Strain-induced long-range charge-density wave order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor

The mechanism of high-temperature superconductivity in copper oxides (cuprate) remains elusive, with the pseudogap phase considered a potential factor. Recent attention has focused on a long-range symmetry-broken charge-density wave (CDW) order in the underdoped regime, induced by strong magnetic fields. Here by 63,65Cu-nuclear magnetic resonance, we report the discovery of a long-range CDW order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor, induced by in-plane strain exceeding ∣ε∣ = 0.15 %, which deliberately breaks the crystal symmetry of the CuO2 plane. We find that compressive/tensile strains reduce superconductivity but enhance CDW, leaving superconductivity to coexist with CDW. The findings show that a long-range CDW order is an underlying hidden order in the pseudogap state, not limited to the underdoped regime, becoming apparent under strain. Our result sheds light on the intertwining of various orders in the cuprates.

Emergent normal fluid in the superconducting ground state of overdoped cuprates

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi2Sr2CuO6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

Prominent Josephson tunneling between twisted single copper oxide planes of Bi2Sr2-xLaxCuO6+y

Josephson tunneling in twisted cuprate junctions provides a litmus test for the pairing symmetry, which is fundamental for understanding the microscopic mechanism of high temperature superconductivity. This issue is rekindled by experimental advances in van der Waals stacking and the proposal of an emergent d+id-wave. So far, all experiments have been carried out on Bi2Sr2CaCu2O8+x (Bi-2212) with double CuO2 planes but show controversial results. Here, we investigate junctions made of Bi2Sr2-xLaxCuO6+y (Bi-2201) with single CuO2 planes. Our on-site cold stacking technique ensures uncompromised crystalline quality and stoichiometry at the interface. Junctions with carefully calibrated twist angles around 45° show strong Josephson tunneling and conventional temperature dependence. Furthermore, we observe standard Fraunhofer diffraction patterns and integer Fiske steps in a junction with a twist angle of 45.0±0.2°. Together, these results pose strong constraints on the d or d+id-wave pairing and suggest an indispensable isotropic pairing component.

Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+δ

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen-Cooper-Schrieffer theory¹. However, it was shown that the superfluid density vanishes when the transition temperature goes to zero^2,3, in contradiction to expectations from Bardeen-Cooper-Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi)₂Sr₂CuO_6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix^4,5. Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

Critical nematic correlations throughout the superconducting doping range in Bi2-zPbzSr2-yLayCuO6+x

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-T_c superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi_2-zPb_zSr_2-yLa_yCuO_6+x. The ratio of the phase correlation length ξ_CDW to the orientation correlation length ξ_orient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.

The magnetic field driven superconductor-metal transition in disordered hole-overdoped cuprates

By solving the Bogoliubov-de Gennes equations for ad-wave superconductor, we explore how the interplay between disorder and the orbital depairing of an external magnetic field influences the superconductor-metal transition of the hole-overdoped cuprates. For highly disordered systems, we find granular Cooper paring to persist above the critical field where the superfluid stiffness goes to zero. We also show that because the vortices are attracted to regions where the superconducting pairing is already weak, the Caroli-de Gennes-Matricon zero-bias peak in the local density of states at the vortex cores disappears already at moderate disorder.

Pseudogap in underdoped cuprate seen in longitudinal magnetoresistance

We report the results of in-plane magnetotransport study of slightly underdoped cuprate La_1.85Sr_0.15CuO₄(LSCO15) with Ni impurity. Increasing Ni contentycauses a sharp drop in longitudinal magnetoresistance (LMR) in LSCO15 to broaden and move towards higher temperatures. TemperatureTmLMR(y)of this local maximum in LMR coincides with temperatureTdev(y), below which ideal resistivity from the parallel-resistor model deviates from itsT²-dependence. A direct comparison with the hole doping evolution of pseudogap (PG) in La2-xSr_xCuO₄(LSCO), possible through the mobile-carrier concentration extracted from the thermopower measurements, allows to equate both characteristic temperaturesTmLMR≅Tdevwith PG opening temperatureT∗. The rate of PG closing by magnetic field parallel to the CuO₂plane, in measurements up to 9 T, is consistent with spin-paramagnetic effect in this configuration and yields PG closing fieldB_pcclose to the second critical fieldBc2predicted for superconducting gap with the help of Werthamer-Helfand-Hohenberg theory. The field anisotropy ofB_pcsuggests that orbital degrees of freedom also play a role in PG formation.

