Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x

Emergence of Competing Stripe Phases in Undoped Infinite-Layer Nickelates

Recent discovery of superconductivity in infinite-layer nickelates has ignited renewed theoretical and experimental interest in the role of electronic correlations in their properties. Here, using first-principles simulations, we show that the parent compound of the nickelate family, LaNiO_{2}, hosts competing low-energy stripe phases, similar to doped cuprates. The stripe states are shown to be driven by multiorbital electronic mechanisms and Peierls distortions. Our study indicates that both strong correlations and electron-phonon coupling effects play a key role in the physics of infinite-layer nickelates, and sheds light on the microscopic origin of electronic inhomogeneity and the lack of long-range order in the nickelates.

Toward Reliable Synthesis of Superconducting Infinite Layer Nickelate Thin Films by Topochemical Reduction

Infinite layer (IL) nickelates provide a new route beyond copper oxides to address outstanding questions in the field of unconventional superconductivity. However, their synthesis poses considerable challenges, largely hindering experimental research on this new class of oxide superconductors. That synthesis is achieved in a two-step process that yields the most thermodynamically stable perovskite phase first, then the IL phase by topotactic reduction, the quality of the starting phase playing a crucial role. Here, a reliable synthesis of superconducting IL  nickelate films is reported after successive topochemical reductions of a parent perovskite phase with nearly optimal stoichiometry. Careful analysis of the transport properties of the incompletely reduced films reveals an improvement in the strange metal behavior of their normal state resistivity over subsequent topochemical reductions, offering insight into the reduction process.

Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed

The currently established electronic phase diagram of cuprates is based on a study of single- and double-layered compounds. These CuO₂ planes, however, are directly contacted with dopant layers, thus inevitably disordered with an inhomogeneous electronic state. Here, we solve this issue by investigating a 6-layered Ba₂Ca₅Cu₆O₁₂(F,O)₂ with inner CuO₂ layers, which are clean with the extremely low disorder, by angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. We find a tiny Fermi pocket with a doping level less than 1% to exhibit well-defined quasiparticle peaks which surprisingly lack the polaronic feature. This provides the first evidence that the slightest amount of carriers is enough to turn a Mott insulating state into a metallic state with long-lived quasiparticles. By tuning hole carriers, we also find an unexpected phase transition from the superconducting to metallic states at 4%. Our results are distinct from the nodal liquid state with polaronic features proposed as an anomaly of the heavily underdoped cuprates.

Jamming and unusual charge density fluctuations of strange metals

The strange metallic regime across a number of high-temperature superconducting materials presents numerous challenges to the classic theory of Fermi liquid metals. Recent measurements of the dynamical charge response of strange metals, including optimally doped cuprates, have revealed a broad, featureless continuum of excitations, extending over much of the Brillouin zone. The collective density oscillations of this strange metal decay into the continuum in a manner that is at odds with the expectations of Fermi liquid theory. Inspired by these observations, we investigate the phenomenology of bosonic collective modes and the particle-hole excitations in a class of strange metals by making an analogy to the phonons of classical lattices falling apart across an unconventional jamming-like transition associated with the onset of rigidity. By making comparisons to the experimentally measured dynamical response functions, we reproduce many of the qualitative features using the above framework. We conjecture that the dynamics of electronic charge density over an intermediate range of energy scales in a class of strongly correlated metals can be at the brink of a jamming-like transition.

Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La_1.885Sr_0.115CuO₄, by studying the effects of large magnetic fields (H) up to 24 Tesla. At low temperatures (T), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the H - T phase diagram.

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.

Simultaneous Imaging of Dopants and Free Charge Carriers by Monochromated EELS

Doping inhomogeneities in solids are not uncommon, but their microscopic observation and understanding are limited due to the lack of bulk-sensitive experimental techniques with high enough spatial and spectral resolution. Here, we demonstrate nanoscale imaging of both dopants and free charge carriers in La-doped BaSnO₃ (BLSO) using high-resolution electron energy-loss spectroscopy (EELS). By analyzing high- and low-energy excitations in EELS, we reveal chemical and electronic inhomogeneities within a single BLSO nanocrystal. The inhomogeneous doping leads to distinctive localized infrared surface plasmons, including a previously unobserved plasmon mode that is highly confined between high- and low-doping regions. We further quantify the carrier density, effective mass, and dopant activation percentage by EELS and transport measurements on the bulk single crystals of BLSO. These results not only represent a practical approach for studying heterogeneities in solids and understanding structure-property relationships at the nanoscale, but also demonstrate the possibility of infrared plasmon tuning by leveraging nanoscale doping texture.

