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DOE OSTI2014

Direct Spectroscopic Evidence for Phase Competition between the Pseudogap and Superconductivity in Bi 2 Sr 2 CaCu 2 O 8+δ

In the high-temperature (T c ) cuprate superconductors, increasing evidence suggests that the pseudogap, existing below the pseudogap temperature T*, has a distinct broken electronic symmetry from that of superconductivity. Particularly, recent scattering experiments on the underdoped cuprates have suggested that a charge ordering competes with superconductivity. However, no direct link of this physics and the important low-energy excitations has been identified. We report an antagonistic singularity at Tc in the spectral weight of Bi 2 Sr 2 CaCu 2 O 8+δ as a compelling evidence for phase competition, which persists up to a high hole concentration p ~ 0.22. Comparison with a theoretical calculation confirms that the singularity is a signature of competition between the order parameters for the pseudogap and superconductivity. Our observation of the spectroscopic singularity at finite temperatures over a wide doping range provides new insights into the nature of the competitive interplay between the two intertwined phases and the complex phase diagram near the pseudogap critical point.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations

Abstract The origin of the pseudogap behavior, found in many high- T c superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a “gap-filling" rather than “gap-closing" behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Electron pairing in the pseudogap state revealed by shot noise in copper oxide junctions

In the quest to understand high-temperature superconductivity in copper oxides, debate has been focused on the pseudogap—a partial energy gap that opens over portions of the Fermi surface in the ‘normal’ state above the bulk critical temperature. The pseudogap has been attributed to precursor superconductivity, to the existence of preformed pairs and to competing orders such as charge-density waves. A direct determination of the charge of carriers as a function of temperature and bias could help resolve among these alternatives. Here we report measurements of the shot noise of tunnelling current in high-quality La 2-x Sr x CuO 4 /La 2 CuO 4 /La 2-x Sr x CuO 4 (LSCO/LCO/LSCO) heterostructures fabricated using atomic layer-by-layer molecular beam epitaxy at several doping levels. The data delineate three distinct regions in the bias voltage–temperature space. Well outside the superconducting gap region, the shot noise agrees quantitatively with independent tunnelling of individual charge carriers. Deep within the superconducting gap, shot noise is greatly enhanced, reminiscent of multiple Andreev reflections. Above the critical temperature and extending to biases much larger than the superconducting gap, there is a broad region in which the noise substantially exceeds theoretical expectations for single-charge tunnelling, indicating pairing of charge carriers. These pairs are detectable deep into the pseudogap region of temperature and bias. The presence of these pairs constrains current models of the pseudogap and broken symmetry states, while phase fluctuations limit the domain of superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Pairing, pseudogap and Fermi arcs in cuprates

We use Angle Resolved Photoemission Spectroscopy (ARPES) to study the relationship between the pseudogap, pairing and Fermi arcs in cuprates. High quality data measured over a wide range of dopings reveals a consistent picture of Fermiology and pairing in these materials. The pseudogap is due to an ordered state that competes with superconductivity rather than preformed pairs. Pairing does occur below T pair ~ 150K and significantly above T c , but well below T* and the doping dependence of this temperature scale is distinct from that of the pseudogap. The d-wave gap is present below T pair , and its interplay with strong scattering creates “artificial” Fermi arcs for T c ≤ T ≤ T pair . However, above T pair , the pseudogap exists only at the antipodal region. This leads to presence of real, gapless Fermi arcs close to the node. The length of these arcs remains constant up to T*, where the full Fermi surface is recovered. As a result, we demonstrate that these findings resolve a number of seemingly contradictory scenarios.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Temperature Evolution of Energy Gap and Band Structure in the Superconducting and Pseudogap States of Bi 2 Sr 2 CaCu 2 O 8+ δ Superconductor Revealed by Laser-Based Angle-Resolved Photoemission Spectroscopy

For this study, we carry out detailed momentum-dependent and temperature-dependent measurements on Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) superconductor in the superconducting and pseudogap states by super-high resolution laser-based angle-resolved photoemission spectroscopy. The precise determination of the superconducting gap for the nearly optimally doped Bi2212 (T c =91 K) at low temperature indicates that the momentum-dependence of the superconducting gap deviates from the standard d-wave form (cos(2Φ)). It can be alternatively fitted by including a high-order term (cos(6Φ)) in which the next nearest-neighbor interaction is considered. We find that the band structure near the antinodal region smoothly evolves across the pseudogap temperature without a signature of band reorganization which is distinct from that found in Bi 2 Sr 2 CuO 6+δ superconductors. This indicates that the band reorganization across the pseudogap temperature is not a universal behavior in cuprate superconductors. These results provide new insights in understanding the nature of the superconducting gap and pseudogap in high-temperature cuprate superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Raman and ARPES combined study on the connection between the existence of the pseudogap and the topology of the Fermi surface in Bi 2 Sr 2 CaCu 2 O 8 + δ

