arXiv subjects

E. Schachinger

Publications and source records attributed to E. Schachinger.

At least 19 recordsLinked to original sources

arXiv2017

Optical Properties of Bogoliubov Quasiparticles

We calculated the optical conductivity $σ(T,Ω)$ of a gas of Bogoliubov quasiparticles (BQP) from their Green's function and the Kubo formula. We compare with corresponding normal state (N) and superconducting state (SC) results. The superconducting case includes the dynamic response of the condensate through additional contributions to the Kubo formula involving the Gor'kov anomalous Green's function. The differences in the optical scattering rate are largest just above the optical gap and become progressively smaller as the photon energy is increased or the temperature is raised. Our results are compared with those obtained using a recently advocated phenomenological procedure for eliminating the effect of the condensate [1]. The $δ$-function contribution at zero photon energy, proportional to the superfluid density, is dropped in the real part of the conductivity $[σ_1(T,Ω)]$ and its Kramers-Kronig transform is subtracted from the imaginary part $σ_2(T,Ω)$. This results in deviations from our BQP and superconducting state optical scattering rates even in the region where these have merged and are, in addition, close to the normal state result.

cond-mat.supr-con↗

arXiv2015

Isotope Effect of Underdoped Cuprates in the Yang-Rice-Zhang Model

The underdoped region of the cuprate's phase diagram displays many novel electronic phenomena both in the normal and the superconducting state. Many of these anomalous properties have found a natural explanation within the resonating valence bond spin liquid phenomenological model of Yang-Rice-Zhang (YRZ) which includes the rise of a pseudogap. This leads to Fermi surface reconstruction and profoundly changes the electronic structure. Here we extend previous work to consider the shift in critical temperature on $^{16}$O to $^{18}$O substitution, The isotope effect has been found experimentally to be very small at optimal doping yet to rapidly increase to very large values with underdoping. The YRZ model provides a natural explanation of this behavior and supports the idea of a pairing mechanism which is mainly spin fluctuations with a subdominant $(\sim 10\%)$ phonon contribution.

cond-mat.supr-con↗

arXiv2014

Eliashberg analysis of the optical conductivity in superconducting Pr$_2$CuO$_{x}$ ($x \simeq 4$)

Superconducting Pr$_2$CuO$_x$, $x\simeq 4$ films with $T^\prime$ structure and a $T_c$ of 27 K have been investigated by millimeter-wave transmission and broadband (infrared-to-ultraviolet) reflectivity measurements in the normal and superconducting state. The results obtained by both experimental methods show a consistent picture of the superconducting condensate formation below $T_c$. An Eliashberg analysis of the data proves $d$-wave superconductivity and unitary-limit impurity scattering of the charge carriers below $T_{c}$. The derived electron-exchange boson interaction spectral function $I^2χ(ω)$ shows only marginal changes at the superconducting transition with the mass enhancement factor $λ$, the first inverse moment of $I^2χ(ω)$, being equal to 4.16 at 30 K and to 4.25 at 4 K.

cond-mat.supr-con↗

arXiv2014

Optical study of superconducting Pr$_2$CuO$_{x}$ with $x\simeq 4$

Superconducting Pr$_2$CuO$_x$, $x\simeq 4$ (PCO) films with $T^\prime$ structure and a $T_c$ of 27 K have been investigated by various optical methods in a wide frequency (7 - 55000 cm$^{-1}$) and temperature (2 to 300 K) range. The optical spectra do not reveal any indication of a normal-state gap formation. A Drude-like peak centered at zero frequency dominates the optical conductivity below 150 K. At higher temperatures, it shifts to finite frequencies. The detailed analysis of the low-frequency conductivity reveals that the Drude peak and a far-infrared (FIR) peak centered at about 300 cm$^{-1}$ persist at all temperatures. The FIR-peak spectral weight is found to grow at the expense of the Drude spectral weight with increasing temperature. The temperature dependence of the penetration depth follows a behavior typical for $d$-wave superconductors. The absolute value of the penetration depth for zero temperature is 1.6 $μ$m, indicating a rather low density of the superconducting condensate.

cond-mat.supr-con↗

arXiv2012

Optical study of superconducting Ga-rich layers in silicon

We performed phase-sensitive terahertz (0.12 - 1.2 THz) transmission measurements of Ga-enriched layers in silicon. Below the superconducting transition, T_{c} = 6.7 K, we find clear signatures of the formation of a superconducting condensate and of the opening of an energy gap in the optical spectra. The London penetration depth, λ(T), and the condensate density, n_{s} = λ^{2} 0)/λ^{2}(T), as functions of temperature demonstrate behavior, typical for conventional superconductors with λ(0) = 1.8 μm. The terahertz spectra can be well described within the framework of Eliashberg theory with strong electron-phonon coupling: the zero-temperature energy gap is 2Δ(0) = 2.64 meV and 2Δ(0)/k_{B}T_{c} = 4.6 \pm 0.1, consistent with the amorphous state of Ga. At temperatures just above T_{c}, the optical spectra demonstrate Drude behavior.

cond-mat.supr-con↗

arXiv2010

Highly anisotropic energy gap in superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ from optical conductivity measurements