A Review on Strain Study of Cuprate Superconductors

Cuprate superconductors have attracted extensive attention due to their broad promising application prospects. Among the factors affecting superconductivity, the effect of strain cannot be ignored, which can significantly enhance or degrade superconductivity. In this review, we discuss and summarize the methods of applying strain to cuprate superconductors, strain measurement techniques, and the influence of strain on superconductivity. Among them, we pay special attention to the study of strain in high-temperature superconducting (HTS) films and coating. We expect this review can guide further research in the field of cuprate superconductors.

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

Twisted van der Waals Josephson Junction Based on a High-Tc Superconductor

Stacking two-dimensional van der Waals (vdW) materials rotated with respect to each other show versatility for studying exotic quantum phenomena. In particular, anisotropic layered materials have great potential for such twistronics applications, providing high tunability. Here, we report anisotropic superconducting order parameters in twisted Bi₂Sr₂CaCu₂O_8+x (Bi-2212) vdW junctions with an atomically clean vdW interface, achieved using the microcleave-and-stack technique. The vdW junctions with twist angles of 0° and 90° showed the maximum Josephson coupling, comparable to that of intrinsic Josephson junctions. As the twist angle approaches 45°, Josephson coupling is suppressed, and eventually disappears at 45°. The observed twist angle dependence of the Josephson coupling can be explained quantitatively by theoretical calculation with the d-wave superconducting order parameter of Bi-2212 and finite tunneling incoherence of the junction. Our results revealed the anisotropic nature of Bi-2212 and provided a novel fabrication technique for vdW-based twistronics platforms compatible with air-sensitive vdW materials.

Direct observation of nodeless superconductivity and phonon modes in electron-doped copper oxide Sr1-xNdxCuO2

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study the electron-doped copper oxide compound Sr_1−xNd_xCuO₂, which has only bare cations separating the CuO₂ planes and thus the simplest infinite-layer structure of all cuprate superconductors. Tunneling conductance spectra of the major CuO₂ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. As well as the bosonic modes, with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings reveal the origin of the bosonic modes in lattice vibrations rather than spin excitations.

(RE)Ba2Cu3O7-δ and the Roeser-Huber Formula

We apply the Roeser–Huber formula to the (RE)Ba2Cu3O7−δ (REBCO with RE= rare earths) high-Tc superconducting material class to calculate the superconducting transition temperature, Tc, using the electronic configuration and the crystallographic data. In a former publication (H. P. Roeser et al., Acta Astronautica 2008, 62, 733–736), the basic idea was described and Tc was successfully calculated for the YBa2Cu3O7−δ compound with two oxygen doping levels δ= 0.04 and 0.45, but several open questions remained. One of the problems remaining was the determination of Tc for the δ= 0.45 sample, which can be explained regarding the various oxygen arrangements being possible within the copper-oxide plane. Having established this proper relation and using the various crystallographic data on the REBCO system available in the literature, we show that the Roeser–Huber equation is capable to calculate the Tc of the various REBCO compounds and the effects of strain and pressure on Tc, when preparing thin film samples. Furthermore, the characteristic length, x, determined for the REBCO systems sheds light on the size of the δTc-pinning sites being responsible for additional flux pinning and the peak effect.

Temperature-Independent Cuprate Pseudogap from Planar Oxygen NMR

Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.

Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review

In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits the NFL properties, so that the C symmetry breaks down, making the differential tunneling conductivity to be an asymmetric function of the bias voltage V. This asymmetry does not take place in normal metals, where Landau Fermi liquid (LFL) theory holds. Under the application of magnetic field, a heavy fermion metal transits to the LFL state, and σ(V) becomes symmetric function of V. These findings are in good agreement with experimental observations. We suggest that the same topological FCQPT underlies the baryon asymmetry in the Universe. We demonstrate that the most fundamental features of the nature are defined by its topological and symmetry properties.

