopy to directly visualize three-doubly-degenerate bands in PdSb$_2$. The ultrahigh energy resolution we are able to achieve allows for the confirmation of all the sixfold degenerate bands at the R point, in remarkable consistency with first-principles calculations. Moreover, we find that this sixfold degenerate crossing has quadratic dispersion as predicted by theory. Finally, we compare sixfold degenerate fermions with previously confirmed fermions to demonstrate the importance of this work: our study indicates a topological fermion beyond the constraints of high energy physics.

The search for novel topological phases of matter in quantum magnets has emerged as a frontier of condensed matter physics. Here we use state-of-the-art angle-resolved photoemission spectroscopy (ARPES) to investigate single crystals of Co$_3$Sn$_2$S$_2$ in its ferromagnetic phase. We report for the first time signatures of a topological Weyl loop. From fundamental symmetry considerations, this magnetic Weyl loop is expected to be gapless if spin-orbit coupling (SOC) is strictly zero but gapped, with possible Weyl points, under finite SOC. We point out that high-resolution ARPES results to date cannot unambiguously resolve the SOC gap anywhere along the Weyl loop, leaving open the possibility that Co$_3$Sn$_2$S$_2$ hosts zero Weyl points or some non-zero number of Weyl points. On the surface of our samples, we further observe a possible Fermi arc, but we are unable to clearly verify its topological nature using the established counting criteria. As a result, we argue that from the point of view of photoemission spectroscopy the presence of Weyl points and Fermi arcs in Co$_3$Sn$_2$S$_2$ remains ambiguous. Our results have implications for ongoing investigations of Co$_3$Sn$_2$S$_2$ and other topological magnets., Comment: Co3Sn2S2; comments welcome. Manuscript unchanged, updated comment: companion paper to arXiv:2105.14034, which is published as Phys. Rev. Lett. 127, 256403 (2021) at https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.256403

Known topological quantum matter, including topological insulators and Dirac/Weyl semimetals, often hosts robust boundary states in the gaps between bulk bands in energy-momentum space. Beyond one-gap systems, quantum crystals may also feature more than one inter-band gap. The manifestation of higher-fold topology with multiple nontrivial gaps in quantum materials remains elusive. In this work, we leverage a photoemission spectroscopy probe to discover the multi-gap topology of a chiral fermion material. We identify two sets of chiral surface states. These Fermi arcs exhibit an emergent ladder structure in energy-momentum space, unprecedented in topological materials. Furthermore, we determine the multi-gap chiral charge $\textbf{C}=(2,2)$. Our results provide a general framework to explore future complex topological materials.

Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co$_2$MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in our samples. Our experimental results suggest a rich interplay of strongly correlated electrons and topology in this quantum magnet., Comment: Incorporates arXiv:1712.09992, with additional data, analysis and discussion

Quantum states induced by single-atomic-impurities are the current frontier of material and information science. Recently the spin-orbit coupled correlated kagome magnets are emerging as a new class of topological quantum materials, although the effect of single-atomic impurities remains unexplored. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy (STM/S) to study the atomic indium impurity in a topological kagome magnet Co3Sn2S2, which is designed to support the spin-orbit quantum state. We find each impurity features a strongly localized bound state. Our systematic magnetization-polarized tunneling probe reveals its spin-down polarized nature with an unusual moment of -5uB, indicative of additional orbital magnetization. As the separation between two impurities progressively shrinks, their respective bound states interact and form quantized molecular orbital states. The molecular orbital of three neighboring impurities further exhibits an intriguing splitting owing to the combination of geometry, magnetism, and spin-orbit coupling, analogous to the splitting of the topological Weyl fermion line12,19. Our work demonstrates the quantum-level interplay between magnetism and spin-orbit coupling at an individual atomic impurity, which provides insights into the emergent impurity behavior in a topological kagome magnet and the potential of spin-orbit quantum impurities for information science.

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this work, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe$_2$. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states as a new platform for exploring Majorana zero modes and quantum information science under field-free conditions., Comment: 11 pages, 3 figures

The interplay between unconventional Cooper pairing and quantum states associated with atomic scale defects is a frontier of research with many open questions. So far, only a few of the high-temperature superconductors allow this intricate physics to be studied in a widely tunable way. We use scanning tunneling microscopy (STM) to image the electronic impact of Co atoms on the ground state of the LiFe$_{1-x}$Co$_x$As system. We observe that impurities progressively suppress the global superconducting gap and introduce low energy states near the gap edge, with the superconductivity remaining in the strong-coupling limit. Unexpectedly, the fully opened gap evolves into a nodal state before the Cooper pair coherence is fully destroyed. Our systematic theoretical analysis shows that these new observations can be quantitatively understood by the nonmagnetic Born-limit scattering effect in a s$\pm$-wave superconductor, unveiling the driving force of the superconductor to metal quantum phase transition., Comment: 22 pages, 12 figures, includes Supplementary Materials. To appear in Phys. Rev. Lett

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on the optical effects from bulk states only, disregarding topological surface responses. Here we propose a new (hitherto unknown) surface-only topological photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the topologically robust photocurrents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photocurrents can be perpendicular to the bulk injection currents regardless of the choice of materials' surface. We then generalize this finding to all cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline-symmetry can be used to induce universal topological responses as well as making it possible to completely disentangle bulk and surface topological responses in many conducting material families.

We survey the electrical transport properties of the single-crystalline, topological chiral semimetal CoSi which was grown via different methods. High-quality CoSi single crystals were found in the growth from tellurium solution. The sample's high carrier mobility enables us to observe, for the first time, quantum oscillations (QOs) in its thermoelectrical signals. Our analysis of QOs reveals two spherical Fermi surfaces around the R point in the Brillouin zone corner. The extracted Berry phases of these electron orbits are consistent with the -2 chiral charge as reported in DFT calculations. Detailed analysis on the QOs reveals that the spin-orbit coupling induced band-splitting is less than 2 meV near the Fermi level, one order of magnitude smaller than our DFT calculation result. We also report the phonon-drag induced large Nernst effect in CoSi at intermediate temperatures.