Ultra-high critical current densities of superconducting YBa2Cu3O7-δ thin films in the overdoped state

The functional properties of cuprates are strongly determined by the doping state and carrier density. We present an oxygen doping study of YBa₂Cu₃O_7-δ (YBCO) thin films from underdoped to overdoped state, correlating the measured charge carrier density, [Formula: see text], the hole doping, p, and the critical current density, [Formula: see text]. Our results show experimental demonstration of strong increase of [Formula: see text] with [Formula: see text], up to Quantum Critical Point (QCP), due to an increase of the superconducting condensation energy. The ultra-high [Formula: see text] achieved, 90 MA cm^-2 at 5 K corresponds to about a fifth of the depairing current, i.e. a value among the highest ever reported in YBCO films. The overdoped regime is confirmed by a sudden increase of [Formula: see text], associated to the reconstruction of the Fermi-surface at the QCP. Overdoping YBCO opens a promising route to extend the current carrying capabilities of rare-earth barium copper oxide (REBCO) coated conductors for applications.

The charge-density-wave signature on the superfluid density of cuprate superconductors

The superfluid density or superconducting (SC) carrier concentrationn_scof cuprates has been the subject of intense investigations but there is not any single theory capable to explain all the available data. Here we show that the behavior ofn_scin under and overdoped cuprates are a consequence of an SC interaction based on charge fluctuations in the incommensurate charge-density-waves (CDW) domains. We have shown that this interaction scales with the CDW amplitude or the pseudogap (PG) energy, yielding local SC amplitudes and Josephson currents. The average Josephson energyEJis proportional to the phase stiffness or superfluid densityρ_sc∝n_sc. We find thatn_sc(p) increases almost linearly with dopingpin the underdoped region and in the charge abundant overdoped only a few fractions of the holes condense leading to two kinds of carriers, a recently confirmed feature. The calculations and theρ_scdata uncover how the PG-CDW-SC intertwined orders operate to yield cuprates properties.

Anomalous Doping Evolution of Superconductivity and Quasiparticle Interference in Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ} Trilayer Cuprates

We use scanning tunneling microscopy to investigate Bi_{2}Sr_{2}Ca_{2}Cu_{3}O_{10+δ} trilayer cuprates from the optimally doped to overdoped regime. We find that the two distinct superconducting gaps from the inner and outer CuO_{2} planes both decrease rapidly with doping, in sharp contrast to the nearly constant T_{C}. Spectroscopic imaging reveals the absence of quasiparticle interference in the antinodal region of overdoped samples, showing an opposite trend to that in single- and double-layer compounds. We propose that the existence of two types of inequivalent CuO_{2} planes and the intricate interaction between them are responsible for these anomalies in trilayer cuprates.

Pseudogap and Weak Multifractality in 2D Disordered Mott Charge-Density-Wave Insulator

We investigate electronic states of Se-substituted 1T-TaS₂ by scanning tunneling microscopy/spectroscopy (STM/STS), where superconductivity emerges from the unique Mott-charge-density-wave (Mott-CDW) state. Spatially resolved STS measurements reveal that a pseudogap replaces the Mott gap with the CDW gaps intact. The pseudogap has little correlation with the unit-cell-to-unit-cell variation in the local Se concentration but appears globally. The correlation length of the local density of states (LDOS) is substantially enhanced at the Fermi energy and decays rapidly at high energies. Furthermore, the statistical analysis of LDOS indicates the weak multifractal behavior of the wave functions. These findings suggest a correlated metallic state induced by disorder and provide a new insight into the emerging superconductivity in two-dimensional materials.

A hybrid magnet based scanning tunneling microscope

In this paper, a scanning tunneling microscope (STM) is presented that operates in a 27.5 T magnetic field within a hybrid magnet. The coarse approach of the STM is realized by using an inertial piezoelectric motor, and the scanning is realized by using a miniature scanner, which stands alone on a sapphire base. A combined vibration isolation system consisting of a brick-rubber-brick stack and two springs is used to isolate the vibration generated from the magnet. An enclosed copper shield is used to prevent sound from entering the tip-sample junction. The sound and vibration isolation measures highly improve the stability of the STM imaging. All the materials selected to construct the STM head are nonmagnetic. The drift rates of the STM in the X-Y plane and Z direction are as low as 26.2 pm/min and 34.6 pm/min, respectively, under ambient conditions. The high performance of the homebuilt STM was demonstrated by graphite hexagonal lattice images obtained in magnet fields ranging from 0 T to 27.5 T even without the protection of a vacuum and low temperatures. As far as known, this is the first STM that operates in a hybrid magnet. It is also the first STM that can obtain graphite hexagonal lattice images in magnetic fields up to 27.5 T. Our results greatly contribute to the further STM studies under ambient conditions and ultrahigh magnetic fields.