Visualization of Multifractal Superconductivity in a Two-Dimensional Transition Metal Dichalcogenide in the Weak-Disorder Regime

Eigenstate multifractality is a distinctive feature of noninteracting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic, weakly disordered single-layer NbSe₂ by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth, and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. The strong spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f(α) shows anomalous scaling behavior typical from 2D weakly disordered systems.

Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-T c superconductor

Charge density modulations have been observed in all families of high-critical temperature (T _c) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa₂Cu₃O_7-δ and Nd_{1+ x} Ba_{2- x} Cu₃O_7-δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli-electron volts, and pervade a large area of the phase diagram.

Atomic manipulation of the gap in Bi2Sr2CaCu2O8+x

Single-atom manipulation within doped correlated electron systems could help disentangle the influence of dopants, structural defects, and crystallographic characteristics on local electronic states. Unfortunately, the high diffusion barrier in these materials prevents conventional manipulation techniques. Here, we demonstrate the possibility to reversibly manipulate select sites in the optimally doped high-temperature superconductor Bi₂Sr₂CaCu₂O_8+x using the local electric field of the tip of a scanning tunneling microscope. We show that upon shifting individual Bi atoms at the surface, the spectral gap associated with superconductivity is seen to reversibly change by as much as 15 milli-electron volts (on average ~5% of the total gap size). Our toy model, which captures all observed characteristics, suggests that the electric field induces lateral movement of local pairing potentials in the CuO₂ plane.

Combinatorial laser molecular beam epitaxy system integrated with specialized low-temperature scanning tunneling microscopy

We present a newly developed facility comprising a combinatorial laser molecular beam epitaxy system and an in situ scanning tunneling microscope (STM). This facility aims at accelerating the materials research in a highly efficient way by advanced high-throughput film synthesis techniques and subsequent fast characterization of surface morphology and electronic states. Compared with uniform films deposited by conventional methods, the so-called combinatorial thin films will be beneficial in determining the accurate phase diagrams of different materials due to the improved control of parameters such as chemical substitution and sample thickness resulting from a rotary-mask method. A specially designed STM working under low-temperature and ultrahigh vacuum conditions is optimized for the characterization of combinatorial thin films in an XY coarse motion range of 15 mm × 15 mm with submicrometer location precision. The overall configuration and some key aspects such as the sample holder design, scanner head, and sample/tip/target transfer mechanism are described in detail. The performance of the device is demonstrated by synthesizing high-quality superconducting FeSe thin films with gradient thickness and imaging surfaces of highly oriented pyrolytic graphite, Au (111), Bi₂Sr₂CaCu₂O_8+δ (BSCCO), and FeSe. In addition, we also have obtained clean noise spectra of tunneling junctions and the superconducting energy gap of BSCCO. The successful manufacturing of such a facility opens a new window for the next generation equipment designed for experimental materials research.

Possible cluster pairing correlation in the checkerboard Hubbard model: a quantum Monte Carlo study

Constrained-path quantum Monte Carlo method is applied to study the pairing correlation in the checkerboard Hubbard model with inhomogeneous nearest-neighbor hopping at a low doping of holes. The inhomogeneous hopping can enhance the pairing correlation among different plaquette clusters. An obvious maximum for the pairing correlation is observed at a certain inhomogeneous hopping. The cluster pairing correlation shows the strongest long-range behavior at the optimal inhomogeneity. The enhancement of cluster pairing correlation might be associated with the transition of the Fermi surface structure. This work indicates that the inhomogeneous hopping could tailor the pairing correlation effectively.

Asymmetric response of electrical conductivity and V valence state to strain in cation-deficient Sr1-yVO3 ultrathin films based on absorption measurements at the V L2- and L3-edges

The correlation between electronic properties and epitaxial strain in a cation-deficient system has rarely been investigated. Cation-deficient SrVO₃ films are taken as a model system to investigate the strain-dependent electrical and electronic properties. Using element- and charge-sensitive soft X-ray absorption, V L-edge absorption measurements have been performed for Sr_1-yVO₃ films of different thicknesses capped with 4 u.c. (unit cell) SrTiO₃ layers, showing the coexistence of V⁴⁺ and V⁵⁺ in thick films. A different correlation between V valence state and epitaxial strain is observed for Sr_1-yVO₃ ultrathin films, i.e. a variation in V valence state is only observed for tensile-strained films. Sr_1-yVO₃ thin films are metallic and exhibit a thickness-driven metal-insulator transition at different critical thicknesses for tensile and compressive strains. The asymmetric response of electrical conductivity to strain observed in cation-deficient Sr_1-yVO₃ films will be beneficial for functional oxide electronic devices.

