An understanding of the nature of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. Here we combine resonant X-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, as well as momentum and real space, with the Bi2Sr2−xLaxCuO 6+δ cuprate family. The observed wavevector rules out simple antinodal nesting in the single particle limit, but matches well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates, and uncover its connection to the pseudogap regime. PACS numbers:Since the discovery of cuprate high-temperature superconductors, several unconventional phenomena have been observed in the region of the phase diagram located between the strongly localized Mott insulator at zero doping and the itinerant Fermi-liquid state that emerges beyond optimal doping [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The so-called 'pseudogap' opens at the temperature T * and obliterates the Fermi surface at the antinodes (AN) of the d-wave superconducting gap function, leaving behind disconnected "Fermi arcs" centered around the nodes. In addition, charge order has been observed on the surface of Bi-and Clbased compounds [4][5][6][7][8], in the bulk of La-based compounds [9][10][11], and most recently in YBa 2 Cu 3 O 6+δ (YBCO) [17][18][19][20], indicating this might be the leading instability in underdoped cuprates. The similarity between the observed charge ordering wavevector and the antinodal nesting vector of the hightemperature Fermi surface has prompted suggestions that a conventional Peierls-like charge-density-wave (CDW) might be responsible for the opening of the pseudogap [7,8,12,19]. We use complementary bulk/surface techniques to examine the validity of this scenario, and explore the connection between charge ordering and fermiology.By applying a suite of complementary tools to a single cuprate material, Bi 2 Sr 2−x La x CuO 6+δ (Bi2201), we reveal that the charge order in this system emerges just below T * , and that its wavevector corresponds to the Fermi arc tips rather than the antinodal nesting vector. We quantify the Fermi surface using ARPES, and we look for charge modulations along the Cu-O bond directions in both real-and reciprocalspace, using STM and REXS. The single-layer Bi2201 is well suited to this purpose owing to: (i) its two-dimensionality and high degree of crystallinity [22,23], and (ii) the possibility of probing the temperature evolution across T * , which is bettercharacterized [15,16] and more accessible than in bilayer sys-

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 two and ten, respectively. We thus establish a platform for investigating functional sub-50-nm RT skyrmions, pointing towards the development of skyrmion-based memory devices.

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.

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 used scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge-density wave (CDW) smoothly interfacing with the familiar tridirectional (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 quantum interface 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 promising direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.competing order | scanning tunneling spectroscopy | transition metal dichalcogenides W hereas a classical phase transition separates two states of matter at different temperatures, two ordered ground states of a material at zero temperature are separated by a quantum critical point (QCP). The competition between proximate ordered phases near the QCP can dramatically influence a large region of the phase diagram (1). Whereas the fluctuations from competing quantum states lead to exotic physics even at higher temperatures, low-temperature studies of these states may lead to a better understanding of the root of the competition. Density waves-charge-or spin-ordered states of collective origin driven by instabilities of the Fermi surface (FS)-exist in close proximity to superconductivity (SC) in several classes of correlated materials (2-4), and various proposals emerged recently to study their interplay in the presence of strong inhomogeneity in these systems (5). In this light, it is surprising that charge-density waves (CDWs) are not fully understood, even in the weakly correlated and stoichiometric transition metal dichalcogenides (TMDCs). Whereas a classic CDW arises from strong FS nesting, resulting in a sharply peaked susceptibility and a Kohn anomaly at the CDW wavevector, the quasi-2D TMDCs are known to deviate from this picture (6, 7).NbSe 2 is a layered TMDC that has generated much recent interest (8-10) as a model system for understanding the interplay of the CDW and SC phases with onset at T CDW ∼ 33 K and T SC ∼ 7 K respectively (11, 12). Despite extensive study (9, 13-16), several key facts about its familiar tridirectional (3Q) CDW remain unresolved, including the role of FS n...

The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (T(c)) superconducting mechanism. Here, we used 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 quasi-particle interference pattern within a single bismuth-based cuprate family, we observed a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting T(c). Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap.

The topological Hall effect (THE) is the Hall response to an emergent magnetic field, a manifestation of the skyrmion Berry-phase. As the magnitude of THE in magnetic multilayers is an open question, it is imperative to develop comprehensive understanding of skyrmions and other chiral textures, and their electrical fingerprint. Here, using Hall-transport and magnetic-imaging in a technologically viable multilayer film, we show that topological-Hall resistivity scales with the isolated-skyrmion density over a wide range of temperature and magnetic-field, confirming the impact of the skyrmion Berry-phase on electronic transport. While we establish qualitative agreement between the topological-Hall resistivity and the topological-charge density, our quantitative analysis shows much larger topological-Hall resistivity than the prevailing theory predicts for the observed skyrmion density. Our results are fundamental for the skyrmion-THE in multilayers, where interfacial interactions, multiband transport and non-adiabatic effects play an important role, and for skyrmion applications relying on THE.

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.

Kondo insulators are primary candidates in the search for strongly correlated topological quantum phases, which may host topological order, fractionalization, and non-Abelian statistics. Within some Kondo insulators, the hybridization gap is predicted to protect a nontrivial topological invariant and to harbor emergent heavy Dirac fermion surface modes. We use high-energy-resolution spectroscopic imaging in real and momentum space on the Kondo insulator, SmB6. On cooling through T * ∆ ≈ 35 K we observe the opening of an insulating gap that expands to ∆ ≈ 10 meV at 2 K. Within the gap, we image the formation of linearly dispersing surface states with effective masses reaching m * = (410 ± 20)me. We thus demonstrate existence of a strongly correlated topological Kondo insulator phase hosting the heaviest known Dirac fermions.