Here, we study the behavior of the pseudogap in overdoped Bi 2 Sr 2 CaCu 2 O 8+δ by electronic Raman scattering (ERS) and angle-resolved photoemission spectroscopy (ARPES) on the same single crystals. Using both techniques we find that, unlike the superconducting gap, the pseudogap related to the antibonding band vanishes above the critical doping p c = 0.22 . Concomitantly, we show from ARPES measurements that the Fermi surface of the antibonding band is holelike below p c and becomes electronlike above p c . This reveals that the existence of the pseudogap depends on the Fermi surface topology in Bi 2 Sr 2 CaCu 2 O 8+δ , and more generally, puts strong constraint on theories of the pseudogap phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + {Sigma} approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + {Sigma} approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Pseudogap in electron-doped cuprates: Strong correlation leading to band splitting

The pseudogap phenomena have been a long-standing mystery of the cuprate high-temperature superconductors. The pseudogap in the electron-doped cuprates has been attributed to band folding due to antiferromagnetic (AFM) long-range order or short-range correlation. We performed an angle-resolved photoemission spectroscopy study of the electron-doped cuprates Pr 1.3−x La 0.7 Ce x CuO 4 showing spin-glass, disordered AFM behaviors, and superconductivity at low temperatures and, by measurements with fine momentum cuts, found that the gap opens on the unfolded Fermi surface rather than the AFM Brillouin zone boundary. The gap did not show a node, following the full symmetry of the Brillouin zone, and its magnitude decreased from the zone-diagonal to (π,0) directions, opposite to the hole-doped case. These observations were reproduced by cluster dynamical-mean-field-theory calculation, which took into account electron correlation precisely within a (CuO 2 ) 4 cluster. In conclusion, the present experimental and theoretical results are consistent with the mechanism that electron or hole doping into a Mott insulator creates an in-gap band that is separated from the upper or lower Hubbard band by the pseudogap.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Pseudogap formation and quantum phase transition in strongly-correlated electron systems

Pseudogap formation is a ubiquitous phenomenon in strongly-correlated superconductors, for example cuprates, heavy-fermion superconductors, and iron pnictides. As the system is cooled, an energy gap opens in the excitation spectrum before entering the superconducting phase. The origin of formation and the relevancy to the superconductivity remain unclear, which is the most challenging problem in condensed matter physics. Here, using the cuprate as a model, we demonstrate that the formation of pseudogap is due to a massive gauge interaction between electrons, where the mass of the gauge boson, determining the interaction length scale, is the consequence of the remnant antiferromagnetic fluctuation inherited from the parent compounds. Extracting from experimental data, we predict that there is a quantum phase transition belonging to the 2D XY universality class at the critical doping where pseudogap transition vanishes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Giant phonon anomaly associated with superconducting fluctuations in the pseudogap phase of cuprates

The pseudogap in underdoped cuprates leads to significant changes in the electronic structure, and was later found to be accompanied by anomalous fluctuations of superconductivity and certain lattice phonons. Here we propose that the Fermi surface breakup due to the pseudogap, leads to a breakup of the pairing order into two weakly coupled sub-band amplitudes, and a concomitant low energy Leggett mode due to phase fluctuations between them. This increases the temperature range of superconducting fluctuations containing an overdamped Leggett mode. In this range inter-sub-band phonons show strong damping due to resonant scattering into an intermediate state with a pair of overdamped Leggett modes. In the ordered state, the Leggett mode develops a finite energy, changing the anomalous phonon damping into an anomaly in the dispersion. Finally, this proposal explains the intrinsic connection between the anomalous pseudogap phase, enhanced superconducting fluctuations and giant anomalies in the phonon spectra.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Strong electron-phonon coupling driven pseudogap modulation and density-wave fluctuations in a correlated polar metal

Abstract There is tremendous interest in employing collective excitations of the lattice, spin, charge, and orbitals to tune strongly correlated electronic phenomena. We report such an effect in a ruthenate, Ca 3 Ru 2 O 7 , where two phonons with strong electron-phonon coupling modulate the electronic pseudogap as well as mediate charge and spin density wave fluctuations. Combining temperature-dependent Raman spectroscopy with density functional theory reveals two phonons, B 2 P and B 2 M , that are strongly coupled to electrons and whose scattering intensities respectively dominate in the pseudogap versus the metallic phases. The B 2 P squeezes the octahedra along the out of plane c -axis, while the B 2 M elongates it, thus modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping; Thus, B 2 P opens the pseudogap, while B 2 M closes it. Moreover, the B 2 phonons mediate incoherent charge and spin density wave fluctuations, as evidenced by changes in the background electronic Raman scattering that exhibit unique symmetry signatures. The polar order breaks inversion symmetry, enabling infrared activity of these phonons, paving the way for coherent light-driven control of electronic transport.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Parametrically amplified Josephson plasma waves in YBa 2 Cu 3 O 6+ x : Evidence for local superconducting fluctuations up to the pseudogap temperature T ∗