Directly visualizing the sign change of d-wave superconducting gap in Bi2Sr2CaCu2O8+δ by phase-referenced quasiparticle interference

The superconducting state is formed by the condensation of Cooper pairs and protected by the superconducting gap. The pairing interaction between the two electrons of a Cooper pair determines the gap function. Thus, it is pivotal to detect the gap structure for understanding the mechanism of superconductivity. In cuprate superconductors, it has been well established that the gap may have a d-wave function. This gap function has an alternative sign change in the momentum space. It is however hard to visualize this sign change. Here we report the measurements of scanning tunneling spectroscopy in Bi2Sr2CaCu2O8+δ and conduct the analysis of phase-referenced quasiparticle interference (QPI). We see the seven basic scattering vectors that connect the octet ends of the banana-shaped contour of Fermi surface. The phase-referenced QPI clearly visualizes the sign change of the d-wave gap. Our results illustrate an effective way for determining the sign change of unconventional superconductors.

Mixed type I and type II superconductivity due to intrinsic electronic inhomogeneities in the type II Dirac semimetal PdTe2

The type II Dirac semimetal PdTe[Formula: see text] is unique in the family of topological parent materials because it displays a superconducting ground state below 1.7 K. Despite wide speculation on the possibility of an unconventional topological superconducting phase, tunneling and heat capacity measurements revealed that the superconducting phase of PdTe[Formula: see text] follows predictions of the microscopic theory of Bardeen, Cooper and Schrieffer for conventional superconductors. The superconducting phase in PdTe[Formula: see text] is further interesting because it also displays properties that are characteristic of type-I superconductors and are generally unexpected for binary compounds. Here, from scanning tunneling spectroscopic measurements we show that the surface of PdTe[Formula: see text] displays intrinsic electronic inhomogeneities in the normal state which leads to a mixed type I and type II superconducting behaviour along with a spatial distribution of critical fields in the superconducting state. Understanding of the origin of such inhomogeneities may be important for understanding the topological properties of PdTe[Formula: see text] in the normal state.

Charge-stripe crystal phase in an insulating cuprate

High-temperature (high-T_c) 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 state^1-3, 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 Bi₂Sr₂CaCu₂O_8+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-T_c cuprates.

Evolution of a Novel Ribbon Phase in Optimally Doped Bi2Sr2CaCu2O8+δ at High Pressure and Its Implication to High- TC Superconductivity

One challenge in studying high-temperature superconductivity (HTSC) stems from a lack of direct experimental evidence linking lattice inhomogeneity and superconductivity. Here, we apply synchrotron hard X-ray nanoimaging and small-angle scattering to reveal a novel micron-scaled ribbon phase in optimally doped Bi₂Sr₂CaCu₂O_8+δ (Bi-2212, with δ = 0.1). The morphology of the ribbon-like phase evolves simultaneously with the dome-shaped T_C behavior under pressure. X-ray absorption studies show that the increasing of T_C is associated with oxygen-hole redistribution in the CuO₂ plan, while T_C starts to decrease with pressure when oxygen holes become immobile. Additional X-ray irradiation experiments reveal that nanoscaled short-range ordering of oxygen vacancies could further lower T_C, which indicates that the optimal T_C is affected not only by an optimal morphology of the ribbon phase, but also an optimal distribution of oxygen vacancies. Our studies thereby provide for the first time compelling experimental evidence correlating the T_C with micron to nanoscale inhomogeneity.

Quantitative Characterization of the Nanoscale Local Lattice Strain Induced by Sr Dopants in La_{1.92}Sr_{0.08}CuO_{4}

The nanometer scale lattice deformation brought about by the dopants in the high temperature superconducting cuprate La_{2-x}Sr_{x}CuO_{4} (x=0.08) was investigated by measuring the associated x-ray diffuse scattering around multiple Bragg peaks. A characteristic diffuse scattering pattern was observed, which can be well described by continuum elastic theory. With the fitted dipole force parameters, the acoustic-type lattice deformation pattern was reconstructed and found to be of similar size to lattice thermal vibration at 7 K. Our results address the long-term concern of dopant introduced local lattice inhomogeneity, and show that the associated nanometer scale lattice deformation is marginal and cannot, alone, be responsible for the patched variation in the spectral gaps observed with scanning tunneling microscopy in the cuprates.

