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Chiral magnets have garnered significant interest due to the emergence of unique phenomena prohibited in inversion-symmetric magnets. While the equilibrium characteristics of chiral magnets have been extensively explored through the Dzyaloshinskii-Moriya interaction (DMI), non-equilibrium properties like magnetic damping have received comparatively less attention. We present the inaugural direct observation of chiral damping through Brillouin light scattering (BLS) spectroscopy. Employing BLS spectrum analysis, we independently deduce the Dzyaloshinskii-Moriya interaction (DMI) and chiral damping, extracting them from the frequency shift and linewidth of the spectrum peak, respectively. The resulting linewidths exhibit clear odd symmetry with respect to the magnon wave vector, unambiguously confirming the presence of chiral damping. Our study introduces a novel methodology for quantifying chiral damping, with potential ramifications on diverse nonequilibrium phenomena within chiral magnets.

Ambient magnetic skyrmions stabilized in multilayer nanostructures are of immense interest due to their relevance to magnetic tunnel junction (MTJ) devices for memory and unconventional computing applications. However, existing skyrmionic nanostructures built using conventional metallic or oxide multilayer nanodots are unable to concurrently fulfill the requirements of nanoscale skyrmion stability and feasibility of all-electrical readout and manipulation. Here, we develop a few-repeat hybrid multilayer platform consisting of metallic [Pt/CoB/Ir]3 and oxide [Pt/CoB/MgO] components that are coupled to evolve together as a single, composite stack. Zero-field (ZF) skyrmions with sizes as small as 50 nm are stabilized in the hybrid multilayer nanodots, which are smoothly modulated by up to 2.5x by varying CoB thickness and dot sizes. Meanwhile, skyrmion multiplets are also stabilized by small bias fields. Crucially, we observe higher order 'target' skyrmions with varying magnetization rotations in moderately-sized, low anisotropy nanodots. These results provide a viable route to realize long-sought skyrmionic MTJ devices and new possibilities for multi-state skyrmionic device concepts.

The interplay of magnetic interactions in chiral multilayer films gives rise to nanoscale topological spin textures, which form attractive elements for next-generation computing. Quantifying these interactions requires several specialized, time-consuming, and resource-intensive experimental techniques. Imaging of ambient domain configurations presents a promising avenue for high-throughput extraction of the parent magnetic interactions. Here we present a machine learning-based approach to determine the key interactions -- symmetric exchange, chiral exchange, and anisotropy -- governing chiral domain phenomenology in multilayers. Our convolutional neural network model, trained and validated on over 10,000 domain images, achieved $R^2 > 0.85$ in predicting the parameters and independently learned physical interdependencies between them. When applied to microscopy data acquired across samples, our model-predicted parameter trends are consistent with independent experimental measurements. These results establish ML-driven techniques as valuable, high-throughput complements to conventional determination of magnetic interactions, and serve to accelerate materials and device development for nanoscale electronics., Comment: 7 pages, 6 figures

Topological spin textures such as magnetic skyrmions hold considerable promise as robust, nanometre-scale, mobile bits for sustainable computing. A longstanding roadblock to unleashing their potential is the absence of a device enabling deterministic electrical readout of individual spin textures. Here we present the wafer-scale realization of a nanoscale chiral magnetic tunnel junction (MTJ) hosting a single, ambient skyrmion. Using a suite of electrical and multi-modal imaging techniques, we show that the MTJ nucleates skyrmions of fixed polarity, whose large readout signal - 20-70% relative to uniform states - corresponds directly to skyrmion size. Further, the MTJ exploits complementary mechanisms to stabilize distinctly sized skyrmions at zero field, thereby realizing three nonvolatile electrical states. Crucially, it can write and delete skyrmions using current densities 1,000 times lower than state-of-the-art. These results provide a platform to incorporate readout and manipulation of skyrmionic bits across myriad device architectures, and a springboard to harness chiral spin textures for multi-bit memory and unconventional computing., Comment: 8 pages, 5 figures

