Publisher Correction: A weak topological insulator state in quasi-one-dimensional bismuth iodide.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

A weak topological insulator state in quasi-one-dimensional bismuth iodide.

The major breakthroughs in understanding of topological materials over the past decade were all triggered by the discovery of the Z2-type topological insulator-a type of material that is insulating in its interior but allows electron flow on its surface. In three dimensions, a topological insulator is classified as either 'strong' or 'weak'1,2, and experimental confirmations of the strong topological insulator rapidly followed theoretical predictions3-5. By contrast, the weak topological insulator (WTI) has so far eluded experimental verification, because the topological surface states emerge only on particular side surfaces, which are typically undetectable in real three-dimensional crystals6-10. Here we provide experimental evidence for the WTI state in a bismuth iodide, ß-Bi4I4. Notably, the crystal has naturally cleavable top and side planes-stacked via van der Waals forces-which have long been desirable for the experimental realization of the WTI state11,12. As a definitive signature of this state, we find a quasi-one-dimensional Dirac topological surface state at the side surface (the (100) plane), while the top surface (the (001) plane) is topologically dark with an absence of topological surface states. We also find that a crystal transition from the ß-phase to the α-phase drives a topological phase transition from a nontrivial WTI to a normal insulator at roughly room temperature. The weak topological phase-viewed as quantum spin Hall insulators stacked three-dimensionally13,14-will lay a foundation for technology that benefits from highly directional, dense spin currents that are protected against backscattering.

Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te).

Majorana quasiparticles in condensed matter are important for topological quantum computing1-3, but remain elusive. Vortex cores of topological superconductors may accommodate Majorana quasiparticles that appear as the Majorana bound state (MBS) at zero energy4,5. The iron-based superconductor Fe(Se,Te) possesses a superconducting topological surface state6-9 that was investigated by scanning tunnelling microscopy (STM) studies, which suggest such a zero-energy vortex bound state (ZVBS)10,11. Here we present ultrahigh energy-resolution spectroscopic imaging (SI)-STM to clarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBS at 0 ± 20 µeV, which constrained its MBS origin, and showed that some vortices host the ZVBS but others do not. We show that the fraction of vortices hosting the ZVBS decreases with increasing magnetic field and that local quenched disorders are not related to the ZVBS. Our observations elucidate the necessary conditions to realize the ZVBS, which paves the way towards controllable Majorana quasiparticles.

Radial Spin Texture in Elemental Tellurium with Chiral Crystal Structure.

The chiral crystal is characterized by a lack of mirror symmetry and inversion center, resulting in the inequivalent right- and left-handed structures. In the noncentrosymmetric crystal structure, the spin and momentum of electrons are expected to be locked in the reciprocal space with the help of the spin-orbit interaction. To reveal the spin textures of chiral crystals, we investigate the spin and electronic structure in a p-type semiconductor, elemental tellurium, with the simplest chiral structure by using spin- and angle-resolved photoemission spectroscopy. Our data demonstrate that the highest valence band crossing the Fermi level has a spin component parallel to the electron momentum around the Brillouin zone corners. Significantly, we have also confirmed that the spin polarization is reversed in the crystal with the opposite chirality. The results indicate that the spin textures of the right- and left-handed chiral crystals are hedgehoglike, leading to unconventional magnetoelectric effects and nonreciprocal phenomena.

Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides.

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle-resolved photoemission, we find that these generically host a co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

Collective Dynamics and Strong Pinning near the Onset of Charge Order in La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4}.

The dynamics of charge-ordered states is one of the key issues in underdoped cuprate high-temperature superconductors, but static short-range charge-order (CO) domains have been detected in almost all cuprates. We probe the dynamics across the CO (and structural) transition in La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4} by measuring nonequilibrium charge transport, or resistance R as the system responds to a change in temperature and to an applied magnetic field. We find evidence for metastable states, collective behavior, and criticality. The collective dynamics in the critical regime indicates strong pinning by disorder. Surprisingly, nonequilibrium effects, such as avalanches in R, are revealed only when the critical region is approached from the charge-ordered phase. Our results on La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4} provide the long-sought evidence for the fluctuating order across the CO transition, and also set important constraints on theories of dynamic stripes.

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}.

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Phase competition in trisected superconducting dome.

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials, such as the cuprate high-temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates, where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping- and temperature-dependence ARPES study of spectral gaps in Bi(2)Sr(2)CaCu(2)O(8+δ), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p = 0.19 for the pseudogap phase and p = 0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T(c) and exists p > 0.19 at higher temperatures. Our data imply a revised phase diagram that reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome.

Electronic structure of a quasi-freestanding MoS2 monolayer.

