Using a maximum entropy technique within a finite band Eliashberg formalism we extract from recent high accuracy nodal direction angular resolved photo-emission spectroscopy (ARPES) data in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) a quasiparticle electron-boson spectral density. Both normal and superconducting state with d-wave gap symmetry are treated. Finite and infinite band results are considered and contrasted. We compare with results obtained for the related transport spectral density which follows from a similar inversion of optical data. We discuss the implication of our results for quasiparticle renormalizations in the antinodal direction.
We find that peaks in the autocorrelation of angle resolved photoemission spectroscopy data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in the superconducting state show dispersive behavior for binding energies smaller than the maximum superconducting energy gap. For higher energies, though, a striking anomalous dispersion is observed that is a consequence of the interaction of the electrons with collective excitations. In contrast, in the pseudogap phase, we only observe dispersionless behavior for the autocorrelation peaks. The implications of our findings in regards to Fourier transformed scanning tun…
A well-known peak-dip-hump structure exists near $(π, 0)$ in superconducting state ARPES spectra of $Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}$ (Bi2212). Here we report results on optimal and overdoped Bi2212 samples indicating the traditional peak-dip-hump structure observed near $(π,0)$ is largely due to bilayer splitting. However a separate, much weaker peak-dip hump (PDH) structure distinct from bilayer splitting can be detected near $(π, 0)$. This new PDH structure is consistent with electronic coupling to the magnetic resonance mode in Bi2212. Both the dispersion and line shape signatures indicate str…
We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy $\w$ employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $θ$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $ω$ is directly obtained from the fitting. The obtained angle resolved self-en…
We deduce the normal state angle-resolved single-particle self-energy $Σ(θ, ω)$ and the Eliashberg function (i.e., the product of the fluctuation spectrum and its coupling to fermions) $α^2 F(θ,ω)$ for the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ from the ultra high resolution laser angle-resolved photoemission spectroscopy (ARPES). The self-energy $Σ(θ, ω)$ at energy $ω$ along several cuts normal to the Fermi surface at the tilt angles $θ$ with respect to the nodal direction in a slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ were extracted by fitting the ARPES momentu…
We study the behavior of the pseudogap in overdoped Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ 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 anti-bonding band vanishes above the critical doping p$_c$ = 0.22. Concomitantly, we show from ARPES measurements that the Fermi surface of the anti-bonding band is hole-like below pc and becomes electron-like above p$_c$. This reveals that the appearance of the pseudogap depends on the Fermi surfa…
We discuss the nature of electron-lattice interaction in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ samples, using isotope effect (IE) in angle resolved photoemission spectroscopy (ARPES) data. The IE in the ARPES line width and the IE in the ARPES dispersion are both quite large, implying a strong electron-lattice correlation. The strength of the electron-lattice interaction is ``intermediate,'' i.e. stronger than the Migdal-Eliashberg regime but weaker than the small polaron regime, requiring a more general picture of the ARPES ``kink'' than the commonly used Migdal-Eliashberg picture. Th…
Both electronic Raman scattering (ERS) and angle-resolved photoemission spectra (ARPES) revealed two energy scales for the gap in different momentum spaces in the cuprates. However, the interpretations were different, and the gap values were also different in two experiments. In order to clarify the origin of these discrepancies, we directly compared ERS and ARPES by calculating ERS from the experimental data of ARPES through the Kubo formula. The calculated ERS spectra were in good agreement with the experimental results except for the B$_{1g}$ peak energies. The doping-dependent B$_{2g}$ pea…
Angle Resolved Photoemission Spectroscopy (ARPES) probes the momentum-space electronic structure of materials, and provides invaluable information about the high-temperature superconducting cuprates. Likewise, the cuprate real-space, inhomogeneous electronic structure is elucidated by Scanning Tunneling Spectroscopy (STS). Recently, STS has exploited quasiparticle interference (QPI) - wave-like electrons scattering off impurities to produce periodic interference patterns - to infer properties of the QP in momentum-space. Surprisingly, some interference peaks in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi-…
A systematic temperature dependent study of the femtosecond optical superconducting (SC) state destruction and recovery in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ cuprate superconductor by means of the all-optical polarization-sensitive multi-pulse spectroscopy is presented. At low temperatures and a partial SC state suppression an anisotropic SC-gap recovery-timescale is suggested by the data. The SC state destruction and recovery dynamics are compared to the recent TR-ARPES-inferred SC-gap dynamics and a qualitative agreement is found. Using a phenomenological response function the experimental …
Angle resolved photoemission spectroscopy (ARPES) provides a detailed view of the renormalized band structure and, consequently, is a key to the self-energy and the single-particle Green's function. Here we summarize the ARPES data accumulated over the whole Brillouin zone for the optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8-δ}$ into a parametric model of the Green's function, which we use for calculating the itinerant component of the dynamic spin susceptibility in absolute units with many-body effects taken into account. By comparison with inelastic neutron scattering (INS) data we show that th…
The Kubo single band sum rule is used to determine the optical spectral weight of a tight binding band with further than nearest neighbour hopping. We find for a wide range of parameters and doping concentrations that the change due to superconductivity at low temperature can be either negative or positive. In contrast, the kinetic energy change is always negative. We use an ARPES determined tight binding parametrization of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ to investigate whether this can account for recent observations of a positive change in the spectral weight due to the onset of superconductiv…
Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials, no consensus on the pairing mechanism has been reached. Recent advances in high resolution angle-resolved photoemission spectroscopies have suggested that a sizeable electron-phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wave vector) of the electronic states. Here, we report on a systematic study about the influence of the electron-phonon coupling parameter "$λ$" in the electronic quasiparticle dispersions alo…
Angle-resolved photoemission spectroscopy (ARPES) is used to study the spectral function of the optimally doped high-T$_c$ superconductor (Bi,Pb)$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in the vicinity of the antinodal point in the superconducting state. Using a parameterized self-energy function, it was possible to describe both the coherent and the incoherent spectral weight of the bonding and the antibonding band. The renormalization effects can be assigned to a very strong coupling to the magnetic resonance mode and at higher energies to a bandwidth renormalization by a factor of two, probably caused b…
Recent angle-resolved photoemission and neutron scattering data have provided new ingredients for the interpretation of scanning tunneling spectra on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. We analyze the low-temperature tunneling spectra, from oxygen overdoped to underdoped samples, including details about the bilayer splitting and the neutron resonance peak. Two van Hove singularities are identified: the first is integrated in the coherence peaks, the second is heavily broadened at higher binding energy. The shape of the tunneling spectra suggests a strong coupling of the quasiparticles with a collec…
We present new results from Angle-Resolved Photoemission experiments (ARPES) on overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+d} (BSCCO) crystals. With greatly improved energy and momentum resolution, we clearly identify the existence of electron-like portions of the Fermi Surface (FS) near \bar{M} at hν=33eV. This is consistent with previously reported data and is robust against various FS crossing criteria. It is not due to an artifact induced from \vec{k}-dependent matrix element effects. We also present evidence for a breakage in the FS pointing to the possible existence of two types of electronic co…
High-quality Bi$_{2-x}$Pb$_{x}$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) single crystals have been successfully grown by the traveling solvent floating zone technique with a wide range of Pb substitution ($x=0-0.8$). The samples are characterized by transmission electron microscope (TEM) and measured by high resolution laser-based angle-resolved photoemission spectroscopy (ARPES) with different photon energies. A systematic evolution of the electronic structure and superstructure with Pb substitution has been revealed for the first time. The superstructure shows a significant change with Pb substitutio…