Surprises in the t-J Model: Implications for Cuprates

Many strongly correlated systems, such as the cuprate superconductors, have the interesting physics of low dimensionality and hence enhanced fluctuation effects. We perform an analysis of the t-J model in the slave boson formulation which accounts for strong correlations, focusing on fluctuation effects that have hitherto not received the attention they deserve. We find several interesting results including the instability of the d-wave superconducting state to internal phase fluctuations giving way to a time reversal broken d+is^{*} superconductor at low doping. This offers an explanation for some recent experimental findings in the cuprate superconductors, including the observation of nodeless superconductivity at low doping. We also suggest further experiments that can validate our claims. On a broader perspective, this work points to the importance of considering fluctuation effects in other two-dimensional strongly correlated systems opening up a plethora of possibilities.

A variable-temperature scanning tunneling microscope operated in a continuous flow cryostat

We present a continuous flow cryostat scanning tunneling microscope (STM) which can be operated at temperatures between 4.9 K and 300 K. A variable temperature insert with 20 mm aperture is installed in the cryostat. A base temperature of 4.9 K at the STM head was achieved with helium exchange gas cooling. By using a novel design of zirconia structure, the size of the STM head was minimized to 9.2 mm in outer diameter. The high compactness and rigidity of the STM head make it less sensitive to vibrations, contributing to the high stability of the tip-sample junction. The drifting rates of the STM at 4.9 K in the X-Y plane and Z direction are 1.96 and 3.05 pm/min, respectively. The performance of the STM was demonstrated by atomically resolved imaging of graphite and NbSe₂ without using external vibrational isolation. Furthermore, the dI/dV spectra of NbSe₂ were resolved near its critical temperature, illustrating the formation process of the superconducting gap as a function of temperature. This STM is ultrahigh vacuum and strong magnetic field compatible, making it promising for direct application in the extreme conditions involving water-cooled magnets and hybrid magnets.

Atomically resolved probe-type scanning tunnelling microscope for use in harsh vibrational cryogen-free superconducting magnet

We present a probe-type scanning tunnelling microscope (STM) with atomic resolution that is designed to be directly inserted and work in a harsh vibrational cryogen-free superconducting magnet system. When a commercial variable temperature insert (VTI) is installed in the magnet and the STM is housed in the VTI, a lowest temperature of 1.6 K can be achieved, at which the STM still operates well. We tested the STM in an 8 T superconducting magnet cooled with a pulse-tube cryocooler and obtained atomically resolved graphite and NbSe₂ images as well as the scanning tunnelling spectrum (i.e., dI/dV spectrum) data of the latter near its critical temperature, which show the formation process of the superconducting gap as a function of temperature. The drifting rates of the STM at 1.6 K in the X-Y plane and Z direction are 1.15 and 1.71 pm/min, respectively. Noise analysis for the tunnelling current shows that the amplitudes of the dominant peaks (6.84 and 10.25 Hz) are as low as 1.5 pA.Hz^-1/2 when we set the current to 0.5 nA and open the feedback loop. This is important as a cryogen-free magnet system has long been considered too harsh for any atomic resolution measurement.

Cooper Pair Density of Bi2Sr2CaCu2O8+ x in Atomic scale at 4.2 K

In pursuit of the elusive mechanism of high- T _C superconductors (HTSC), spectroscopic imaging scanning tunneling microscopy (SI-STM) is an indispensable tool for surveying local properties of HTSC. Since a conventional STM utilizes metal tips, which allow the examination of only quasiparticles and not superconducting (SC) pairs, Josephson tunneling using STM has been demonstrated by many authors in the past. An atomically resolved scanning Josephson tunneling microscopy (SJTM), however, was realized only recently on Bi₂Sr₂CaCu₂O_{8+ x} (Bi-2212) below 50 mK and on the Pb(110) surface at 20 mK. Here we report the atomically resolved SJTM on Bi₂Sr₂CaCu₂O_{8+ x} at 4.2 K using Bi-2212 tips created in situ. The I- V characteristics show clear zero bias conductance peaks following Ambegaokar-Baratoff (AB) theory. A gap map was produced for the first time using an atomically resolved Josephson critical current map I _C( r) and AB theory. Surprisingly, we found that this new gap map is anticorrelated to the gap map produced by a conventional method relying on the coherence peaks. Quasiparticle resonance due to a single isolated zinc atom impurity was also observed by SJTM, indicating that atomically resolved SJTM was achieved at 4.2 K. Our result provides a starting point for realizing SJTM at even higher temperatures, rendering possible investigation of the existence of SC pairs in HTSC above the T _C.