Topological Phase Transition with Nanoscale Inhomogeneity in (Bi1- xIn x)2Se3

Topological insulators are a class of band insulators with nontrivial topology, a result of band inversion due to the strong spin-orbit coupling. The transition between topological and normal insulator can be realized by tuning the spin-orbit coupling strength and has been observed experimentally. However, the impact of chemical disorders on the topological phase transition was not addressed in previous studies. Herein, we report a systematic scanning tunneling microscopy/spectroscopy and first-principles study of the topological phase transition in single crystals of In-doped Bi₂Se₃. Surprisingly, no band gap closure was observed across the transition. Furthermore, our spectroscopic-imaging results reveal that In defects are extremely effective "suppressors" of the band inversion, which leads to microscopic phase separation of topological-insulator-like and normal-insulator-like nano regions across the "transition". The observed topological electronic inhomogeneity demonstrates the significant impact of chemical disorders in topological materials, shedding new light on the fundamental understanding of topological phase transition.

Dynamics of correlation-frozen antinodal quasiparticles in superconducting cuprates

Many puzzling properties of high-critical temperature (Tc) superconducting (HTSC) copper oxides have deep roots in the nature of the antinodal quasiparticles, the elementary excitations with wave vector parallel to the Cu-O bonds. These electronic states are most affected by the onset of antiferromagnetic correlations and charge instabilities, and they host the maximum of the anisotropic superconducting gap and pseudogap. We use time-resolved extreme-ultraviolet photoemission with proper photon energy (18 eV) and time resolution (50 fs) to disclose the ultrafast dynamics of the antinodal states in a prototypical HTSC cuprate. After photoinducing a nonthermal charge redistribution within the Cu and O orbitals, we reveal a dramatic momentum-space differentiation of the transient electron dynamics. Whereas the nodal quasiparticle distribution is heated up as in a conventional metal, new quasiparticle states transiently emerge at the antinodes, similarly to what is expected for a photoexcited Mott insulator, where the frozen charges can be released by an impulsive excitation. This transient antinodal metallicity is mapped into the dynamics of the O-2p bands, thus directly demonstrating the intertwining between the low- and high-energy scales that is typical of correlated materials. Our results suggest that the correlation-driven freezing of the electrons moving along the Cu-O bonds, analogous to the Mott localization mechanism, constitutes the starting point for any model of high-Tc superconductivity and other exotic phases of HTSC cuprates.

A self-consistent determination of the RVB and SC gaps in the YRZ ansatz

A correct understanding of the origin of the pseudogap in high temperature (high-T _c) cuprate superconductors is considered to be a peripheral breakthrough in the understanding of the microscopic mechanism of the high-T _c superconductivity. Yang-Rice-Zhang (YRZ) ansatz is an important phenomenological theory to describe the phenomenon of pseudogap. However, in the framework of YRZ, the pseudogap (resonant valence bond (RVB) gap) and the superconducting (SC) gap are unable to have a self-consistent determination at different doping concentrations, and this severely limits the application of the YRZ ansatz. Based on the YRZ ansatz, this study develops a technical method to determine the RVB and SC gaps in a self-consistent manner. It is revealed that the self-consistent calculations of the doping dependence of RVB, SC gaps and spectral function are not only consistent with the empirical gap formula in the YRZ framework, but also consistent with the doping evolution of the Fermi surface observed in the angle-resolved photoemission spectroscopy (ARPES) experiments. Our method will greatly extend the applications of the YRZ ansatz, and will deepen our understanding of the origin of pseudogap as well as the mechanism of high-T _c superconductivity.