The normal state single particle spectral function of the high temperature superconducting cuprates, measured by the angle resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here we show that an unprecedentedly detailed description of the data is provided by a spectral function arising from the Extremely Correlated Fermi Liquid state of the t-J model proposed recently by Shastry. The description encompasses both laser and conventional synchrotron ARPES data on optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, and also conventional synchrotro…
We report an ARPES investigation of the circular dichroism in the first Brillouin zone (BZ) of under- and overdoped Pb-Bi2212 samples. We show that the dichroism has opposite signs for bonding and antibonding components of the bilayer-split CuO-band and is antisymmetric with respect to reflections in both mirror planes parallel to the c-axis. Using this property of the energy and momentum intensity distributions we prove the existence of the bilayer splitting in the normal state of the underdoped compound and compare its value with the splitting in overdoped sample. In agreement with previous …
Raman scattering cross sections depend on photon polarization. In the cuprates nodal and antinodal directions are weighted more strongly in $B_{2g}$ and $B_{1g}$ symmetry, respectively. On the other hand in angle-resolved photoemission spectroscopy (ARPES), electronic properties are measured along well-defined directions in momentum space rather than their weighted averages. In contrast, the optical conductivity involves a momentum average over the entire Brillouin zone. Newly measured Raman response data on high-quality Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals up to high energies have be…
We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increa…
Improved resolution in both, energy and momentum in ARPES-data has lead to the establishment of a definite energy scale in the dressed quasiparticle dispersion relations. The observed structure around 80 meV has been taken as evidence for coupling to phonons and has re-focused the debate about the mechanism of superconductivity in the cuprates. Here we address the relative merits of phonon as opposed to spin fluctuation mechanisms. Both possibilities are consistent with ARPES. On the other hand, when considerations are extended to infrared optical data, a spin fluctuation mechanism provides a …
Common approach is used to calculate band due to strong-coupling large polaron (SCLP) photodissociation in ARPES and in optical conductivity (OC) spectra. It is based on using the coherent-states representation for the phonon field in SCLP. The calculated positions of both band maximums are universal functions of one parameter - the SCLP binding energy Ep: ARPES band maximum lies at binding energy about 3.2Ep; the OC band maximum is at the photon energy about 4.2Ep. The half-widths of the bands are mainly determined by Ep and slightly depend on Frohlich electron-phonon coupling constant: for i…
Electron-phonon interaction in copper oxide superconductors is still enigmatic. Strong coupling for certain optic phonons is now well established experimentally, but theoretical understanding is challenging. Scattering of electrons near the Fermi surface by the longitudinal acoustic (LA) phonons is expected from basic theory because these phonons modulate electron density. We used inelastic neutron scattering on a large single crystal sample of optimally-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ to show that low-energy LA phonons could couple to electronic density fluctuations only at small phonon w…
Among the quasi one-dimensional transition metal tetrachalcogenides (MSe$_4$)$_n$I (M=Nb,Ta), the $n=3$ compounds are the only ones not displaying charge density waves. Instead, they show structural transitions with puzzling transport behavior. They are semiconductors at the lowest temperatures, but their transport gaps are significantly smaller than those inferred from ARPES and optical conductivity. Recently, a metallic polytype of (TaSe$_4$)$_3$I has been found with ferromagnetism and superconductivity coexisting at low temperature, in contrast to previous reports. In this work we present d…
Recent photoemission work on underdoped cuprates between Tc and T*, the pseudogap temperature, are interpreted within the framework of a previously developed negative-U scenario. From this exposition, incorporating a developed 2q diagonal striping model, detailed understanding follows of the ARPES results, together with certain STM and far infrared optical data. Identification of the origin of the magnetic circular dichroism and related effects exhibited by such materials below T* also appears to have been achieved.
Citing the disappearance of a sharp peak in the electron self-energy, extracted from optics and angle-resolved photoemission spectroscopy (ARPES) experiments in deeply over-doped copper-oxide superconductors with Tc of 55-60K, Hwang, Timusk et al. argue that sharp modes, be they phononic or magnetic in origin, are not important for superconductivity in the cuprates. If true, this would have been an important progress. We show, however, their conclusions are unfounded because of the insensitivity of the optics experiment in studying strongly anisotropic material like the cuprates, and a misrepr…
We show that the spectral lineshape of superconducting La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) can be well described by the coupling of the charge carriers to collective incommensurate charge-density wave (CDW) excitations. Our results imply that besides antiferromagnetic (AF) fluctuations also low-energy CDW modes can contribute to the observed dip-hump structure in the Bi2212 photoemission spectra. In case of underdoped LSCO we propose a possible interpretation of ARPES data in terms of a grid pattern of fluctuating stripes where the charge and spin scatteri…
We use a new technique to directly extract an estimate of the quasiparticle self-energy from the optical conductivity which can be easily related to both theory and angle-resolved photoemission spectroscopy (ARPES) experiments. In the high Tc cuprate Bi-2212 we find evidence for a new high energy scale at 900 meV in addition to the two previously well known ones at roughly 50 and 400 meV. The intermediate scale at 400 meV has been recently seen in ARPES as a large kink which optics finds to be weaker and shifted. In YBCO, the three energy scales are shifted to lower energy relative to Bi-2212 …
A large body of spectroscopic data on the cuprate high temperature superconductors (CHTSC) is reviewed in order to determine their order parameter. ASJ, INS, B2g Raman spectra, optical data, NIS "dips", ARPES "dips" and ARPES "kinks" all show the same excitation energy (40 meV for OP95 systems), proportional to the superconducting transition temperature, and it is therefore identified with the order parameter.
Coupling of the charge carriers in the high temperature superconducting oxides to bosonic modes has been widely reported using a variety of experimental probes. These include angular resolved photoemission (ARPES), scanning tunnelling spectroscopy (STS), Raman scattering (RS) and infrared optical spectroscopy (IRS). The energy scale investigated has been mostly limited to a relatively small range up to 300 meV or so. Although some ARPES experiments report boson structure up to 800 meV in the dressed electron dispersion curves the data are not analyzed to recover the spectral density of the flu…
We compare electronic structures of single FeSe layer films on SrTiO$_3$ substrate (FeSe/STO) and K$_x$Fe$_{2-y}$Se$_{2}$ superconductors obtained from extensive LDA and LDA+DMFT calculations with the results of ARPES experiments. It is demonstrated that correlation effects on Fe-3d states are sufficient in principle to explain the formation of the shallow electron -- like bands at the M(X)-point. However, in FeSe/STO these effects alone are apparently insufficient for the simultaneous elimination of the hole -- like Fermi surface around the $Γ$-point which is not observed in ARPES experiments…
We study thermal broadening of the hole spectral function of the two-dimensional t-J model (and its extensions) within the non-crossing approximation with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle resolved photo-emission spectroscopy(ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any adhoc broadening. In addition,…
Angle resolved photoemission (ARPES) data from the electron doped cuprate superconductor Sm$_{1.86}$Ce$_{0.14}$CuO$_4$ shows a much stronger pseudo-gap or "hot-spot" effect than that observed in other optimally doped $n$-type cuprates. Importantly, these effects are strong enough to drive the zone-diagonal states below the chemical potential, implying that d-wave superconductivity in this compound would be of a novel "nodeless" gap variety. The gross features of the Fermi surface topology and low energy electronic structure are found to be well described by reconstruction of bands by a $\sqrt{…
We analyze existing optical data in the superconducting state of LiFeAs at $T =$ 4 K, to recover its electron-boson spectral density. A maximum entropy technique is employed to extract the spectral density $I^2χ(ω)$ from the optical scattering rate. Care is taken to properly account for elastic impurity scattering which can importantly affect the optics in an $s$-wave superconductor, but does not eliminate the boson structure. We find a robust peak in $I^2χ(ω)$ centered about $Ω_R \cong$ 8.0 meV or 5.3 $k_B T_c$ (with $T_c =$ 17.6 K). Its position in energy agrees well with a similar structure…
Based on the analysis of the measurement data of angle-resolved photoemission spectroscopy (ARPES) and optics, we show that the charge transfer gap is significantly smaller than the optical one and is reduced by doping in electron doped cuprate superconductors. This leads to a strong charge fluctuation between the Zhang-Rice singlet and the upper Hubbard bands. The basic model for describing this system is a hybridized two-band $t$-$J$ model. In the symmetric limit where the corresponding intra- and inter-band hopping integrals are equal to each other, this two-band model is equivalent to the …