Re-entrant charge order in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime

In the underdoped regime, the cuprate high-temperature superconductors exhibit a host of unusual collective phenomena, including unconventional spin and charge density modulations, Fermi surface reconstructions, and a pseudogap in various physical observables. Conversely, overdoped cuprates are generally regarded as conventional Fermi liquids possessing no collective electronic order. In partial contradiction to this widely held picture, we report resonant X-ray scattering measurements revealing incommensurate charge order reflections for overdoped (Bi,Pb)_2.12Sr_1.88CuO_6+δ (Bi2201), with correlation lengths of 40-60 lattice units, that persist up to temperatures of at least 250 K. The value of the charge order wavevector decreases with doping, in line with the extrapolation of the trend previously observed in underdoped Bi2201. In overdoped materials, however, charge order coexists with a single, unreconstructed Fermi surface without nesting or pseudogap features. The discovery of re-entrant charge order in Bi2201 thus calls for investigations in other cuprate families and for a reconsideration of theories that posit an essential relationship between these phenomena.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below T _c, as well as in a wide temperature region above T _c, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T ^*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q  =  0 phase transitions, of both nematic and loop currents characters.

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.

The study of electronic nematicity in an overdoped (Bi, Pb)2Sr2CuO6+δ superconductor using scanning tunneling spectroscopy

The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi₂Sr₂CaCu₂O_8+δ, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)₂Sr₂CuO_6+δ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.

Mottness at finite doping and charge-instabilities in cuprates

The influence of the Mott physics on the doping-temperature phase diagram of copper oxides represents a major issue that is subject of intense theoretical and experimental effort. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p→Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping p_cr ≈0.16 irrespective of the temperature, and it can be well described by dynamical mean field theory calculations. We argue that the onset of the low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < p_cr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.

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.

Suppression of Superfluid Density and the Pseudogap State in the Cuprates by Impurities

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at Ω_{1}≈4  meV and Ω_{2}≈15  meV, allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity-affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and nonmagnetic impurities in these materials.

Dispersing artifacts in FT-STS: a comparison of set point effects across acquisition modes

Fourier-transform scanning tunnelling spectroscopy (FT-STS), or quasiparticle interference, has become an influential tool for the study of a wide range of important materials in condensed matter physics. However, FT-STS in complex materials is often challenging to interpret, requiring significant theoretical input in many cases, making it crucial to understand potential artifacts of the measurement. Here, we compare the most common modes of acquiring FT-STS data and show through both experiment and simulations that artifact features can arise that depend on how the tip height is stabilized throughout the course of the measurement. The most dramatic effect occurs when a series of dI/dV maps at different energies are acquired with simultaneous constant current feedback; here a feature that disperses in energy appears that is not observed in other measurement modes. Such artifact features are similar to those arising from real physical processes in the sample and are susceptible to misinterpretation.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

Collapse of Ferromagnetism and Fermi Surface Instability near Reentrant Superconductivity of URhGe

We present thermoelectric power and resistivity measurements in the ferromagnetic superconductor URhGe for a magnetic field applied along the hard magnetization b axis of the orthorhombic crystal. Reentrant superconductivity is observed near the spin reorientation transition at H_{R}=12.75  T, where a first order transition from the ferromagnetic to the polarized paramagnetic state occurs. Special focus is given to the longitudinal configuration, where both the electric and heat current are parallel to the applied field. The validity of the Fermi-liquid T^{2} dependence of the resistivity through H_{R} demonstrates clearly that no quantum critical point occurs at H_{R}. Thus, the ferromagnetic transition line at H_{R} becomes first order implying the existence of a tricritical point at finite temperature. The enhancement of magnetic fluctuations in the vicinity of the tricritical point stimulates the reentrance of superconductivity. The abrupt sign change observed in the thermoelectric power with the thermal gradient applied along the b axis together with the strong anomalies in the other directions is definitive macroscopic evidence that in addition a significant change of the Fermi surface appears through H_{R}.

Bipartite electronic superstructures in the vortex core of Bi2Sr2CaCu2O8+δ

The central issue in the physics of cuprate superconductivity is the mutual relationship among superconductivity, pseudogap and broken-spatial-symmetry states. A magnetic field B suppresses superconductivity, providing an opportunity to investigate the competition among these states. Although various B-induced electronic superstructures have been reported, their energy, spatial and momentum-space structures are unclear. Here, we show using spectroscopic-imaging scanning tunnelling microscopy on Bi₂Sr₂CaCu₂O_8+δ that there are two distinct B-induced electronic superstructures, both being localized in the vortex core but appearing at different energies. In the low-energy range where the nodal Bogoliubov quasiparticles are well-defined, we observe the so-called vortex checkerboard that we identify as the B-enhanced quasiparticle interference pattern. By contrast, in the high-energy region where the pseudogap develops, the broken-spatial-symmetry patterns that pre-exist at B=0 T is locally enhanced in the vortex core. This evidences the competition between superconductivity and the broken-spatial-symmetry state that is associated with the pseudogap.

Field-induced electronic structures with spatial, momentum and energy resolution reveal the nature of interaction among multiple phases in correlated materials. Here, Machida et al. report two magnetic field-induced electronic superstructures in Bi₂Se₂CaCu₂O_8+δ, evidencing competition between superconductivity and emerging states.

Sequence of Quantum Phase Transitions in Bi2Sr2CaCu2O(8+δ) Cuprates Revealed by In Situ Electrical Doping of One and the Same Sample

Our recently discovered electrical doping technique allows a broad-range variation of carrier concentration without changing the chemical composition. We show that it is possible to induce superconductivity in a nondoped insulating sample and to tune it reversibly all the way to an overdoped metallic state. This way, we can investigate the whole doping diagram of one and the same sample. Our study reveals two distinct critical points. The one at the overdoped side is associated with the onset of the pseudogap and with the metal-to-insulator transition in the c-axis transport. The other at optimal doping is associated with the appearance of a "dressed" electron energy. Our study confirms the existence of multiple phase transitions under the superconducting dome in cuprates.

Hidden Fermionic Excitation Boosting High-Temperature Superconductivity in Cuprates

The dynamics of a microscopic cuprate model, namely, the two-dimensional Hubbard model, is studied with a cluster extension of the dynamical mean-field theory. We find a nontrivial structure of the frequency-dependent self-energies, which describes an unprecedented interplay between the pseudogap and superconductivity. We show that these properties are well described by quasiparticles hybridizing with (hidden) fermionic excitations, emergent from the strong electronic correlations. The hidden fermion enhances superconductivity via a mechanism distinct from a conventional boson-mediated pairing, and originates the normal-state pseudogap. Though the hidden fermion is elusive in experiments, it can solve many experimental puzzles.

Effects of pressure and distortion on superconductivity in Tl₂Ba₂CaCu₂O(8+δ)

The systematic evolution of the structural, vibrational, and superconducting properties of nearly optimally doped Tl2Ba2CaCu2O(8+δ) with pressure up to 30 GPa is studied by x-ray diffraction, Raman scattering, and magnetic susceptibility measurements. No phase transformation is observed in the studied pressure regime. The obtained lattice parameters and unit-cell volume continuously decrease with pressure by following the expected equation of state. The axial ratio of c/a exhibits an anomaly starting from 9 GPa. At such a pressure level, the deviation from the nonlinear variation of the phonon frequencies is detected. Both the above observations indicate the enhancement of the distortion upon compression. The superconducting transition temperature is found to exhibit a parabolic behavior with a maximum of 114 K around 7 GPa. We demonstrate that the interplay between the intrinsic pressure variables and distortion controls the superconductivity.

Fermi-surface-free superconductivity in underdoped (Bi,Pb)(Sr,La)2CuO(6+δ) (Bi2201)

Fermi-surface-free superconductivity arises when the superconducting order pulls down spectral weight from a band that is completely above the Fermi energy in the normal state. We show that this can arise in hole-doped cuprates when a competing order causes a reconstruction of the Fermi surface. The change in Fermi surface topology is accompanied by a characteristic rise in the spectral weight. Our results support the presence of a trisected superconducting dome, and suggest that superconductivity is responsible for stabilizing the (π,π) magnetic order at higher doping.

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.

Collapse of the normal-state pseudogap at a Lifshitz transition in the Bi(2)Sr(2)CaCu(2)O(8+δ) cuprate superconductor

We report a fine tuned doping study of strongly overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

The nature of the pseudogap regime of cuprate superconductors at low hole density remains unresolved. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low-energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge-density wave order at intermediate temperatures and quantum oscillations at high magnetic fields and low temperatures. Here we show that a model of competing charge-density wave and superconducting orders provides a unified description of the intermediate and low-temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero-field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge-density and superconducting orders. Our results are compatible with experimental trends.

Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking

The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.