Several transition-metal dichalcogenides exhibit a striking crossover from indirect to direct band gap semiconductors as they are thinned down to a single monolayer. Here, we demonstrate how an electronic structure characteristic of the isolated monolayer can be created at the surface of a bulk MoS2 crystal. This is achieved by intercalating potassium in the interlayer van der Waals gap, expanding its size while simultaneously doping electrons into the conduction band. Our angle-resolved photoemission measurements reveal resulting electron pockets centered at the K̅ and K' points of the Brillouin zone, providing the first momentum-resolved measurements of how the conduction band dispersions evolve to yield an approximately direct band gap of ∼1.8 eV in quasi-freestanding monolayer MoS2. As well as validating previous theoretical proposals, this establishes a novel methodology for manipulating electronic structure in transition-metal dichalcogenides, opening a new route for the generation of large-area quasi-freestanding monolayers for future fundamental study and use in practical applications.

Dependence of carrier doping on the impurity potential in transition-metal-substituted FeAs-based superconductors.

In order to examine to what extent the rigid-band-like electron doping scenario is applicable to the transition metal-substituted Fe-based superconductors, we have performed angle-resolved photoemission spectroscopy studies of Ba(Fe(1-x)Ni(x))(2)As(2) (Ni-122) and Ba(Fe(1-x)Cu(x))(2)As(2) (Cu-122), and compared the results with Ba(Fe(1-x)Co(x))(2)As(2) (Co-122). We find that Ni 3d-derived features are formed below the Fe 3d band and that Cu 3d-derived ones further below it. The electron and hole Fermi surface (FS) volumes are found to increase and decrease with substitution, respectively, qualitatively consistent with the rigid-band model. However, the total extra electron number estimated from the FS volumes (the total electron FS volume minus the total hole FS volume) is found to decrease in going from Co-, Ni-, to Cu-122 for a fixed nominal extra electron number, that is, the number of electrons that participate in the formation of FS decreases with increasing impurity potential. We find that the Néel temperature T(N) and the critical temperature T(c) maximum are determined by the FS volumes rather than the nominal extra electron concentration or the substituted atom concentration.

Real-time manifestation of strongly coupled spin and charge order parameters in stripe-ordered La(1.75)Sr(0.25)NiO(4) nickelate crystals using time-resolved resonant x-ray diffraction.

We investigate the order parameter dynamics of the stripe-ordered nickelate, La(1.75)Sr(0.25)NiO(4), using time-resolved resonant x-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters' amplitude dynamics are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer reorientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the nonequilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom.

Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212.

The superconducting gap--an energy scale tied to the superconducting phenomena--opens on the Fermi surface at the superconducting transition temperature (T(c)) in conventional BCS superconductors. In underdoped high-T(c) superconducting copper oxides, a pseudogap (whose relation to the superconducting gap remains a mystery) develops well above T(c) (refs 1, 2). Whether the pseudogap is a distinct phenomenon or the incoherent continuation of the superconducting gap above T(c) is one of the central questions in high-T(c) research. Although some experimental evidence suggests that the two gaps are distinct, this issue is still under intense debate. A crucial piece of evidence to firmly establish this two-gap picture is still missing: a direct and unambiguous observation of a single-particle gap tied to the superconducting transition as function of temperature. Here we report the discovery of such an energy gap in underdoped Bi2Sr2CaCu2O8+delta in the momentum space region overlooked in previous measurements. Near the diagonal of Cu-O bond direction (nodal direction), we found a gap that opens at T(c) and has a canonical (BCS-like) temperature dependence accompanied by the appearance of the so-called Bogoliubov quasi-particles, a classical signature of superconductivity. This is in sharp contrast to the pseudogap near the Cu-O bond direction (antinodal region) measured in earlier experiments.

Unconventional short-range structural fluctuations in cuprate superconductors.

The interplay between structural and electronic degrees of freedom in complex materials is the subject of extensive debate in physics and materials science. Particularly interesting questions pertain to the nature and extent of pre-transitional short-range order in diverse systems ranging from shape-memory alloys to unconventional superconductors, and how this microstructure affects macroscopic properties. Here we use neutron and X-ray diffuse scattering to uncover universal structural fluctuations in La2-xSrxCuO4 and Tl2Ba2CuO6+δ, two cuprate superconductors with distinct point disorder effects and with optimal superconducting transition temperatures that differ by more than a factor of two. The fluctuations are present in wide doping and temperature ranges, including compositions that maintain high average structural symmetry, and they exhibit unusual, yet simple scaling behaviour. The scaling regime is robust and universal, similar to the well-known critical fluctuations close to second-order phase transitions, but with a distinctly different physical origin. We relate this behaviour to pre-transitional phenomena in a broad class of systems with structural and magnetic transitions, and propose an explanation based on rare structural fluctuations caused by intrinsic nanoscale inhomogeneity. We also uncover parallels with superconducting fluctuations, which indicates that the underlying inhomogeneity plays an important role in cuprate physics.

Skyrmions in a doped antiferromagnet.

