Emergent layer stacking arrangements in c-axis confined MoTe2.

The layer stacking order in 2D materials strongly affects functional properties and holds promise for next-generation electronic devices. In bulk, octahedral MoTe2 possesses two stacking arrangements, the ferroelectric Weyl semimetal Td phase and the higher-order topological insulator 1T' phase. However, in thin flakes of MoTe2, it is unclear if the layer stacking follows the Td, 1T', or an alternative stacking sequence. Here, we use atomic-resolution scanning transmission electron microscopy to directly visualize the MoTe2 layer stacking. In thin flakes, we observe highly disordered stacking, with nanoscale 1T' and Td domains, as well as alternative stacking arrangements not found in the bulk. We attribute these findings to intrinsic confinement effects on the MoTe2 stacking-dependent free energy. Our results are important for the understanding of exotic physics displayed in MoTe2 flakes. More broadly, this work suggests c-axis confinement as a method to influence layer stacking in other 2D materials.

Low-energy quasi-circular electron correlations with charge order wavelength in Bi2Sr2CaCu2O8+δ.

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the qx-qy scattering plane in underdoped Bi2Sr2CaCu2O8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the qx-qy scattering plane with radius equal to the magnitude of the charge order wave vector, qCO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [qx = ±qCO, qy = 0] and [qx = 0, qy = ±qCO]) as the origin of the observed correlations.

Tracking the nematicity in cuprate superconductors: a resistivity study under uniaxial pressure.

Overshadowing the superconducting dome in hole-doped cuprates, the pseudogap state is still one of the mysteries that no consensus can be achieved. It has been suggested that the rotational symmetry is broken in this state and may result in a nematic phase transition, whose temperature seems to coincide with the onset temperature of the pseudogap stateT∗around optimal doping level, raising the question whether the pseudogap results from the establishment of the nematic order. Here we report results of resistivity measurements under uniaxial pressure on several hole-doped cuprates, where the normalized slope of the elastoresistivityζcan be obtained as illustrated in iron-based superconductors. The temperature dependence ofζalong particular lattice axis exhibits kink feature atTkand shows Curie-Weiss-like behavior above it, which may suggest a spontaneous nematic transition. WhileTkseems to be the same asT∗around the optimal doping and in the overdoped region, they become very different in underdoped La2-xSrxCuO4. Our results suggest that the nematic order, if indeed existing, is an electronic phase within the pseudogap state.

Little-Parks like oscillations in lightly doped cuprate superconductors.

Understanding the rich and competing electronic orders in cuprate superconductors may provide important insight into the mechanism of high-temperature superconductivity. Here, by measuring Bi2Sr2CaCu2O8+x in the extremely underdoped regime, we obtain evidence for a distinct type of ordering, which manifests itself as resistance oscillations at low magnetic fields (≤10 T) and at temperatures around the superconducting transition. By tuning the doping level p continuously, we reveal that these low-field oscillations occur only when p < 0.1. The oscillation amplitude increases with decreasing p but the oscillation period stays almost constant. We show that these low-field oscillations can be well described by assuming a periodic superconducting structure with a mesh size of about 50 nm. Such a charge order, which is distinctly different from the well-established charge density wave and pair density wave, seems to be an unexpected piece of the puzzle on the correlated physics in cuprates.

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor.

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

Observation of a thermoelectric Hall plateau in the extreme quantum limit.

The thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here, we demonstrate that the thermoelectric Hall conductivity αxy in the three-dimensional Dirac semimetal ZrTe5 acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields.

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor.

Majorana zero modes (MZMs) are spatially localized, zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold promise for topological quantum computing. Owing to the particle-antiparticle equivalence, MZMs exhibit quantized conductance at low temperature. By using variable-tunnel-coupled scanning tunneling spectroscopy, we studied tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e 2/h quantum conductance (where e is the electron charge and h is Planck's constant). By contrast, no plateaus were observed on either finite energy vortex bound states or in the continuum of electronic states outside the superconducting gap. This behavior of the zero-mode conductance supports the existence of MZMs in FeTe0.55Se0.45.

Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La2-x Ba x CuO4.