It has long been speculated that electronic flat band systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity. Although flat bands are known to exist in a few systems such as heavy fermion materials and twisted bilayer graphene, their microscopic roles and underlying mechanisms in generating emergent behavior remain elusive. Here we use scanning tunneling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flat band. Increasing magnetic field up to +-8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spin-orbit coupled flat band. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flat band superconductivity and anomalous quantum transport., Comment: Nature Physics online

The quantum behaviour of electrons in materials lays the foundation for modern electronic and information technology. Quantum materials with novel electronic and optical properties have been proposed as the next frontier, but much remains to be discovered to actualize the promise. Here we report the first observation of topological quantum properties of chiral crystals in the RhSi family. We demonsrate that this material hosts novel phase of matter exhibiting nearly ideal topological surface properties that emerge as a consequence of the crystals' structural chirality or handedness. We also demonstrate that the electrons on the surface of this crystal show a highly unusual helicoid structure that spirals around two high-symmetry momenta signalling its topological electronic chirality. Such helicoid Fermi arcs on the surface experimentally characterize the topological charges of $\pm{2}$, which arise from the bulk chiral fermions. The existence of bulk high-fold degenerate fermions are guaranteed by the crystal symmetries, however, in order to determine the topological charge in the chiral crystals it is essential to identify and study the helical arc states. Remarkably, these topological conductors we discovered exhibit helical Fermi arcs which are of length $\pi$, stretching across the entire Brillouin zone and orders of magnitude larger than those found in all known Weyl semimetals. Our results demonstrate novel electronic topological state of matter on a structurally chiral crystal featuring helicoid Fermi arc surface states. The exotic electronic chiral fermion state realised in these materials can be used to detect a quantised photogalvanic optical response or the chiral magnetic effect and its optical version in future devices as described by G. Chang \textit{et.al.,} `Topological quantum properties of chiral crystals' Nature Mat. 17, 978-985 (2018)., Comment: 28 pages, 12 figures

Owing to the unusual geometry of kagome lattices-lattices made of corner-sharing triangles-their electrons are useful for studying the physics of frustrated, correlated and topological quantum electronic states. In the presence of strong spin-orbit coupling, the magnetic and electronic structures of kagome lattices are further entangled, which can lead to hitherto unknown spin-orbit phenomena. Here we use a combination of vector-magnetic-field capability and scanning tunnelling microscopy to elucidate the spin-orbit nature of the kagome ferromagnet Fe3Sn2 and explore the associated exotic correlated phenomena. We discover that a many-body electronic state from the kagome lattice couples strongly to the vector field with three-dimensional anisotropy, exhibiting a magnetization-driven giant nematic (two-fold-symmetric) energy shift. Probing the fermionic quasi-particle interference reveals consistent spontaneous nematicity-a clear indication of electron correlation-and vector magnetization is capable of altering this state, thus controlling the many-body electronic symmetry. These spin-driven giant electronic responses go well beyond Zeeman physics and point to the realization of an underlying correlated magnetic topological phase. The tunability of this kagome magnet reveals a strong interplay between an externally applied field, electronic excitations and nematicity, providing new ways of controlling spin-orbit properties and exploring emergent phenomena in topological or quantum materials., Comment: Nature, online (2018)

We utilize a combination of vector magnetic field and scanning tunneling microscopy to elucidate the 3D field-based electronic phase diagram of a correlated iron-based superconductor, LiFeAs. We observe, under a zero-field-cooled method, an ordered hexagonal vortex lattice ground-state in contrast to the disordered lattice observed under a field-cooled method. It transforms into a four-fold-symmetric state by increasing c-axis field and distorts elliptically upon tilting the field in-plane. The vortex lattice transformations correlate with the field dependent superconducting gap that characterizes the Cooper pairing strength. The anisotropy of the vortex lattice agrees with the field enhanced Bogoliubov quasiparticle scattering channel that is determined by the pairing symmetry with respect to its Fermi surface structure. Our systematic tuning of the vortex lattice symmetry and study of its correlation with Cooper pairing demonstrates the many-body interplay between the superconducting order parameter and emergent vortex matter.

We use photoemission spectroscopy to discover the first topological magnet in three dimensions, the material Co$_2$MnGa.

Topological semimetals can be classified by the connectivity and dimensionality of the band cross- ing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimet- al are 0D points, whereas the band crossings of a nodal-line semimetal are 1D closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topolog- ical surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified., Comment: 5 pages, 4 figures; Related papers at http://physics.princeton.edu/zahidhasangroup/index_CC.html

The experimental discovery of the topological Dirac semimetal establishes a platform to search for various exotic quantum phases in real materials. ZrSiS-type materials have recently emerged as topological nodal-line semimetals where gapped Dirac-like surface states are observed. Here, we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of ZrGeTe, a nonsymmorphic symmetry protected Dirac semimetal. We observe two Dirac-like gapless surface states at the same $\bar X$ point of the Brillouin zone. Our theoretical analysis and first-principles calculations reveal that these are protected by crystalline symmetry. Hence, ZrGeTe appears as a rare example of a naturally fine tuned system where the interplay between symmorphic and non-symmorphic symmetry leads to rich phenomenology, and thus opens for opportunities to investigate the physics of Dirac semimetallic and topological insulating phases realized in a single material., Comment: 20 pages, 7 figures

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbPs (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions, and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbPs already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology.