Antinodal Quasiparticles Research Articles

Doping dependence of scattering rate for linear-in-temperature resistivity in cuprate superconductors

The origin of the linear-in-temperature (T-linear) resistivity in cuprate superconductors remains a profound mystery in condensed matter physics. Here, we investigate the dependence of the T-linear resistivity coefficient on doping, i.e., A1(p), for three typical regions in the temperature versus doping phase diagram of hole-doped cuprates, from which the doping dependence of the scattering rate, i.e., α1(p), is further derived. It is found that for region I (p<p* and T>T*), α1(p) is almost a constant; for region II (p>p* and T>Tcoh), α1(p)∝p; for region III (p>p* and T<Tcoh), α1(p)∝p(pc−p), where T* is the onset temperature of the pseudogap phase, p* indicates the doping at which T* goes to zero, Tcoh marks the onset of antinodal quasiparticle coherence, and pc is the doping where the low-temperature linear behavior in the overdoped regime vanishes. Moreover, the deduced α1(p) relations are verified with the experimental data from previous reports. The discovered scattering rate versus doping relationship will shed light on the scattering mechanism underlying the T-linear resistivity in cuprate superconductors. Published by the American Physical Society 2024

Thermodynamics of the pseudogap in cuprates

The key thermodynamic characteristics of the pseudogap state in cuprate superconductors are reviewed. These include YBa2Cu3O7−δ, Y0.8Ca0.2Ba2Cu3O7−δ, YBa2Cu4O8, Bi2Sr2CaCu2O8+δ, La2−xSrxCuO4, and Tl2Ba2CuO4. The electronic specific heat was extracted using a differential technique, and the evolution of the specific-heat coefficient γ and electronic entropy S as a function of temperature, doping, and magnetic field reveals a canonical behavior summarized by the following. The normal-state gap which opens in the pseudogap domain apparently remains open to the highest temperatures investigated. The gap decreases in magnitude with increasing doping and closes abruptly at a critical doping of p ≈ 0.19 holes/Cu, independent of temperature. In this picture, the pseudogap is separated from the pseudogap-free region of the phase diagram by a vertical line similar to the vertical line separating the incoherent and coherent antinodal quasiparticle states found in ARPES. The important role of fluctuations is evident by a diverging enhancement of γ(T) on either side of Tc, and this enables extraction of the mean-field transition temperature Tcmf>Tc, defining a crescent of parapairing above Tc(p) which extends across the entire superconducting phase diagram and which is quite distinct from pseudogap phenomenology. The data are consistent with d-wave pairing and the BCS ratios are extracted, revealing canonical near-weak-coupling behavior across the over-doped region with a sudden suppression occurring at p ≈ 0.19 when the pseudogap sets in.

Why the anti-nodal quasiparticle dispersion is so flat in the superconducting cuprates?

The emergence of the coherent quasiparticle peak and the development of the peak-dip-hump structure in the anti-nodal region below T c is the most prominent non-BCS signature of the under-doped high-T c cuprates, in which no coherent quasiparticle can be defined in the anti-nodal region above T c. The peak-dip-hump structure has been commonly interpreted as the result of the coupling of the electron to some Bosonic mode. However, such an electron–Boson coupling picture does not answer the question of why the quasiparticle dispersion is so flat in the anti-nodal region, a behavior totally unexpected for Bogoliubov quasiparticle in a d-wave BCS superconductor. Here we show that the sharp quasiparticle peak in the anti-nodal region should be understood as a new pole in the electron Green’s function generated by the strong coupling of the electron to diffusive spin fluctuation around the antiferromagnetic wave vector Q = (π, π), rather than a nearly free Bogoliubov quasiparticle in a d-wave BCS superconductor. More specifically, we find that the normal self-energy of the electron from the scattering with the diffusive spin fluctuation manifests itself mainly as a level repulsion effect and is responsible for the reduction of both the quasiparticle dispersion and the quasiparticle dissipation rate in the anti-nodal region. We argue that the peak-dip separation in the anti-nodal spectrum should not be interpreted as the energy of the pairing glue.

Why is the antinodal quasiparticle in the electron-doped cuprate Pr1.3−xLa0.7CexCuO4 immune to the antiferromagnetic band-folding effect?

A recent ARPES measurement on electron-doped cuprate Pr1.3−xLa0.7CexCuO4 finds that the antiferromagnetic (AFM) band-folding gap along the boundary of the antiferromagnetic Brillouin zone (AFBZ) exhibits dramatic momentum dependence. In particular, it vanishes in a finite region around the antinodal point, in which a single broadened peak emerges at the unrenormalized quasiparticle energy. Such an observation is argued to be inconsistent with the AFM band-folding picture, which predicts a constant band splitting along the AFBZ boundary. On the other hand, it is claimed that the experimental results are consistent with the prediction of the cluster dynamical mean-field theory (CDMFT) simulation on the Hubbard model, in which the obserevd spectral gap is interpreted as an s-wave pseudogap between the Hubbard bands and the in-gap states. Here we show that the observed momentum dependence of the spectral gap along the AFBZ boundary is indeed consistent with the AFM band-folding picture, provided that we assume the existence of a strongly momentum-dependent quasiparticle scattering rate. More specifically, we show that the quasiparticle scattering rate acts to reduce the spectral gap induced by the AFM band-folding effect. The new quasiparticle poles corresponding to the AF-split bands can even be totally eliminated when the scattering rate exceeds the bare band-folding gap, leaving the system with a single pole at the unrenormalized quasiparticle energy. We predict that the AFM band-folding gap should close in a square root fashion as we move toward along the AFBZ boundary. Our results illustrate that the quasiparticle scattering rate can play a much more profound role than simply broadening the quasiparticle peak in the quasiparticle dynamics of strongly correlated electron systems.

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.

BCS coupling in a 1D Luttinger liquid

In this work we investigate the effect produced by the BCS coupling in spinless fermions in one spatial dimension. Using bosonization techniques our initial model is rewritten in terms of a sine-Gordon field and a free massless scalar field. As a result the Cooper pair in our scenario is made up of soliton and antisoliton particles. We calculate the single particle Green’s function, the pair correlation function and the optical conductivity associated with the physical fermions and we show how they differ from their conventional quasiparticle analogues. Finally, we compare our results with related experimental findings for high temperature superconductors and we display how they fit qualitatively well the related observed effects produced by the anti-nodal quasiparticles in those materials.

Pseusogap in Cuprates by Electronic Raman Scattering

We present Raman experiments on underdoped and overdoped Bi2Sr2CaCu2O8+δ (Bi-2212) single crystals. We reveal the pseudogap in the electronic Raman spectra in the B1g and B2g geometries. In these geometries we probe respectively, the antinodal (AN) and nodal (N) regions corresponding to the principal axes and the diagonal of the Brillouin zone. The pseudogap appears in underdoped regime and manifests itself in the B1g spectra by a strong depletion of the low energy electronic continuum as the temperature decreases. We define a temperature T* below which the depletion appears and the pseudogap energy, ωPG the energy at which the depeletion closes.The pseudogap is also present in the B2g spectra but the depletion opens at higher energy than in the B1g spectra. We observe the creation of new electronic states inside the depletion as we enter the superconducting phase. This leads us to conclude (as proposed by S. Sakai et al. [1]) that the pseudogap has a different structure than the superconducting gap and competes with it. We show that the nodal quasiparticle dynamic is very robust and almost insensitive to the pseudogap phase contrary to the antinodal quasiparticle dynamic. We finally reveal, in contrast to what it is usually admitted, an increase of the nodal quasiparticle spectral weight with underdoping. We interpret this result as the consequence of a possible Fermi surface disturbances in the doping range p = 0.1 − 0.2.

Robust Nodald-Wave Spectrum in Simulations of a Strongly Fluctuating Competing Order in Underdoped Cuprate Superconductors

We resolve an existing discrepancy between convincing evidence for competing order in underdoped cuprates and spectroscopic data consistent with a homogeneous d-wave superconductor in the very same compounds. Specifically, we show that fluctuations of the competing order generate strongly inhomogeneous states whose spectra are almost indistinguishable from the pure d-wave superconductor. This is in contrast to the commonly studied case of homogeneously coexisting order, which typically generates a reconstructed Fermi surface with closed Fermi pockets. The signatures of the fluctuating competing order can be found mainly in a splitting of the antinodal band, and, for strong magnetic order, in small induced nodal gaps similar to those found in recent experiments on underdoped La(2-x)Sr(x)CuO4.

Relaxation and Thermal Conductivity of Hot and Thermal Quasiparticles and Fermi Liquid Interactions in d-wave Superconductors

In this paper, we calculate theoretically the relaxation rates of hot, thermal and antinodal quasiparticles by using Fermi’s golden rule. The transition probabilities at low temperatures express in terms of Bogoliubov coefficients, singlet and triplet scattering amplitudes and dimensionless Landau parameters. The values of Landau parameters may be determined by comparison with the experimental data. Furthermore, we calculate thermal conductivity coefficients of YBCO in terms of antinodal quasiparticle relaxation rates which are in accordance with experimental results.

Nodal quasiparticle meltdown in ultrahigh-resolution pump–probe angle-resolved photoemission

High-$T_c$ cuprate superconductors are characterized by a strong momentum-dependent anisotropy between the low energy excitations along the Brillouin zone diagonal (nodal direction) and those along the Brillouin zone face (antinodal direction). Most obvious is the d-wave superconducting gap, with the largest magnitude found in the antinodal direction and no gap in the nodal direction. Additionally, while antinodal quasiparticle excitations appear only below $T_c$, superconductivity is thought to be indifferent to nodal excitations as they are regarded robust and insensitive to $T_c$. Here we reveal an unexpected tie between nodal quasiparticles and superconductivity using high resolution time- and angle-resolved photoemission on optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We observe a suppression of the nodal quasiparticle spectral weight following pump laser excitation and measure its recovery dynamics. This suppression is dramatically enhanced in the superconducting state. These results reduce the nodal-antinodal dichotomy and challenge the conventional view of nodal excitation neutrality in superconductivity.

Electronic Raman scattering in copper oxide superconductors: Understanding the phase diagram

Electronic Raman scattering measurements have been performed on hole doped copper oxide superconductors as a function of temperature and doping level. In the superconducting state coherent Bogoliubov quasiparticles develop preferentially over the nodal region in the underdoped regime. We can then define the fraction of coherent Fermi surface, $f_c$ around the nodes for which quasiparticles are well defined and superconductivity sets in. We find that $f_c$ is doping dependent and leads to the emergence of two energy scales. We then establish in a one single gap shem, that the critical temperature $T_{c} \propto f_{c}\Delta_{max}$ where $\Delta_{max}$ is the maximum amplitude of the d-wave superconducting gap. In the normal state, the loss of antinodal quasiparticles spectral weight detected in the superconducting state persists and the spectral weight is only restored above the pseudogap temperature $T*$. Such a dichotomy in the quasiparticles dynamics is then responsible for the emergence of the two energy scales in the superconducting state and the appearance of the pseudogap in the normal state. We propose a 3D phase diagram where both the temperature and the energy phase diagrams have been plotted together. We anticipate that the development of coherent excitations on a restricted part of the Fermi surface only is a general feature in high $T_c$ cuprate superconductors as the Mott insulating is approaching.

Dichotomy in the T -linear resistivity in hole-doped cuprates

From analysis of the in-plane resistivity ρ(ab)(T) of La(2-x)Sr(x)CuO(4), we show that normal state transport in overdoped cuprates can be delineated into two regimes in which the electrical resistivity varies approximately linearly with temperature. In the low-temperature limit, the T-linear resistivity extends over a very wide doping range, in marked contrast to expectations from conventional quantum critical scenarios. The coefficient of this T-linear resistivity scales with the superconducting transition temperature T(c), implying that the interaction causing this anomalous scattering is also associated with the superconducting pairing mechanism. At high temperatures, the coefficient of the T-linear resistivity is essentially doping independent beyond a critical doping p(crit)=0.19 at which the ratio of the two coefficients is maximal. Taking our cue from earlier thermodynamic and photoemission measurements, we conclude that the opening of the normal-state pseudogap at p(crit) is driven by the loss of coherence of anti-nodal quasi-particles at low temperatures.

Evidence for a Minigap in YBCO Grain Boundary Josephson Junctions

Self-assembled YBaCuO diffusive grain boundary submicron Josephson junctions offer a realization of a special regime of the proximity effect, where normal state coherence prevails on the superconducting coherence in the barrier region. Resistance oscillations from the current-voltage characteristic encode mesoscopic information on the junction and more specifically on the minigap induced in the barrier. Their persistence at large voltages is evidence of the long lifetime of the antinodal (high energy) quasiparticles.

Checkerboard superconducting order and antinodal Bogoliubov quasiparticle interference

Numerical study of momentum-dependent gap function is presented to make clear the origin of superconductivity in copper oxides. We claim that antinodal region with pronounced nesting feature of the Fermi contour gives rise to superconducting pairing with large momentum under screened Coulomb repulsion. Such a pairing results in both spatial checkerboard pattern of the superconducting state below Tc and a gapped state of incoherent pairs in a broad temperature range above Tc. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy and predict antinodal Bogoliubov quasiparticle interference other than observed in the nodal region.

Checkerboard superconducting order and antinodal Bogoliubov quasiparticle interference

We argue that both pseudogap and superconducting states of the cuprates arise exactly in the antinodal region with nesting of the Fermi contour as spatially inhomogeneous incoherent and coherent states of pairs with large momentum. Numerical study of momentum-dependent gap function results in a checkerboard pair density wave spatial order. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy (ARPES) and predict antinodal quasiparticle interference.

Photoemission signatures of valence-bond stripes in cuprates: Long-range vs. short-range order

Recent experiments indicate that the tendency toward the formation of unidirectional charge density waves (“stripes”) is common to various underdoped cuprates. We discuss momentum-resolved spectral properties of valence-bond stripes, comparing the situations of ideal and short-range stripe order, the latter being relevant for weak and/or disorder-pinned stripes. We find clear signatures of ordered stripes, although matrix element effects suppress most shadow band features. With decreasing stripe correlation length, stripe signatures are quickly washed out, the only remaining effect being a broadening of antinodal quasiparticles. This insensitivity of photoemission to short-range stripe order may be employed to distinguish it from nematic order, e.g. in underdoped YBa2Cu3O6+δ.

Spatial dichotomy of quasiparticle dynamics in underdoped thin-filmYBa2Cu3O7−δsuperconductors

By the spatial-temporal-resolved femtosecond spectroscopy on well-textured (110)- and (100)-YBCO thin films, two distinctly temperature-dependent characteristics of quasiparticle relaxation in the nodal and antinodal directions are clearly identified. One temperature dependence associated with a high-energy gap has been observed along the ab diagonal for the whole hole-doping region and along the $b$ axis except near optimal doping, while the other temperature dependence related to the opening of the superconducting gap appears along $b$ axis regardless of the hole concentration. This spatial dichotomy between the nodal and antinodal quasiparticle dynamics and the evolution of gap symmetry with hole doping are discussed for enlightenment on the nature of the phase diagram of hole-doped cuprates. These strongly suggest that the two characteristics may have different physical origins and compete with each other.

Two energy scales and two distinct quasiparticle dynamics in the superconducting state of underdoped cuprates

The superconducting state of underdoped cuprates is often described in terms of a single energy-scale, associated with the maximum of the (d-wave) gap. Here, we report on electronic Raman scattering results, which show that the gap function in the underdoped regime is characterized by two energy scales, depending on doping in opposite manners. Their ratios to the maximum critical temperature are found to be universal in cuprates. Our experimental results also reveal two different quasiparticle dynamics in the underdoped superconducting state, associated with two regions of momentum space: nodal regions near the zeros of the superconducting gap and antinodal regions. While antinodal quasiparticles quickly loose coherence as doping is reduced, coherent nodal quasiparticles persist down to low doping levels. A theoretical analysis using a new sum-rule allows us to relate the low-frequency-dependence of the Raman response to the temperature-dependence of the superfluid density, both controlled by nodal excitations.

Normal-state electronic structure in the heavily overdoped regime ofBi1.74Pb0.38Sr1.88CuO6+δsingle-layer cuprate superconductors: An angle-resolved photoemission study

We explore the electronic structure in the heavily overdoped regime of the single layer cuprate superconductor Bi1.74Pb0.38Sr1.88CuO6+delta. We found that the nodal quasiparticle behavior is dominated mostly by phonons, while the antinodal quasiparticle lineshape is dominated by spin fluctuations. Moreover, while long range spin fluctuations diminish at very high doping, the local magnetic fluctuations still dominate the quasiparticle dispersion, and the system exhibits a strange metal behavior in the entire overdoped regime.

Enhanced coherence of antinodal quasiparticles in a dirtyd-wave superconductor

Recent ARPES experiments show a narrow quasiparticle peak at the gap edge along the antinodal [1,0]-direction for the overdoped cuprate superconductors. We show that within weak coupling BCS theory for a d-wave superconductor the s-wave single-impurity scattering cross section vanishes for energies of the gap edge. This coherence effect occurs through multiple scattering off the impurity. For small impurity concentrations the spectral function has a pronounced increase of the (scattering) lifetime for antinodal quasiparticles but shows a very broad peak in the nodal direction, in qualitative agreement with experiment and in strong contrast to the behavior observed in underdoped cuprates.