Charge order is universal among high-T c cuprates, but its relation to superconductivity is unclear. While static order competes with superconductivity, dynamic order may be favorable and even contribute to Cooper pairing. Using time-resolved resonant soft x-ray scattering at a free-electron laser, we show that the charge order in prototypical La2-x Ba x CuO4 exhibits transverse fluctuations at picosecond time scales. These sub-millielectron volt excitations propagate by Brownian-like diffusion and have an energy scale remarkably close to the superconducting T c. At sub-millielectron volt energy scales, the dynamics are governed by universal scaling laws defined by the propagation of topological defects. Our results show that charge order in La2-x Ba x CuO4 exhibits dynamics favorable to the in-plane superconducting tunneling and establish time-resolved x-rays as a means to study excitations at energy scales inaccessible to conventional scattering techniques.

Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5.

The discovery of the quantum Hall effect (QHE)1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. Although the possibility of generalizing the QHE to three-dimensional (3D) electronic systems3,4 was proposed decades ago, it has not been demonstrated experimentally. Here we report the experimental realization of the 3D QHE in bulk zirconium pentatelluride (ZrTe5) crystals. We perform low-temperature electric-transport measurements on bulk ZrTe5 crystals under a magnetic field and achieve the extreme quantum limit, where only the lowest Landau level is occupied, at relatively low magnetic fields. In this regime, we observe a dissipationless longitudinal resistivity close to zero, accompanied by a well-developed Hall resistivity plateau proportional to half of the Fermi wavelength along the field direction. This response is the signature of the 3D QHE and strongly suggests a Fermi surface instability driven by enhanced interaction effects in the extreme quantum limit. By further increasing the magnetic field, both the longitudinal and Hall resistivity increase considerably and display a metal-insulator transition, which represents another magnetic-field-driven quantum phase transition. Our findings provide experimental evidence of the 3D QHE and a promising platform for further exploration of exotic quantum phases and transitions in 3D systems.

Charge-stripe crystal phase in an insulating cuprate.

High-temperature (high-Tc) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases1. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi2Sr2CaCu2O8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a0 period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-Tc cuprates.

Evidence for Majorana bound states in an iron-based superconductor.

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe0.55Se0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

Superconductor-Insulator Transitions in Exfoliated Bi2Sr2CaCu2O8+δ Flakes.

We realize superconductor-insulator transitions (SIT) in mechanically exfoliated Bi2Sr2CaCu2O8+δ (BSCCO) flakes and address simultaneously their transport properties as well as the evolution of density of states. Back-gating via the solid ion conductor (SIC) engenders a SIT in BSCCO due to the modulation of carrier density by intercalated lithium ions. Scaling analysis indicates that the SIT follows the theoretical description of a two-dimensional quantum phase transition (2D-QPT). We further carry out tunneling spectroscopy in graphite(G)/BSCCO heterojunctions. We observe V-shaped gaps in the critical regime of the SIT. The density of states in BSCCO gets symmetrically suppressed by further going into the insulating regime. Our technique of combining solid state gating with tunneling spectroscopy can be easily applied to the study of other two-dimensional materials.

Higgs Mode in the d-Wave Superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+x} Driven by an Intense Terahertz Pulse.

We investigate the terahertz (THz)-pulse-driven nonlinear response in the d-wave cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+x} (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We observe an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is markedly enhanced below T_{c}. The corresponding third-order nonlinear effect exhibits both A_{1g} and B_{1g} symmetry components, which are decomposed from polarization-resolved measurements. A comparison with a BCS calculation of the nonlinear susceptibility indicates that the A_{1g} component is associated with the Higgs mode of the d-wave order parameter.

Structural phase transitions of (Bi1-xSbx)2(Te1-ySey)3 compounds under high pressure and the influence of the atomic radius on the compression processes of tetradymites.

Recently, A2B3-type tetradymites have developed into a hot topic in physical and material research fields, where the A and B atoms represent V and VI group elements, respectively. In this study, in situ angle-dispersive X-ray diffraction measurements were performed on Bi2Te2Se, BiSbTeSe2, and Sb2Te2Se tetradymites under high pressure. Bi2Te2Se transforms from a layered rhombohedral structure (phase I) into 7-fold monoclinic (phase II) and body-centered tetragonal (phase IV) structures at about 8.0 and 14.3 GPa, respectively, without an 8-fold monoclinic structure (phase III) similar to that in Bi2Te3. Thus, the compression behavior of Bi2Te2Se is the same as that of Bi2Se3, which could also be obtained from first-principles calculations and in situ high-pressure electrical resistance measurements. Under high pressure, BiSbTeSe2 and Sb2Te2Se undergo similar structural phase transitions to Bi2Te2Se, which indicates that the compression process of tellurides can be modulated by doping Se in Te sites. According to these high-pressure investigations of A2B3-type tetradymites, the decrease of the B-site atomic radius shrinks the stable pressure range of phase III and expands that of phase II, whereas the decrease of the A-site atomic radius induces a different effect, i.e. expanding the stable pressure range of phase III and shrinking that of phase II. The influence of the atomic radius on the compression process of tetradymites is closely related to the chemical composition and the atom arrangement in the quintuple layer.

