Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

Fledgling Quantum Spin Hall Effect in Pseudo Gap Phase of Bi2212

We studied the emergence of the quantum spin Hall (QSH) states for the pseudo-gap (PG) phase of Bi2212 bilayer system, assumed to be D-density wave (DDW) ordered, starting with a strong Rashba spin-orbit coupling (SOC) armed, and the time reversal symmetry (TRS) complaint Bloch Hamiltonian. The presence of strong SOC gives rise to non-trivial, spin-momentum locked spin texture tunable by electric field. The emergence of quantum anomalous Hall effect with TRS broken Chiral DDW Hamiltonian of Das Sarma et al. is found to be possible.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors

One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase (PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra (ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parameters with the total momentum of the Cooper pair to be zero and finite. The finite momentum pairing is accompanied with a spatial modulation of pairing order, i.e. a pair density wave (PDW). These PDW phases are intertwined with modulations of charge density and intra-unit cell form factors. The coexistence of the two different pairing orders provides the unique two-gaps like spectra observed by ARPES for superconducting cuprates. As temperature raises, the zero-momentum pairing order vanishes while the finite momentum pairing orders are kept, thus Fermi arcs are realized. The calculated quasiparticle spectra have the similar doping and temperature dependence as reported by ARPES and scanning tunneling spectroscopy (STS). The consequence of breaking symmetry between x and y due to the unidirectional PDW and the possibility to probe such a PDW state in the PG phase is discussed.

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.

Pseudogap phase of cuprate superconductors confined by Fermi surface topology

The properties of cuprate high-temperature superconductors are largely shaped by competing phases whose nature is often a mystery. Chiefly among them is the pseudogap phase, which sets in at a doping p* that is material-dependent. What determines p* is currently an open question. Here we show that the pseudogap cannot open on an electron-like Fermi surface, and can only exist below the doping p _FS at which the large Fermi surface goes from hole-like to electron-like, so that p* ≤ p _FS. We derive this result from high-magnetic-field transport measurements in La_1.6-x Nd_0.4Sr _x CuO₄ under pressure, which reveal a large and unexpected shift of p* with pressure, driven by a corresponding shift in p _FS. This necessary condition for pseudogap formation, imposed by details of the Fermi surface, is a strong constraint for theories of the pseudogap phase. Our finding that p* can be tuned with a modest pressure opens a new route for experimental studies of the pseudogap.

Spin susceptibility of charge-ordered YBa2Cu3O y across the upper critical field

The value of the upper critical field H_c2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-T_c copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use ¹⁷O NMR to measure the spin susceptibility [Formula: see text] of the CuO₂ planes at low temperature in charge-ordered YBa₂Cu₃O _y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest H_c2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces H_c2 in underdoped YBa₂Cu₃O _y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

Charge-density-wave order takes over antiferromagnetism in Bi2Sr2-x La x CuO6 superconductors

Superconductivity appears in the cuprates when a spin order is destroyed, while the role of charge is less known. Recently, charge density wave (CDW) was found below the superconducting dome in YBa₂Cu₃O_y when a high magnetic field is applied perpendicular to the CuO₂ plane, which was suggested to arise from incipient CDW in the vortex cores that becomes overlapped. Here by ⁶³Cu-nuclear magnetic resonance, we report the discovery of CDW induced by an in-plane field, setting in above the dome in single-layered Bi₂Sr_2−xLa_xCuO₆. The onset temperature T_CDW takes over the antiferromagnetic order temperature T_N beyond a critical doping level at which superconductivity starts to emerge, and scales with the pseudogap temperature T*. These results provide important insights into the relationship between spin order, CDW and the pseudogap, and their connections to high-temperature superconductivity.

Whilst superconductivity usually appears when magnetic order is suppressed, the role of charge is less known. Here, Kawasaki et al. report a charge density wave (CDW) above the superconducting transition induced by an in-plane magnetic field in Bi₂Sr_2-xLa_xCuO₆, with the CDW onset temperature scaling with the pseudogap temperature.

Nuclear magnetic resonance probe head design for precision strain control

We present the design and construction of an NMR probe to investigate single crystals under strain at cryogenic temperatures. The probe head incorporates a piezoelectric-based apparatus from Razorbill Instruments that enables both compressive and tensile strain tuning up to strain values on the order of 0.3% with a precision of 0.001%.   ⁷⁵As NMR in BaFe₂As₂ reveals large changes to the electric field gradient and indicates that the strain is homogeneous to within 16% over the volume of the NMR coil.

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.

Disappearance of nodal gap across the insulator-superconductor transition in a copper-oxide superconductor

The parent compound of the copper-oxide high-temperature superconductors is a Mott insulator. Superconductivity is realized by doping an appropriate amount of charge carriers. How a Mott insulator transforms into a superconductor is crucial in understanding the unusual physical properties of high-temperature superconductors and the superconductivity mechanism. Here we report high-resolution angle-resolved photoemission measurement on heavily underdoped Bi₂Sr₂-xLaxCuO(₆+δ) system. The electronic structure of the lightly doped samples exhibit a number of characteristics: existence of an energy gap along the nodal direction, d-wave-like anisotropic energy gap along the underlying Fermi surface, and coexistence of a coherence peak and a broad hump in the photoemission spectra. Our results reveal a clear insulator-superconductor transition at a critical doping level of ~0.10 where the nodal energy gap approaches zero, the three-dimensional antiferromagnetic order disappears, and superconductivity starts to emerge. These observations clearly signal a close connection between the nodal gap, antiferromagnetism and superconductivity.

