Universal versus material-dependent two-gap behaviors of the high-Tc cuprate superconductors: angle-resolved photoemission study of La2-xSrxCuO4

Tracing the dynamics of superconducting order via transient terahertz third-harmonic generation

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify nonequilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently, nonlinear THz third-harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here, we extend this idea to light-driven nonequilibrium states in superconducting La2-xSrxCuO4, establishing an optical pump-THz-THG drive protocol to access the transient superconducting order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional TH spectroscopy to disentangle the effects of optically excited quasiparticles from the pure order-parameter dynamics, which are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

Observing the Influence of Reduced Dimensionality on Fermionic Superfluids

Understanding the origins of unconventional superconductivity has been a major focus of condensed matter physics for many decades. While many questions remain unanswered, experiments have found the highest critical temperatures in layered two-dimensional materials. However, to what extent the remarkable stability of these strongly correlated 2D superfluids is affected by their reduced dimensionality is still an open question. Here, we use dilute gases of ultracold fermionic atoms as a model system to directly observe the influence of dimensionality on the stability of strongly interacting fermionic superfluids. We find that the superfluid gap follows the same universal function of the interaction strength regardless of dimensionality, which suggests that there is no inherent difference in the stability of two- and three-dimensional fermionic superfluids. Finally, we compare our data to results from solid state systems and find a similar relation between the interaction strength and the gap for a wide range of two- and three-dimensional superconductors.

Differentiated roles of Lifshitz transition on thermodynamics and superconductivity in La2-xSrxCuO4

The effect of Lifshitz transition on thermodynamics and superconductivity in hole-doped cuprates has been heavily debated but remains an open question. In particular, an observed peak of electronic specific heat is proposed to originate from fluctuations of a putative quantum critical point p* (e.g., the termination of pseudogap at zero temperature), which is close to but distinguishable from the Lifshitz transition in overdoped La-based cuprates where the Fermi surface transforms from hole-like to electron-like. Here we report an in situ angle-resolved photoemission spectroscopy study of three-dimensional Fermi surfaces in La_2-xSr_xCuO₄ thin films (x = 0.06 to 0.35). With accurate k_z dispersion quantification, the said Lifshitz transition is determined to happen within a finite range around x = 0.21. Normal state electronic specific heat, calculated from spectroscopy-derived band parameters, reveals a doping-dependent profile with a maximum at x = 0.21 that agrees with previous thermodynamic microcalorimetry measurements. The account of the specific heat maximum by underlying band structures excludes the need for additionally dominant contribution from the quantum fluctuations at p*. A d-wave superconducting gap smoothly across the Lifshitz transition demonstrates the insensitivity of superconductivity to the dramatic density of states enhancement.

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.

Observation of small Fermi pockets protected by clean CuO2 sheets of a high-T c superconductor

In cuprate superconductors with high critical transition temperature (T _c), light hole-doping to the parent compound, which is an antiferromagnetic Mott insulator, has been predicted to lead to the formation of small Fermi pockets. These pockets, however, have not been observed. Here, we investigate the electronic structure of the five-layered Ba₂Ca₄Cu₅O₁₀(F,O)₂, which has inner copper oxide (CuO₂) planes with extremely low disorder, and find small Fermi pockets centered at (π/2, π/2) of the Brillouin zone by angle-resolved photoemission spectroscopy and quantum oscillation measurements. The d-wave superconducting gap opens along the pocket, revealing the coexistence between superconductivity and antiferromagnetic ordering in the same CuO₂ sheet. These data further indicate that superconductivity can occur without contribution from the antinodal region around (π, 0), which is shared by other competing excitations.

Pauli-limit upper critical field of high-temperature superconductor La1.84Sr0.16CuO4

The upper critical field of a cuprate high-temperature superconductor, La_1.84Sr_0.16CuO₄, was investigated by high-frequency self-resonant contactless electrical conductivity measurements in magnetic fields up to 102 T. An irreversible transition was observed at 85 T (T = 4.2 K), defined as the upper critical field. The temperature-dependent upper critical field was argued on the basis of the Werthamer-Helfand-Hohenberg theory. The Pauli-limiting pair-breaking process with a small contribution of the spin-orbit coupling explained the first-order phase transition exhibiting a hysteresis observed at low temperatures.

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.

Evolution of electron Fermi surface with doping in cobaltates

The notion of the electron Fermi surface is one of the characteristic concepts in the field of condensed matter physics, and it plays a crucial role in the understanding of the physical properties of doped Mott insulators. Based on the t-J model, we study the nature of the electron Fermi surface in the cobaltates, and qualitatively reproduce the essential feature of the evolution of the electron Fermi surface with doping. It is shown that the underlying hexagonal electron Fermi surface obeys Luttinger's theorem. The theory also predicts a Fermi-arc phenomenon at the low-doped regime, where the region of the hexagonal electron Fermi surface along the [Formula: see text]-K direction is suppressed by the electron self-energy, and then six disconnected Fermi arcs located at the region of the hexagonal electron Fermi surface along the [Formula: see text]-M direction emerge. However, this Fermi-arc phenomenon at the low-doped regime weakens with the increase of doping.