Magnetic skyrmions have emerged as promising elements for encoding information towards biomimetic computing applications due to their pseudoparticle nature and efficient coupling to spin currents. A key hindrance for skyrmionic devices is their instability against elongation at zero magnetic field (ZF). Prevailing materials approaches focussed on tailoring skyrmion energetics have found ZF configurations to be highly sensitive, which imposes significant growth constraints and limits their device scalability. Here we propose that designer ZF skyrmion configurations can be robustly stabilized within chiral multilayer stacks by exploiting a duet of interlayer exchange couplings (IECs). Microscopic imaging experiments show that varying the two IECs enables the coarse and fine-tuning of ZF skyrmion stability and density. Micromagnetic simulations reveal that the duo-IEC approach is distinguished by its influence on the kinetics of skyrmion nucleation, in addition to the ability to tailor energetics, resulting in a substantially expanded parameter space, and enhanced stability for individual ZF skyrmions. Our work underscores the importance of IEC as a means of stabilizing and controlling ZF skyrmions, paving the way to scalable skyrmion-based devices.

The realization of chiral spin textures - comprising myriad distinct, nanoscale arrangements of spins with topological properties - has established pathways for engineering robust, energy-efficient and scalable elements for non-volatile nanoelectronics. Particularly, current-induced manipulation of spin textures in nanowire racetracks and tunnel junction based devices are actively investigated for applications in memory, logic and unconventional computing. In this article, we paint a background on the progress of spin textures, as well as the relevant state-of-the-art techniques used for their development. In particular, we clarify the competing energy landscape of chiral spin textures, such as skyrmions and chiral domain walls, to tune their size, density and zero-field stability. Next, we discuss the spin texture phenomenology and their response to extrinsic factors arising from geometric constraints, inter-wire interactions and thermal-electrical effects. Finally, we reveal promising chiral spintronic memory and neuromorphic devices, and discuss emerging material and device engineering opportunities., Comment: 12 pages, 5 figures

Controllable writing and deleting of nanoscale magnetic skyrmions are key requirements for their use as information carriers for next-generation memory and computing technologies. While several schemes have been proposed, they require complex fabrication techniques or precisely tailored electrical inputs, which limits their long-term scalability. Here we demonstrate an alternative approach for writing and deleting skyrmions using conventional electrical pulses within a simple, two-terminal wire geometry. X-ray microscopy experiments and micromagnetic simulations establish the observed skyrmion creation and annihilation as arising from Joule heating and Oersted field effects of the current pulses, respectively. The unique characteristics of these writing and deleting schemes, such as spatial and temporal selectivity, together with the simplicity of the 2-terminal device architecture, provide a flexible and scalable route to the viable applications of skyrmions., Comment: Merged Manuscript & Supplementary Information

Magnetic skyrmions form in chiral multilayers from the shrinking or fission of elongated stripe textures. Here we report an experimental and theoretical study of the temperature dependence of this stripe-to-skyrmion transition in Co/Pt-based multilayers. Field-reversal magnetometry and Lorentz microscopy experiments over 100 - 350 K establish the increased efficacy of stripe-to-skyrmion fission at higher temperatures - driven primarily by the thermal evolution of key magnetic interactions - thereby enhancing skyrmion density. Atomistic calculations elucidate that the energy barrier to fission governs the thermodynamics of the skyrmion formation. Our results establish a mechanistic picture of the stripe-to-skyrmion transition and advance the use of thermal knobs for efficient skyrmion generation., Comment: 11 pages, 11 figures

Magnetic skyrmions are topologically wound nanoscale textures of spins whose ambient stability and electrical manipulation in multilayer films have led to an explosion of research activities. While past efforts focused predominantly on isolated skyrmions, recently ensembles of chiral spin textures, consisting of skyrmions and magnetic stripes, were shown to possess rich interactions with potential for device applications. However, several fundamental aspects of chiral spin texture phenomenology remain to be elucidated, including their domain wall structure, thermodynamic stability, and morphological transitions. Here we unveil the evolution of these textural characteristics on a tunable multilayer platform - wherein chiral interactions governing spin texture energetics can be widely varied - using a combination of full-field electron and soft X-ray microscopies with numerical simulations. With increasing chiral interactions, we demonstrate the emergence of N\'eel helicity, followed by a marked reduction in domain compressibility, and finally a transformation in the skyrmion formation mechanism. Together with an analytical model, these experiments establish a comprehensive microscopic framework for investigating and tailoring chiral spin texture character in multilayer films.

The symmetric (Heisenberg) exchange interaction is fundamental to magnetism and assumes critical importance in designing magnetic materials for novel emergent phenomena and device applications. However, quantifying exchange is extremely challenging for ultrathin ($\sim$ 1 nm) magnetic films, as techniques and approximations reliably used for bulk materials are largely inapplicable in the two-dimensional (2D) limit. Here we present and contrast the measurement of exchange stiffness, $A$, by several methods on a series of five Co/Pt-based ultrathin ($1-2$ nm) films. We compare results from (a) spin-wave spectroscopy by Brillouin light scattering (BLS), (b) three analytical models describing the temperature dependence of magnetization obtained by magnetometry, (c) microscopic domain periodicity measurements and simulations, and (d) ab initio density functional theory (DFT) calculations. While different methods present some qualitatively consistent trends across samples, we note, for any given sample, considerable differences (up to $5\times$) in the absolute values of $A$ across the techniques, consistent with discrepancies of $A$ reported in literature for nominally similar samples. We analyze possible sources of the discrepancies across various methods, notably including their relationship to the spin-wave dispersion, and the wave-vector ranges probed. We compare the strengths and limitations of the techniques, and outline directions for their future use in characterizing exchange interactions in ultrathin films., Comment: 14 pages, 9 figures

We examine the atomic intermixing phenomenon in three distinct amorphous CoB-based multilayer thin film platforms - Pt/CoB/Ir, Ir/CoB/Pt and Pt/CoB/MgO - which are shown to stabilise room-temperature chiral magnetic textures. Intermixing occurs predominantly between adjacent metallic layers. Notably, it is stack-order dependent, and particularly extensive when Ir sits atop CoB. Intermixing induced variations in magnetic properties are ascribed to the formation of magnetic dead layer arising from CoIr alloying in the metallic stacks. It also produces systematic variations in saturation magnetization, by as much as 30%, across stacks. Crucially, the resulting crossover CoB thickness for the transition from perpendicular to in-plane magnetic anisotropy differs by more than 2x across the stacks. Finally, with thermal annealing treatment over moderate temperatures of 150-300 degree Celsius, the magnetic anisotropy increases monotonically across all stacks, coupled with discernibly larger Hc for the metallic stacks. These are attributed to thermally induced CoPt alloying and MgO crystallization in the metallic and oxide stacks, respectively. Remarkably, the CoB in the Pt/CoB/MgO stacks retains its amorphous nature after annealing. Our results set the stage for harnessing the collective attributes of amorphous CoB-based material platforms and associated annealing processes for modulating magnetic interactions, enabling the tuning of chiral magnetic texture properties in ambient conditions., Comment: Supplementary information included

Magnetic skyrmions are nanoscale spin textures touted as next-generation computing elements. When subjected to lateral currents, skyrmions move at considerable speeds. Their topological charge results in an additional transverse deflection known as the skyrmion Hall effect (SkHE). While promising, their dynamic phenomenology with current, skyrmion size, geometric effects and disorder remain to be established. Here we report on the ensemble dynamics of individual skyrmions forming dense arrays in Pt/Co/MgO wires by examining over 20,000 instances of motion across currents and fields. The skyrmion speed reaches 24 m/s in the plastic flow regime and is surprisingly robust to positional and size variations. Meanwhile, the SkHE saturates at $\sim 22^\circ$, is substantially reshaped by the wire edge, and crucially increases weakly with skyrmion size. Particle model simulations suggest that the SkHE size dependence - contrary to analytical predictions - arises from the interplay of intrinsic and pinning-driven effects. These results establish a robust framework to harness SkHE and achieve high-throughput skyrmion motion in wire devices., Comment: v1 with supplementary information

Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting, and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of $1T$-VSe$_2$. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe$_2$ largely retains the bulk electronic structure, hosting a tri-directional CDW. However, monolayer VSe$_2$ -- consistently across distinct substrates -- exhibits a dimensional crossover, hosting two CDWs with distinct wavelengths and transition temperatures. Electronic structure calculations reveal that while one CDW is bulk-like and arises from the well-known Peierls mechanism, the other is decidedly unconventional. The observed CDW-lattice decoupling and the emergence of a flat band suggest that the new CDW could arise from enhanced electron-electron interactions in the 2D limit. These findings establish monolayer-VSe$_2$ as a host of coexisting charge orders with distinct origins, and enable the tailoring of electronic phenomena via emergent interactions in 2D materials., Comment: 8 pages, 5 figures

Competing interactions produce finite-size textures in myriad condensed matter systems, typically forming elongated stripe or round bubble domains. Transitions between stripe and bubble phases, driven by field or temperature, are expected to be reversible in nature. Here we report on the distinct character of the analogous transition for nanoscale spin textures in chiral Co/Pt-based multilayer films, known to host N\'{e}el skyrmions, using microscopy, magnetometry, and micromagnetic simulations. Upon increasing field, individual stripes fission into multiple skyrmions, and this transition exhibits a macroscopic signature of irreversibility. Crucially, upon field reversal, the skyrmions do not fuse back into stripes, with many skyrmions retaining their morphology down to zero field. Both the macroscopic irreversibility and the microscopic zero-field skyrmion density are governed by the thermodynamic material parameter determining chiral domain stability. These results establish the thermodynamic and microscopic framework underlying ambient skyrmion generation and stability in chiral multilayer films and provide immediate directions for their functionalization in devices., Comment: v1 with supplementary materials

Scanning diamond magnetometers based on the optically detected magnetic resonance of the nitrogen-vacancy centre offer very high sensitivity and non-invasive imaging capabilities when the stray fields emanating from ultrathin magnetic materials are sufficiently low (< 10 mT). Beyond this low-field regime, the optical signal quenches and a quantitative measurement is challenging. While the field-dependent NV photoluminescence can still provide qualitative information on magnetic morphology, this operation regime remains unexplored particularly for surface magnetisation larger than $\sim$ 3 mA. Here, we introduce a multi-angle reconstruction technique (MARe) that captures the full nanoscale domain morphology in all magnetic-field regimes leading to NV photoluminescence quench. To demonstrate this, we use [Ir/Co/Pt]$_{14}$ multilayer films with surface magnetisation an order of magnitude larger than previous reports. Our approach brings non-invasive nanoscale magnetic field imaging capability to the study of a wider pool of magnetic materials and phenomena.

The long-sought Majorana fermion is expected to manifest in a topological-superconductor heterostructure as a zero bias conductance peak (ZBCP). As one promising platform for such heterostructures, we investigate the cleaved surface of the topological semimetal Sb(111) using scanning tunneling microscopy and spectroscopy. Remarkably, we find a robust ZBCP on some terraces of the cleaved surface, although no superconductor is present. Using quasiparticle interference imaging, Landau level spectroscopy and density functional theory, we show that the ZBCP originates from a van Hove singularity pushed up to the Fermi level by a sub-surface stacking fault. Amidst the sprint to stake claims on new Majorana fermion systems, our finding highlights the importance of using a local probe together with detailed modeling to check thoroughly for crystal imperfections that may give rise to a trivial ZBCP unrelated to Majorana physics., Comment: 10 pages, 8 figures

Strongly correlated topological surface states are promising platforms for next-generation quantum applications, but they remain elusive in real materials. The correlated Kondo insulator SmB$_6$ is one of the most promising candidates, with theoretically predicted heavy Dirac surface states supported by transport and scanning tunneling microscopy (STM) experiments. However, a puzzling discrepancy appears between STM and angle-resolved photoemission (ARPES) experiments on SmB$_6$. Although ARPES detects spin-textured surface states, their velocity is an order of magnitude higher than expected, while the Dirac point -- the hallmark of any topological system -- can only be inferred deep within the bulk valence band. A significant challenge is that SmB$_6$ lacks a natural cleavage plane, resulting in ordered surface domains limited to 10s of nanometers. Here we use STM to show that surface band bending can shift energy features by 10s of meV between domains. Starting from our STM spectra, we simulate the full spectral function as an average over multiple domains with different surface potentials. Our simulation shows excellent agreement with ARPES data, and thus resolves the apparent discrepancy between large-area measurements that average over multiple band-shifted domains and atomically-resolved measurements within a single domain.

Magnetic skyrmions are nanoscale spin structures recently discovered at room temperature (RT) in multilayer films. Employing their novel topological properties towards exciting technological prospects requires a mechanistic understanding of the excitation and relaxation mechanisms governing their stability and dynamics. Here we report on the magnetization dynamics of RT N\'eel skyrmions in Ir/Fe/Co/Pt multilayer films. We observe a ubiquitous excitation mode in the microwave absorption spectrum, arising from the gyrotropic resonance of topological skyrmions, and robust over a wide range of temperatures and sample compositions. A combination of simulations and analytical calculations establish that the spectrum is shaped by the interplay of interlayer and interfacial magnetic interactions unique to multilayers, yielding skyrmion resonances strongly renormalized to lower frequencies. Our work provides fundamental spectroscopic insights on the spatiotemporal dynamics of topological spin structures, and crucial directions towards their functionalization in nanoscale devices.

Magnetic skyrmions are chiral spin structures that have recently been observed at room temperature (RT) in multilayer thin films. Their topological stability should enable high scalability in confined geometries - a sought-after attribute for device applications. While umpteen theoretical predictions have been made regarding the phenomenology of sub-100 nm skyrmions confined in dots, in practice their formation in the absence of an external magnetic field and evolution with confinement remain to be established. Here we demonstrate the confinement-induced stabilization of sub-100 nm RT skyrmions at zero field (ZF) in Ir/Fe(x)/Co(y)/Pt nanodots over a wide range of magnetic and geometric parameters. The ZF skyrmion size can be as small as ~50 nm, and varies by a factor of 4 with dot size and magnetic parameters. Crucially, skyrmions with varying thermodynamic stability exhibit markedly different confinement phenomenologies. These results establish a comprehensive foundation for skyrmion phenomenology in nanostructures, and provide immediate directions for exploiting their properties in nanoscale devices.

Skyrmions are topologically protected, two-dimensional, localized hedgehogs and whorls of spin. Originally invented as a concept in field theory for nuclear interactions, skyrmions are central to a wide range of phenomena in condensed matter. Their realization at room temperature (RT) in magnetic multilayers has generated considerable interest, fueled by technological prospects and the access granted to fundamental questions. The interaction of skyrmions with charge carriers gives rise to exotic electrodynamics, such as the topological Hall effect (THE), the Hall response to an emergent magnetic field, a manifestation of the skyrmion Berry-phase. The proposal that THE can be used to detect skyrmions needs to be tested quantitatively. For that it is imperative to develop comprehensive understanding of skyrmions and other chiral textures, and their electrical fingerprint. Here, using Hall transport and magnetic imaging, we track the evolution of magnetic textures and their THE signature in a technologically viable multilayer film as a function of temperature ($T$) and out-of-plane applied magnetic field ($H$). We show that topological Hall resistivity ($\rho_\mathrm{TH}$) scales with the density of isolated skyrmions ($n_\mathrm{sk}$) over a wide range of $T$, confirming the impact of the skyrmion Berry-phase on electronic transport. We find that at higher $n_\mathrm{sk}$ skyrmions cluster into worms which carry considerable topological charge, unlike topologically-trivial spin spirals. While we establish a qualitative agreement between $\rho_\mathrm{TH}(H,T)$ and areal density of topological charge $n_\mathrm{T}(H,T)$, our detailed quantitative analysis shows a much larger $\rho_\mathrm{TH}$ than the prevailing theory predicts for observed $n_\mathrm{T}$., Comment: Major revision of the original version. The extensive Supplementary Information is available upon request