Evidence of chiral order in the charge-ordered phase of superconducting La1.875Ba0.125Cuo4 single crystals using polar Kerr-effect measurements

High resolution polar Kerr effect measurements were performed on La1.875Ba0.125CuO4 single crystals revealing that a finite Kerr signal is measured below an onset temperature TK that coincides with the charge ordering transition temperature TCO. We further show that the sign of the Kerr signal cannot be trained with the magnetic field, is found to be the same on opposite sides of the same crystal, and is odd with respect to strain in the diagonal direction of the unit cell. These observations are consistent with a chiral "gyrotropic" order above Tc for La1.875Ba0.125CuO4; similarities to other cuprates suggest that it is a universal property in the pseudogap regime.

Emergence of charge order from the vortex state of a high-temperature superconductor

Evidence is mounting that charge order competes with superconductivity in high Tc cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa2Cu3Oy has maximum strength inside the superconducting dome, similar to compounds of the La2-x(Sr,Ba)xCuO4 family. In YBa2Cu3Oy, this occurs at doping levels of p=0.11-0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi2Sr2CaCu2O8+δ, can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.

Charge order driven by Fermi-arc instability in Bi2Sr(2-x)La(x)CuO(6+δ)

The understanding of the origin of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. We combined resonant x-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, and in momentum and real space within one cuprate family, Bi2Sr(2-x)La(x)CuO(6+δ). The observed wave vectors rule out simple antinodal nesting in the single-particle limit but match well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations of electronic order in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates and uncover its intimate connection to the pseudogap regime.

Evolution of electron-boson spectral density in the underdoped region of Bi2Sr(2-x)La(x)CuO6

We use a maximum entropy technique to obtain the electron-boson spectral density from optical scattering rate data across the underdoped region of the Bi2Sr(2-x)La(x)CuO6 (Bi-2201) phase diagram. Our method involves a generalization of previous work which explicitly includes finite temperature and the opening of a pseudogap which modifies the electronic structure. We find that the mass enhancement factor λ associated with the electron-boson spectral density increases monotonically with reduced doping and closer proximity to the Mott antiferromagnetic insulating state. This observation is consistent with increased coupling to the spin fluctuations. At the same time the system has reduced metallicity because of increased pseudogap effects which we model with a reduced effective density of states around the Fermi energy with the range of the modifications in energy set by the pseudogap scale.

Quantum oscillations in YBa2Cu3O(6+δ) from period-8 d-density wave order

We consider quantum oscillation experiments in YBa(2)Cu(3)O(6+δ) from the perspective of Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula for the conductivity. The specific density wave order responsible for reconstruction is a period-8 d-density wave in which the current density is unidirectionally modulated, which is also naturally accompanied by a period-4 charge order, consistent with recent nuclear magnetic resonance experiments. This scenario leads to a natural explanation as to why only oscillations from a single electron pocket of a frequency of about 500 T is observed, and a hole pocket of roughly twice the frequency as dictated by the twofold commensurate order and the Luttinger sum rule is not observed. In contrast period-8 d-density wave leads to a hole pocket of roughly half the frequency of the electron pocket. The observation of this slower frequency will require higher, but not unrealistic, magnetic fields than those commonly employed. There is already some suggestion of the slower frequency in a measurement in fields as high as 85 T.

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang et al (2006 Phys. Rev. B 73 174501). This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons with experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.

NMR signal averaging in 62T pulsed fields

Nuclear Magnetic Resonance (NMR) experiments in pulsed high magnetic fields up to 62T at the Dresden High Magnetic Field Laboratory (Hochfeld-Magnetlabor Dresden) are reported. The time dependence of the magnetic field is investigated by observing various free induction decays (FIDs) in the vicinity of the maximum of the field pulse. By analyzing each FID's phase and its evolution with time the magnetic field's time dependence can be determined with high precision. Assuming a quadratic or cubic dependence on time near the field maximum its confidence is found to be better than ± 0.03ppm at low fields and ± 0.8ppm near 62T. In turn, the thus obtained time dependence of the field can be used to demodulate and phase-correct all FIDs so that they appear phase-locked to each other. As a consequence signal averaging is possible. The increase in signal-to-noise ratio is found to be close to that expected theoretically. This shows that the intrinsic time dependence of the pulsed fields can be removed so that the NMR signals appear to be taken at rather stable static field. This opens up the possibility of performing precise shift measurements and signal averaging also of unknown, weak signals if a reference signal is measured during the same field pulse with a double-resonance probe.

From a single-band metal to a high-temperature superconductor via two thermal phase transitions

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T(c)), entangled in an energy-momentum-dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.