Pseudogap in cuprates driven by D-wave flux-phase order proximity effects: a theoretical analysis from Raman and ARPES experiments

One of the puzzling characteristics of the pseudogap phase of high-Tc cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an associated pseudogap. Angle-resolved photoemission spectroscopy and electronic Raman scattering are two valuable tools which have shown universal features which are rather material-independent, and presumably intrinsic to the pseudogap phase. The doping and temperature dependence of the Fermi arcs and the pseudogap observed by photoemission near the antinode correlates with the non-Fermi liquid behaviour observed by Raman for the B(1g) mode. In contrast, and similar to the nodal quasiparticles detected by photoemission, the Raman B(2g) mode shows Fermi liquid features. We show that these two experiments can be analysed, in the context of the t-J model, by self-energy effects in the proximity to a D-wave flux-phase order instability. This approach supports a crossover origin for the pseudogap, and a scenario of two competing phases. The B(2g) mode shows, in an underdoped case, a depletion at intermediate energy which has attracted renewed interest. We study this depletion and discuss its origin and relation with the pseudogap.

Pairing and the phase diagram of the normal coherence length ξN(T, x) above Tc of La(2-x)Sr(x)CuO4 thin films probed by the Josephson effect

The long range proximity effect in high-T_c c-axis Josephson junctions with a high-T_c barrier of lower T_c is still a puzzling phenomenon. It leads to supercurrents in junctions with much thicker barriers than would be allowed by the conventional proximity effect. Here we measured the T − x (Temperature-doping level) phase diagram of the barrier coherence length ξ_N(T, x), and found an enhancement of ξ_N at moderate under-doping and high temperatures. This indicates that a possible origin of the long range proximity effect in the cuprate barrier is the conjectured pre-formed pairs in the pseudogap regime, which increase the length scale over which superconducting correlations survive in the seemingly normal barrier. In more details, we measured the supercurrents I_c of Superconducting - Normal - Superconducting SNS c-axis junctions, where S was optimally doped Y Ba₂Cu₃O_7−δ below T_c (90 K) and N was La_2−xSr_xCuO₄ above its T_c (<25 K) but in the pseudogap regime. From the exponential decay of I_c(T) ∝ exp[−d/ξ_N(T)], where d is the barrier thickness, the ξ_N(T) values were extracted. By repeating these measurements for different barrier doping levels x, the whole phase diagram of ξ_N(T, x) was obtained.

Superconductivity. Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet

High-temperature superconductivity in cuprates arises from an electronic state that remains poorly understood. We report the observation of a related electronic state in a noncuprate material, strontium iridate (Sr2IrO4), in which the distinct cuprate fermiology is largely reproduced. Upon surface electron doping through in situ deposition of alkali-metal atoms, angle-resolved photoemission spectra of Sr2IrO4 display disconnected segments of zero-energy states, known as Fermi arcs, and a gap as large as 80 millielectron volts. Its evolution toward a normal metal phase with a closed Fermi surface as a function of doping and temperature parallels that in the cuprates. Our result suggests that Sr2IrO4 is a useful model system for comparison to the cuprates.

Superconducting pairing and the pseudogap in the nematic dynamical stripe phase of La2-xSrxCuO4

Fully absorption coefficient corrected Raman spectra were obtained in La2-xSrxCuO4. The B1g spectra have a Fleury-Loudon type two-magnon peak (resonant term) whose energy decreases from 3180 cm(-1) (394 meV) to 440 cm(-1) (55 meV) on increasing the carrier density from x = 0 to 0.25, while the B2g spectra have a 1000-3500 cm(-1) (124-434 meV) hump (hill) whose lower-edge energy increases from x = 0 to 0.115 and then stays constant to x = 0.25. The B2g hump is assigned to the electronic scattering (non-resonant term) of the spectral function with magnetic self-energy. The completely different carrier density dependence arises from anisotropic magnetic excitations of spin-charge stripes. The B1g spectra were assigned to the sum of k ∥  and k⊥ stripe excitations and the B2g spectra to k⊥ stripe excitations according to the calculation by Seibold and Lorenzana (2006 Phys. Rev. B 73 144515). The k ∥  and k⊥ stripe excitations in fluctuating spin-charge stripes were separately detected for the first time. The appearance of only k⊥ stripe excitations in the electronic scattering arises from the charge hopping perpendicular to the stripe. This is the same direction as the Burgers vector of the edge dislocation in metal. The successive charge hopping in the Burgers vector direction across the charge stripes may cause Cooper pairs as predicted by Zaanen et al (2004 Ann. Phys. 310 181). Indeed, this is supported by the experimental fact that the superconducting coherent length coincides with the inter-charge stripe distance in the wide carrier density range. The one-directional charge hopping perpendicular to the stripe causes the flat Fermi surface and the pseudogap near (π,0) and (0,π), but the states around (π/2,π/2) cannot be produced. The low-energy Raman scattering disclosed that the electronic states at the Fermi arc around (π/2,π/2) are coupled to the A1g soft phonon of the tetragonal-orthorhombic phase transition. This suggests that the Fermi arc is produced by the electron-phonon interaction. All the present Raman data suggest that Cooper pairs are formed at moving edge dislocations of dynamical charge stripes.