Experiments that subject underdoped YBa 2 Cu 3 O 6+x (YBCO) to intense terahertz pulses at temperatures between the transition temperature T c and the pseudogap scale T ∗ have revealed a reflectivity edge that resembles that of the superconducting state, together with second harmonic generation of a probe pulse modulated at a similar frequency. These have been interpreted in terms of parametric amplification of the lower Josephson plasmon mode. Since this mode is often associated with coherent oscillations between bilayers in the YBCO structure, these experiments have led to the suggestion that the intense pump has created (or revealed) in-plane pair coherence up to T ∗ ≈ 400 K. In this paper we propose an alternative explanation by assuming the existence of local pair amplitude and phase at equilibrium for T c < T < T ∗ . The phase correlation spans only a few lattice constants and we do not assume any pump-induced enhancement of this correlation, either in-plane or between bilayers. Instead, the coherent drive, via a parametric amplification process, induces coherence in the Josephson currents between members of bilayers. When combined with a Floquet framework, the reflectivity data can be explained. The key point is that in the lower Josephson plasmon, the coupling between bilayers is mainly capacitive; the Josephson current between bilayers can be set to zero without strongly affecting the parametric amplification process. Importantly, while superconducting coherence may not be created by the pump, the pseudogap phase must possess a local pairing amplitude at equilibrium. Consequently, these experiments have strong implications for the understanding of the pseudogap phase.

parametric amplification↗
DOE OSTI2019

Evidence for a vestigial nematic state in the cuprate pseudogap phase

The CuO 2 antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < Δ*, where Δ* is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy Δ*. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). Here, we demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi 2 Sr 2 CaCu 2 O 8 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering

Over the past two decades, improvements in computational algorithms have shown a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. Firstly, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. In contrast, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reveals a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

It is generally believed that in a two-dimensional metal, whose ground state is antiferromagnetically ordered with Q = (π,π), thermal (static) magnetic fluctuations give rise to precursor behavior above TN in which the spectral function of a hot fermion (the one for which k and k + Q are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of T > T N and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, such as, e.g., Eliashberg theory for magnetically mediated superconductivity. We also analyze the potential pseudogap behavior at T = 0. Here, we argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Breaking electron pairs in the pseudogap regime of SmTiO 3 − SrTiO 3 − SmTiO 3 quantum wells

The strongly correlated two-dimensional electron liquid within SmTiO 3 /SrTiO 3 /SmTiO 3 quantum well structures exhibits a pseudogap phase when the quantum well width is sufficiently narrow. Using low-temperature transport and optical experiments that drive the quantum-well system out of equilibrium, we find evidence of mobile, long-lived, negatively charged quasiparticles, consistent with the idea that the pseudogap phase arises from strongly bound electron pairs. As a result, these experimental results establish a connection between quantum confinement and enhanced electron pairing, which may provide a pathway to higher-temperature superconductors.

Correlated electronics↗
DOE OSTI2018

Revealing the pseudogap in Sr 3 (Ru 0.985 Fe 0.015 ) 2 O 7 by optical spectroscopy

We report resistivity, magnetization, and optical spectroscopy study on single-crystal sample of Sr 3 (Ru 0.985 Fe 0.015 ) 2 O 7 . An upturn is observed in resistivity at about 30 K. Below 30 K, the dip in resistivity R(ω), the suppression in scattering rate 1/τ(ω), the peaklike feature in optical conductivity σ 1 (ω), and the remainder of spectral weight all suggest the formation of a pseudogap. In addition, one phonon peak at about 600cm –1 is distinguished at all temperatures, which has asymmetric line shape. Such asymmetric line shape can be fit by a Fano function, and the resulting Fano factor 1/q 2 and linewidth γ show significant increases below 30 K, giving further evidence for the formation of a pseudogap, which might originate from the partial k-space gap opening due to density wave instability.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Photo-enhanced antinodal conductivity in the pseudogap state of high-Tc cuprates

A major challenge in understanding the cuprate superconductors is to clarify the nature of the fundamental electronic correlations that lead to the pseudogap phenomenon. Here we use ultrashort light pulses to prepare a non-thermal distribution of excitations and capture novel properties that are hidden at equilibrium. Using a broadband (0.5–2 eV) probe, we are able to track the dynamics of the dielectric function and unveil an anomalous decrease in the scattering rate of the charge carriers in a pseudogap-like region of the temperature (T) and hole-doping (p) phase diagram. In this region, delimited by a well-defined T*neq(p) line, the photoexcitation process triggers the evolution of antinodal excitations from gapped (localized) to delocalized quasiparticles characterized by a longer lifetime. The novel concept of photo-enhanced antinodal conductivity is naturally explained within the singleband Hubbard model, in which the short-range Coulomb repulsion leads to a k-space differentiation between nodal quasiparticles and antinodal excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