Invariom modeling of disordered structures: case studies on a dipeptide, an amino acid, and cefaclor, a cephalosporin antibiotic

Routines to facilitate the treatment of disorder in invariom modeling have been implemented in the open-source program MolecoolQt, a visualization program for charge-density work, and InvariomTool, a pre-processor program. Two published structures of an amino acid and a dipeptide and the new structure of cefaclor, a cephalosporin antibiotic, provide examples with increasing amounts of disorder, which can now be successfully modeled with invarioms. Like for ordered structures, these non-spherical scattering factors predicted by density functional theory significantly improve the structural model (figures of merit and standard deviations) also in these cases. Furthermore, they allow rapid calculation and comparison of the electrostatic potential and the molecular dipole moment for the different conformers present in the crystal structures.

High resolution electron energy loss spectroscopy with two-dimensional energy and momentum mapping

High resolution electron energy loss spectroscopy (HREELS) is a powerful technique to probe vibrational and electronic excitations at surfaces. The dispersion relation of surface excitations, i.e., energy as a function of momentum, has in the past, been obtained by measuring the energy loss at a fixed angle (momentum) and then rotating sample, monochromator, or analyzer. Here, we introduce a new strategy for HREELS, utilizing a specially designed lens system with a double-cylindrical Ibach-type monochromator combined with a commercial VG Scienta hemispherical electron energy analyzer, which can simultaneously measure the energy and momentum of the scattered electrons. The new system possesses high angular resolution (<0.1°), detecting efficiency and sampling density. The capabilities of this system are demonstrated using Bi2Sr2CaCu2O(8+δ). The time required to obtain a complete dispersion spectrum is at least one order of magnitude shorter than conventional spectrometers, with improved momentum resolution and no loss in energy resolution.

Point nodes persisting far beyond Tc in Bi2212

In contrast to a complex feature of antinodal state, suffering from competing orders, the pairing gap of cuprates is obtained in the nodal region, which therefore holds the key to the superconducting mechanism. One of the biggest question is whether the point nodal state as a hallmark of d-wave pairing collapses at T_c like the BCS-type superconductors, or it instead survives above T_c turning into the preformed pair state. A difficulty in this issue comes from the small magnitude of the nodal gap, which has been preventing experimentalists from solving it. Here we use a laser ARPES capable of ultrahigh-energy resolution, and detect the point nodes surviving far beyond T_c in Bi2212. By tracking the temperature evolution of spectra, we reveal that the superconductivity occurs when the pair-breaking rate is suppressed smaller than the single-particle scattering rate on cooling, which governs the value of T_c in cuprates.

The pairing gap of the high-T_c cuprates has been expected to close at the transition temperature, similarly to the case of conventional superconductors. Here the authors perform ARPES measurements on Bi2212, and reveal a point nodal gap formation beyond T_c, characterized in terms of three parameters.

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi_{2}Sr_{2}CaCu_{2}O_{8} can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long-standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.

Nanoscale interplay of strain and doping in a high-temperature superconductor

The highest-temperature superconductors are electronically inhomogeneous at the nanoscale, suggesting the existence of a local variable that could be harnessed to enhance the superconducting pairing. Here we report the relationship between local doping and local strain in the cuprate superconductor Bi(2)Sr(2)CaCu(2)O(8+x). We use scanning tunneling microscopy to discover that the crucial oxygen dopants are periodically distributed in correlation with local strain. Our picoscale investigation of the intraunit-cell positions of all oxygen dopants provides essential structural input for a complete microscopic theory.

Doping dependence of the nonmagnetic impurity resonance in cuprate superconductors

Motivated by the observation that the nonmagnetic impurity induced resonance strength is reduced with underdoping in Bi(2)Sr(2)Ca(Cu(1-y)Zn(y))(2)O(8+x), we study the doping dependence of the nonmagnetic impurity induced resonance in cuprates from the viewpoint of resonating valence bond (RVB) spin liquid theory. It is revealed that the pseudogap state in the Yang, Rice and Zhang ansatz (Yang et al 2006 Phys. Rev. B 73 174501; Rice et al 2012 Rep. Prog. Phys. 75 016502) does not support an impurity resonance state due to the overdamping of the quasiparticle. In the coexistence of the d-wave superconductivity and the RVB gap, our theory provides an alternative but consistent explanation for the reduction of the resonance strength with underdoping, as well as the absence of the resonance in the large gap region.