Skyrmions are nanoscale spin configurations with topological properties that hold great promise for spintronic devices. Here, we establish their N\'eel texture, helicity, and size in Ir/Fe/Co/Pt multilayer films by constructing a multipole expansion to model their stray field signatures and applying it to magnetic force microscopy (MFM) images. Furthermore, the demonstrated sensitivity to inhomogeneity in skyrmion properties, coupled with a unique capability to estimate the pinning force governing dynamics, portends broad applicability in the burgeoning field of topological spin textures., Comment: 6 pages, 4 figures, significantly revised and upgraded. For the updated supplementary material please contact one of the corresponding authors

Studies of magnetization dynamics have incessantly facilitated the discovery of fundamentally novel physical phenomena, making steady headway in the development of magnetic and spintronics devices. The dynamics can be induced and detected electrically, offering new functionalities in advanced electronics at the nanoscale. However, its scattering mechanism is still disputed. Understanding the mechanism in thin films is especially important, because most spintronics devices are made from stacks of multilayers with nanometer thickness. The stacks are known to possess interfacial magnetic anisotropy, a central property for applications, whose influence on the dynamics remains unknown. Here, we investigate the impact of interfacial anisotropy by adopting CoFeB/MgO as a model system. Through systematic and complementary measurements of ferromagnetic resonance (FMR), on a series of thin films, we identify narrower FMR linewidths at higher temperatures. We explicitly rule out the temperature dependence of intrinsic damping as a possible cause, and it is also not expected from existing extrinsic scattering mechanisms for ferromagnets. We ascribe this observation to motional narrowing, an old concept so far neglected in the analyses of FMR spectra. The effect is confirmed to originate from interfacial anisotropy, impacting the practical technology of spin-based nanodevices up to room temperature., Comment: 23 pages,3 figures

Spin-orbit coupling (SOC) describes the relativistic interaction between the spin and momentum degrees of freedom of electrons, and is central to the rich phenomena observed in condensed matter systems. In recent years, new phases of matter have emerged from the interplay between SOC and low dimensionality, such as chiral spin textures and spin-polarized surface and interface states. These low-dimensional SOC-based realizations are typically robust and can be exploited at room temperature. Here we discuss SOC as a means of producing such fundamentally new physical phenomena in thin films and heterostructures. We put into context the technological promise of these material classes for developing spin-based device applications at room temperature.

Magnetic skyrmions are nanoscale topological spin structures offering great promise for next-generation information storage technologies. The recent discovery of sub-100 nm room temperature (RT) skyrmions in several multilayer films has triggered vigorous efforts to modulate their physical properties for their use in devices. Here we present a tunable RT skyrmion platform based on multilayer stacks of Ir/Fe/Co/Pt, which we study using X-ray microscopy, magnetic force microscopy and Hall transport techniques. By varying the ferromagnetic layer composition, we can tailor the magnetic interactions governing skyrmion properties, thereby tuning their thermodynamic stability parameter by an order of magnitude. The skyrmions exhibit a smooth crossover between isolated (metastable) and disordered lattice configurations across samples, while their size and density can be tuned by factors of 2 and 10 respectively. We thus establish a platform for investigating functional sub-50 nm RT skyrmions, pointing towards the development of skyrmion-based memory devices., Comment: v2 with minor revisions