Collective spin excitations in the singlet-correlated band model: a comparison with resonant inelastic x-ray scattering

We analyse the spin excitations near the optimal doping of superconducting layered cuprates taking into account both the local and the itinerant spin components self-consistently. The obtained expression allows us to reproduce well the basic features of the resonant inelastic x-ray scattering and neutron scattering data experiments using a reasonable set of tight-binding parameters corresponding to the angle-resolved photoemission spectroscopy data. We also find that the spin excitation branch along the (0,0) - (0,π) symmetry direction in the first Brillouin zone shows a splitting at T < Tc. Possible experiments for verification of that prediction are briefly discussed.

Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212

An energy gap is, in principle, a dominant parameter in superconductivity. However, this view has been challenged for the case of high-T_c cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature T_c. Here we show that a nodal-gap energy 2Δ_N closely follows 8.5 k_BT_c with underdoping and is also proportional to the product of an antinodal gap energy Δ^* and a square-root superfluid density √P_s for Bi₂Sr₂CaCu₂O_8+δ, using low-energy synchrotron-radiation angle-resolved photoemission. The quantitative relations imply that the distinction between the nodal and antinodal gaps stems from the separation of the condensation and formation of electron pairs, and that the nodal-gap suppression represents the substantial phase incoherence inherent in a strong-coupling superconducting state. These simple gap-based formulae reasonably describe a crucial part of the unconventional mechanism governing T_c.

In conventional superconductors, the critical temperature is proportional to the superconducting energy gap, but this is not so in unconventional superconductors. Anzai et al. identify an alternative relationship involving nodal and antinodal gaps in an underdoped cuprate superconductor.

Evolution from a nodeless gap to d(x(2)-y(2))-wave in underdoped La(2-x)Sr(x)CuO4

Using angle-resolved photoemission spectroscopy (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and nonsuperconducting La(2-x)Sr(x)CuO(4) cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a d(x(2)-y(2)) form with increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the pairing mechanism and how superconductivity emerges from a Mott insulator.

Phase competition in trisected superconducting dome

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

Theory of a continuous stripe melting transition in a two-dimensional metal: a possible application to cuprate superconductors

We construct a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results [G. Aeppli et al., Science 278, 1432 (1997)] on singular stripe fluctuations in the cuprates, and provide a possible explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.

Observation of two Andreev-like energy scales in La2-xSrxCuO4 superconductor-normal-metal-superconductor junctions

Conductance spectra measurements of highly transparent junctions made of superconducting La2-xSrxCuO4 electrodes and a nonsuperconducting La1.65Sr0.35CuO4 barrier are reported. At low temperatures below Tc, these junctions have two prominent Andreev-like conductance peaks with clear steps at energies Δ1 and Δ2 with Δ2>2Δ1. No such peaks appear above Tc. The doping dependence at 2 K shows that both Δ1 and Δ2 scale roughly as Tc. Δ1 is identified as the superconducting energy gap, while a few scenarios are proposed as for the origin of Δ2.

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

We report the results of the Knight shift by ⁶³,⁶⁵Cu-NMR measurements on single-layered copper-oxide Bi₂Sr(₂-x)La(x)CuO(₆+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ⁶³Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.

Enhanced superconducting gaps in the trilayer high-temperature Bi2Sr2Ca2Cu3O(10+δ) cuprate superconductor

We report the first observation of the multilayer band splitting in the optimally doped trilayer cuprate Bi2Sr2Ca2Cu3O(10+δ) (Bi2223) by angle-resolved photoemission spectroscopy. The observed energy bands and Fermi surfaces are originated from the outer and inner CuO2 planes (OP and IP). The OP band is overdoped with a large d-wave gap around the node of Δ0∼43  meV while the IP is underdoped with an even large gap of Δ0∼60  meV. These energy gaps are much larger than those for the same doping level of the double-layer cuprates, which leads to the large Tc in Bi2223. We propose possible origins of the large superconducting gaps for the OP and IP: (1) minimal influence of out-of-plane disorder and a proximity effect and (2) interlayer tunneling of Cooper pairs between the OP and IP.

Evidence for two competing order parameters in underdoped cuprate superconductors from a model analysis of Fermi-Arc effects

Preformed pairs above T{c} and the two-gap scenarios are two main proposals for describing the low-doping pseudogap phase of high-T{c} cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the d charge-density wave theory or the flux phase of the t-J model.