Cu(Ir₁ - xCrx)₂S₄: a model system for studying nanoscale phase coexistence at the metal-insulator transition

Increasingly, nanoscale phase coexistence and hidden broken symmetry states are being found in the vicinity of metal-insulator transitions (MIT), for example, in high temperature superconductors, heavy fermion and colossal magnetoresistive materials, but their importance and possible role in the MIT and related emergent behaviors is not understood. Despite their ubiquity, they are hard to study because they produce weak diffuse signals in most measurements. Here we propose Cu(Ir_{1 − x}Cr_x)₂S₄ as a model system, where robust local structural signals lead to key new insights. We demonstrate a hitherto unobserved coexistence of an Ir⁴⁺ charge-localized dimer phase and Cr-ferromagnetism. The resulting phase diagram that takes into account the short range dimer order is highly reminiscent of a generic MIT phase diagram similar to the cuprates. We suggest that the presence of quenched strain from dopant ions acts as an arbiter deciding between the competing ground states.

Macroscopic quantum-type potentials in theoretical systems biology

We review in this paper the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine systems theoretical biology. We emphasize in particular the concept of quantum-type potentials, since, in many situations, the effect of the fractality of space—or of the underlying medium—can be reduced to the addition of such a potential energy to the classical equations of motion. Various equivalent representations—geodesic, quantum-like, fluid mechanical, stochastic—of these equations are given, as well as several forms of generalized quantum potentials. Examples of their possible intervention in high critical temperature superconductivity and in turbulence are also described, since some biological processes may be similar in some aspects to these physical phenomena. These potential extra energy contributions could have emerged in biology from the very fractal nature of the medium, or from an evolutive advantage, since they involve spontaneous properties of self-organization, morphogenesis, structuration and multi-scale integration. Finally, some examples of applications of the theory to actual biological-like processes and functions are also provided.

Effect of magnetic criticality and Fermi-surface topology on the magnetic penetration depth

We investigate the effect of antiferromagnetic (AF) quantum criticality on the magnetic penetration depth λ(T) in line-nodal superconductors, including the cuprates, the iron pnictides, and the heavy-fermion superconductors. The critical magnetic fluctuation renormalizes the current vertex and drastically enhances the zero-temperature penetration depth λ(0), which is more remarkable in the iron-pnictide case due to the Fermi-surface topology. Additional temperature (T) dependence of the current renormalization makes the expected T-linear behavior at low temperatures approach T(1.5) asymptotically. These anomalous behaviors are consistent with experimental observations. We stress that λ(T) is a good probe to detect the AF quantum critical point in the superconducting state.

Universal superfluid transition and transport properties of two-dimensional dirty bosons

We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.

Imaging the evolution of metallic states in a correlated iridate

The Ruddlesden-Popper series of iridates (Srn+1IrnO3n+1) have been the subject of much recent attention due to the anticipation of emergent phenomena arising from the cooperative action of spin-orbit-driven band splitting and Coulomb interactions. However, an ongoing debate over the role of correlations in the formation of the charge gap and a lack of understanding of the effects of doping on the low-energy electronic structure have hindered experimental progress in realizing many of the predicted states. Using scanning tunnelling spectroscopy we map out the spatially resolved density of states in Sr3Ir2O7 (Ir327). We show that its parent compound, argued to exist only as a weakly correlated band insulator, in fact possesses a substantial ~ 130 meV charge excitation gap driven by an interplay between structure, spin-orbit coupling and correlations. We find that single-atom defects are associated with a strong electronic inhomogeneity, creating an important distinction between the intrinsic and spatially averaged electronic structure. Combined with first-principles calculations, our measurements reveal how defects at specific atomic sites transfer spectral weight from higher energies to the gap energies, providing a possible route to obtaining metallic electronic states from the parent insulating states in the iridates.

Observation of electronic inhomogeneity and charge density waves in a bilayer La(2-2x)Sr(1+2x)Mn2O7 single crystal

We employed a scanning tunneling microscope to image the (001) surface topography and local density of states (LDOS) in La(2-2x)Sr(1+2x)Mn(2)O(7) (x=0.32, LSMO) single crystals below the Curie temperature (T(C)≈120 K). The LDOS maps revealed a stripelike modulation propagating along the tetragonal a axis with a wavelength of about 16 Å, which is indicative of a charge density wave (CDW). The observed CDW in the x=0.32 sample is far from the Fermi surface nesting instability as compared with the data of angle resolved photoemission spectroscopy in an x=0.40 sample. The stripe model developed previously for cuprates can explain the observed CDW in our LSMO sample, indicating that competing interactions between localized and itinerant phases are the origin of the spatial modulations present intrinsically in cuprates and manganites.