We report on a thermoelectric investigation of the stripe and superconducting phases of the cuprate La$_{2-x}$Ba$_{x}$CuO$_{4}$ near the $x=1/8$ doping known to host stable stripes. We use the doping and magnetic field dependence of field-symmetric Nernst effect features to delineate the phenomenology of these phases. Our measurements are consistent with prior reports of time-reversal symmetry breaking signatures above the superconducting $T_{{\rm c}}$, and crucially detect a sharp, robust, field-invariant peak at the stripe charge order temperature, $T_{{\rm {\scriptscriptstyle CO}}}$. Our observations suggest the onset of a nontrivial charge ordered phase at $T_{{\rm {\scriptscriptstyle CO}}}$, and the subsequent presence of spontaneously generated vortices over a broad temperature range before the emergence of bulk superconductivity in LBCO.

Low temperature scanning tunneling microscopy is used to image the doped topological insulator Bi$_{2-x}$Fe$_x$Se$_3$. Interstitial Fe defects allow the detection of quasiparticle interference (QPI), and the reconstruction of the empty state band structure. Quantitative comparison between measured data and density functional theory calculations reveals the unexpected coexistence of quantum well states (QWS) with topological surface states (TSS) on the atomically clean surface of Bi$_{2-x}$Fe$_x$Se$_3$. Spectroscopic measurements quantify the breakdown of linear dispersion due to hexagonal warping. Nonetheless, both QWS and TSS remain spin-polarized and protected from backscattering to almost 1 eV above the Dirac point, suggesting their utility for spin-based applications., Comment: 5 pages, 4 figures

Many promising building blocks of future electronic technology - including non-stoichiometric compounds, strongly correlated oxides, and strained or patterned films - are inhomogeneous on the nanometer length scale. Exploiting the inhomogeneity of such materials to design next-generation nanodevices requires a band structure probe with nanoscale spatial resolution. To address this demand, we report the first simultaneous observation and quantitative reconciliation of two candidate probes - Landau level spectroscopy and quasiparticle interference imaging - which we employ here to reconstruct the multi-component surface state band structure of the topological semimetal antimony(Sb). We thus establish the technique of band structure tunneling microscopy (BSTM), whose unique advantages include nanoscale access to non-rigid band structure deformation, empty state dispersion, and magnetic field dependent states. We use BSTM to elucidate the relationship between bulk conductivity and surface state robustness in topological materials, and to quantify essential metrics for spintronics applications., Comment: 10 pages, 5 figures

Topological insulators host spin-polarized surface states which robustly span the band gap and hold promise for novel applications. Recent theoretical predictions have suggested that topologically protected surface states may similarly span the hybridization gap in some strongly correlated heavy fermion materials, particularly SmB6. However, the process by which the Sm 4f electrons hybridize with the 5d electrons on the surface of SmB6, and the expected Fermi-level gap in the density of states out of which the predicted topological surface states must arise, have not been directly measured. We use scanning tunneling microscopy to conduct the first atomic resolution spectroscopic study of the cleaved surface of SmB6, and to reveal a robust hybridization gap which universally spans the Fermi level on four distinct surface morphologies despite shifts in the f band energy. Using a cotunneling model, we separate the density of states of the hybridized bands from which the predicted topological surface states must be disentangled. On all surfaces we observe residual spectral weight spanning the hybridization gap down to the lowest T, which is consistent with a topological surface state., Comment: V2 update: added supplemental materials

The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (Tc) superconducting mechanism. Here we employ magnetic-field-dependent scanning tunneling microscopy to provide phase-sensitive proof that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an overdoped cuprate. Furthermore, by tracking the hole doping (p) dependence of the quasiparticle interference pattern within a single Bi-based cuprate family, we observe a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting Tc. Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap., Comment: For higher-resolution figures, please see the published version

The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high temperature superconductivity is not understood. Here we use scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge density wave (CDW) smoothly interfacing with the familiar tri-directional (triangular) CDW on the surface of the stoichiometric superconductor NbSe$_2$. Our low temperature measurements rule out thermal fluctuations, and point to local strain as the tuning parameter for this quantum phase transition. We use this discovery to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe$_2$. Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a new direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials., Comment: PNAS in press