Magnetization and magnetoresistance have been measured in insulating antiferromagnetic La2Cu0.97Li0.03O4 over a wide range of temperatures, magnetic fields, and field orientations. The magnetoresistance step associated with a weak ferromagnetic transition exhibits a striking nonmonotonic temperature dependence, consistent with the presence of Skyrmions.

Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates.

The origin of the weak insulating behavior of the resistivity, i.e. [Formula: see text], revealed when magnetic fields (H) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all [Formula: see text], where [Formula: see text] is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of T and H. The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa2Cu3O6+x and YBa2Cu4O8, and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates.

Doping-dependent nodal fermi velocity of the high-temperature superconductor Bi2Sr2CaCu2O(8+δ) revealed using high-resolution angle-resolved photoemission spectroscopy.

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O(8+δ) (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is nonuniversal, in contrast with assumed phenomenology. This is used together with laser ARPES measurements of the gap velocity (v2) to resolve discrepancies with thermal conductivity measurements.

An unusual isotope effect in a high-transition-temperature superconductor.

In conventional superconductors, the electron pairing that allows superconductivity is caused by exchange of virtual phonons, which are quanta of lattice vibration. For high-transition-temperature (high-T(c)) superconductors, it is far from clear that phonons are involved in the pairing at all. For example, the negligible change in T(c) of optimally doped Bi2Sr2CaCu2O8+delta (Bi2212; ref. 1) upon oxygen isotope substitution (16O --> 18O leads to T(c) decreasing from 92 to 91 K) has often been taken to mean that phonons play an insignificant role in this material. Here we provide a detailed comparison of the electron dynamics of Bi2212 samples containing different oxygen isotopes, using angle-resolved photoemission spectroscopy. Our data show definite and strong isotope effects. Surprisingly, the effects mainly appear in broad high-energy humps, commonly referred to as 'incoherent peaks'. As a function of temperature and electron momentum, the magnitude of the isotope effect closely correlates with the superconducting gap--that is, the pair binding energy. We suggest that these results can be explained in a dynamic spin-Peierls picture, where the singlet pairing of electrons and the electron-lattice coupling mutually enhance each other.

Vortex phase diagram and the normal state of cuprates with charge and spin orders.

The phase diagram of underdoped cuprates in a magnetic field (H) is key to understanding the anomalous normal state of these high-temperature superconductors. However, the upper critical field (H c2), the extent of superconducting (SC) phase with vortices, and the role of charge orders at high H remain controversial. Here we study stripe-ordered La-214, i.e., cuprates in which charge orders are most pronounced and zero-field SC transition temperatures T c 0 are lowest. This enables us to explore the vortex phases in a previously inaccessible energy scale window. By combining linear and nonlinear transport techniques sensitive to vortex matter, we determine the T - H phase diagram, directly detect H c2, and reveal novel properties of the high-field ground state. Our results demonstrate that quantum fluctuations and disorder play a key role as T → 0, while the high-field ground state is likely a metal, not an insulator, due to the presence of stripes.

Pair density wave at high magnetic fields in cuprates with charge and spin orders.

In underdoped cuprates, the interplay of the pseudogap, superconductivity, and charge and spin ordering can give rise to exotic quantum states, including the pair density wave (PDW), in which the superconducting (SC) order parameter is oscillatory in space. However, the evidence for a PDW state remains inconclusive and its broader relevance to cuprate physics is an open question. To test the interlayer frustration, the crucial component of the PDW picture, we perform transport measurements on charge- and spin-stripe-ordered La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4 in perpendicular magnetic fields (H⊥), and also with an additional field applied parallel to CuO2 layers (H∥). We detect several phenomena predicted to arise from the existence of a PDW, including an enhancement of interlayer SC phase coherence with increasing H∥. These data also provide much-needed transport signatures of the PDW in the regime where superconductivity is destroyed by quantum phase fluctuations.

Doublon-holon pairing mechanism via exchange interaction in two-dimensional cuprate Mott insulators.

Coupling of charge and spin degrees of freedom is a critical feature of correlated electron oxides, as represented by the spin-related mechanism of a Cooper pair under high-T c superconductivity. A doublon-holon pair generated on an antiferromagnetic spin background is also predicted to attract each other via the spin-spin interaction J, similar to a Cooper pair, while its evidence is difficult to obtain experimentally. Here, we investigate such an excitonic effect by electroreflectance spectroscopy using terahertz electric field pulses in undoped cuprates: Nd2CuO4, Sr2CuO2Cl2, and La2CuO4. Analyses of the spectral changes of reflectivity under electric fields reveal that the splitting of odd-parity and even-parity excitons, a measure of doublon-holon binding energy, increases with J. This trend is reproduced by t-J-type model calculations, providing strong evidence of the spin-related doublon-holon pairing. Agreement with the calculations supports the s-wave symmetry of the doublon-holon pair in contrast to the d-wave Cooper pair in doped cuprates.