Anomalous doping variation of the nodal low-energy feature of superconducting (Bi,Pb)2(Sr,La)2CuO(6+δ) crystals revealed by laser-based angle-resolved photoemission spectroscopy

The nodal band dispersion in (Bi,Pb)(2)(Sr,La)(2)CuO(6+δ) (Bi2201) is investigated over a wide range of doping by using 7-eV laser-based angle-resolved photoemission spectroscopy. We find that the low-energy band renormalization ("kink"), recently discovered in Bi(2)Sr(2)CaCu(2)O(8+δ) (Bi2212), also occurs in Bi2201, but at a binding energy around half that in Bi2212. Surprisingly, the coupling energy dramatically increases with a decrease of carrier concentration, showing a sharp enhancement across the optimal doping. These properties (material and doping dependence of the coupling energy) demonstrate the significant correlation among the mode coupling, the energy gap close to the node, and the strong electron correlation. Our results suggest forward scattering arising from the interplay between the electrons and in-plane polarized acoustic phonon branch as the origin of the low-energy renormalization.

Direct probe of interplay between local structure and superconductivity in FeTe₀.₅₅Se₀.₄₅

The relationship between atomically defined structures and physical properties in functional materials remains a subject of constant interest. We explore the interplay between local crystallographic structure, composition, and local superconductive properties in iron chalcogenide superconductors. Direct structural analysis of scanning tunneling microscopy data allows local lattice distortions and structural defects across an FeTe0.55Se0.45 surface to be explored on a single unit-cell level. Concurrent superconducting gap (SG) mapping reveals suppression of the SG at well-defined structural defects, identified as a local structural distortion. The strong structural distortion causes the vanishing of the superconducting state. This study provides insight into the origins of superconductivity in iron chalcogenides by providing an example of atomic-level studies of the structure-property relationship.

A cryogenic scattering-type scanning near-field optical microscope

Scattering-type scanning near-field optical microscopy (s-SNOM) provides few nanometer optical spatial resolution and is compatible with nearly any form of linear and nonlinear optical spectroscopy. We have developed a versatile s-SNOM instrument operating under cryogenic and variable temperature (∼20-500 K) and compatible with high magnetic fields (up to 7 T). The instrument features independent tip and sample scanning and free-space light delivery with an integrated off-axis parabolic mirror for tip-illumination and signal collection with a numerical aperture of N.A. = 0.45. The optics operate from the UV to THz range allowing for continuous wave, broadband, and ultrafast s-SNOM spectroscopy, including different variants of tip-enhanced spectroscopy. We discuss the instrument design, implementation, and demonstrate its performance with mid-infrared Drude response s-SNOM probing of the domain formation associated with the metal-insulator transitions of VO2 (TMIT ≃ 340 K) and V2O3 (TMIT ≃ 150 K). This instrument enables the study of mesoscopic order and domains of competing quantum phases in correlated electron materials over a wide range of controlled electric and magnetic fields, strain, current, and temperature.

Scanning tunneling spectroscopy of superconducting LiFeAs single crystals: evidence for two nodeless energy gaps and coupling to a bosonic mode

The superconducting compound LiFeAs is studied by scanning tunneling microscopy and spectroscopy. A gap map of the unreconstructed surface indicates a high degree of homogeneity in this system. Spectra at 2 K show two nodeless superconducting gaps with Δ(1)=5.3±0.1 meV and Δ(2)=2.5±0.2 meV. The gaps close as the temperature is increased to the bulk T(c), indicating that the surface accurately represents the bulk. A dip-hump structure is observed below T(c) with an energy scale consistent with a magnetic resonance recently reported by inelastic neutron scattering.

ns-Tc correlations in granular superconductors

Following a short discussion of the granular model for an inhomogeneous superconductor, we review the Uemura and Homes correlations and show how both follow in two limits of a simple granular superconductor model. Definite expressions are given for the almost universal coefficients appearing in these relationships in terms of known constants.