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5.

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm2/(V ⋅ s)] multilayer ZrTe5 flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a [Formula: see text] dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.

Low vibration high numerical aperture automated variable temperature Raman microscope.

Raman micro-spectroscopy is well suited for studying a variety of properties and has been applied to a wide range of areas. Combined with tuneable temperature, Raman spectra can offer even more insights into the properties of materials. However, previous designs of variable temperature Raman microscopes have made it extremely challenging to measure samples with low signal levels due to thermal and positional instabilities as well as low collection efficiencies. Thus contemporary Raman microscope has found limited applicability to probing the subtle physics involved in phase transitions and hysteresis. This paper describes a new design of a closed-cycle, Raman microscope with full polarization rotation. High collection efficiency, thermal stability, and mechanical stability are ensured by both deliberate optical, cryogenic, and mechanical design. Measurements on two samples, Bi2Se3 and V2O3, which are challenging due to low thermal conductivities, low signal levels, and/or hysteretic effects, are measured with previously undemonstrated temperature resolution.

Kondo-like zero-bias conductance anomaly in a three-dimensional topological insulator nanowire.

Zero-bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero-bias peaks in nanowires--for example, weak localization, Andreev bound states, or the Kondo effect. Here, we discuss observations of differential-conductance peaks at zero-bias voltage in non-superconducting electronic transport through a 3D topological insulator (Bi(1.33)Sb(0.67))Se3 nanowire. The zero-bias conductance peaks show logarithmic temperature dependence and often linear splitting with magnetic fields, both of which are signatures of the Kondo effect in quantum dots. We characterize the zero-bias peaks and discuss their origin.

Mapping the Electronic Structure of Each Ingredient Oxide Layer of High-T\{c} Cuprate Superconductor Bi{2}Sr{2}CaCu{2}O{8+δ}.

Understanding the mechanism of high transition temperature (T{c}) superconductivity in cuprates has been hindered by the apparent complexity of their multilayered crystal structure. Using a cryogenic scanning tunneling microscopy (STM), we report on layer-by-layer probing of the electronic structures of all ingredient planes (BiO, SrO, CuO{2}) of Bi{2}Sr{2}CaCu_2}O{8+δ} superconductor prepared by argon-ion bombardment and annealing technique. We show that the well-known pseudogap (PG) feature observed by STM is inherently a property of the BiO planes and thus irrelevant directly to Cooper pairing. The SrO planes exhibit an unexpected van Hove singularity near the Fermi level, while the CuO{2} planes are exclusively characterized by a smaller gap inside the PG. The small gap becomes invisible near T{c}, which we identify as the superconducting gap. The above results constitute severe constraints on any microscopic model for high T{c} superconductivity in cuprates.

Aharonov-Bohm oscillations in a quasi-ballistic three-dimensional topological insulator nanowire.

Aharonov-Bohm oscillations effectively demonstrate coherent, ballistic transport in mesoscopic rings and tubes. In three-dimensional topological insulator nanowires, they can be used to not only characterize surface states but also to test predictions of unique topological behaviour. Here we report measurements of Aharonov-Bohm oscillations in (Bi1.33Sb0.67)Se3 that demonstrate salient features of topological nanowires. By fabricating quasi-ballistic three-dimensional topological insulator nanowire devices that are gate-tunable through the Dirac point, we are able to observe alternations of conductance maxima and minima with gate voltage. Near the Dirac point, we observe conductance minima for zero magnetic flux through the nanowire and corresponding maxima (having magnitudes of almost a conductance quantum) at magnetic flux equal to half a flux quantum; this is consistent with the presence of a low-energy topological mode. The observation of this mode is a necessary step towards utilizing topological properties at the nanoscale in post-CMOS applications.

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3.

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr0.08(Bi0.1Sb0.9)1.92Te3. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship [Formula: see text] is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm(2). These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.