We have measured the complex dynamical conductivity, $σ= σ_{1} + iσ_{2}$, of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ ($T_{c} = 22$ K) at terahertz frequencies and temperatures 2 - 30 K. In the frequency dependence of $σ_{1}$ below $T_{c}$, we observe clear signatures of the superconducting energy gap opening. The temperature dependence of $σ_{1}$ demonstrates a pronounced coherence peak at frequencies below 15 cm$^{-1}$ (1.8 meV). The temperature dependence of the penetration depth, calculated from $σ_{2}$, shows power-law behavior at the lowest temperatures. Analysis of the conductivity data with a two-gap model, gives the smaller isotropic s-wave gap of $Δ_{A} = 3$ meV, while the larger gap is highly anisotropic with possible nodes and its rms amplitude is $Δ_{0} = 8$ meV. Overall, our results are consistent with a two-band superconductor with an $s_{\pm}$ gap symmetry.

cond-mat.supr-con↗

arXiv2010

Electron-boson glue function derived from electronic Raman scattering

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 been inverted using a modified maximum entropy inversion technique to extract from $B_{1g}$ and $B_{2g}$ Raman data corresponding electron-boson spectral densities (glue) are compared to the results obtained with known ARPES and optical inversions. We find that the $B_{2g}$ spectrum agrees qualitatively with nodal direction ARPES while the $B_{1g}$ looks more like the optical spectrum. A large peak around $30 - 40\,$meV in $B_{1g}$, much less prominent in $B_{2g}$, is taken as support for the importance of $(π,π)$ scattering at this frequency.

cond-mat.supr-con↗

arXiv2010

Nodes in the Order Parameter of Superconducting Iron Pnictides Observed by Infrared Spectroscopy

The temperature and frequency dependences of the conductivity are derived from optical reflection and transmission measurements of electron doped BaFe$_2$As$_2$ crystals and films. The data is consistent with gap nodes or possibly a very small gap in the crossover region between these two possibilities. This can arise when one of the several pockets known to exist in these systems has extended s-wave gap symmetry with an anisotropic piece canceling or nearly so the isotropic part in some momentum direction. Alternatively, a node can be lifted by impurity scattering which reduces anisotropy. We find that the smaller gap on the hole pocket at the $Γ$ point in the Brillouin zone is isotropic s-wave while the electron pocket at the $M$ point has a larger gap which is anisotropic and falls in the crossover region.

cond-mat.supr-con↗

arXiv2010

Eliashberg Analysis of Optical Spectra Reveals Strong Coupling of Charge Carriers to Spin Fluctuations in Superconducting Iron Pnictides

The temperature and frequency dependences of the optical conductivity of Co and Ni-doped BaFe2As2 are analyzed and the electron-boson spectral density a2F(w) extracted using Eliashberg's formalism. The characteristic energy of a large peak in the spectrum around 10 meV coincide with the resonance peak in the spin excitation spectra, giving compelling evidence that in iron-based superconductors spin fluctuations strongly couple to the charge carriers and mediate superconductivity. In addition the spectrum is found to evolve with temperature towards a less structured background at higher energies as in the spin susceptibility.

cond-mat.supr-con↗

arXiv2009

Microwave conductivity in the ferropnictides with specific application to Ba$_{1-x}$K$_x$Fe$_2$As$_2$

We calculate the microwave conductivity of a two band superconductor with $s^\pm$ gap symmetry. Inelastic scattering is included approximately in a BCS model augmented by a temperature dependent quasiparticle scattering rate assumed, however, to be frequency independent. The possibility that the s-wave gap on one or the other of the electron or hole pockets is anisotropic is explored including cases with and without gap nodes on the Fermi surface. A comparison of our BCS results with those obtained in the Two Fluid Model (TFM) is provided as well as with the case of the cuprates where the gap has d-wave symmetry and with experimental results in Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The presently available microwave conductivity data in this material provides strong evidence for large anisotropies in the electron pocket s-wave gap. While a best fit favors a gap with nodes on the Fermi surface this disagrees with some but not all penetration depth measurements which would favor a node-less gap as do also thermal conductivity and nuclear magnetic resonance data.

cond-mat.supr-con↗

arXiv2009

Characteristics of oxygen isotope substitutions in the quasiparticle spectrum of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$

There is an ongoing debate about the nature of the bosonic excitations responsible for the quasiparticle self energy in high temperature superconductors -- are they phonons or spin fluctuations? We present a careful analysis of the bosonic excitations as revealed by the `kink' feature at 70 meV in angle resolved photoemission data using Eliashberg theory for a d-wave superconductor. Starting from the assumption that nodal quasiparticles are not coupled to the $(π,π)$ magnetic resonance, the sharp structure at $70 $meV can be assigned to phonons. We find that not only can we account for the shifts of the kink energy seen on oxygen isotope substitution but also get a quantitative estimate of the fraction of the area under the electron-boson spectral density which is due to phonons. We conclude that for optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ phonons contribute $\sim 10$% and non-phononic excitations $\sim 90$%.

cond-mat.supr-con↗

arXiv2009

Spin Dynamics in Cuprates: Optical Conductivity of HgBa2CuO4

The electron-boson spectral density function I^2ChiOmega responsible for carrier scattering of the high temperature superconductor HgBa2CuO4 (Tc = 90 K) is calculated from new data on the optical scattering rate. A maximum entropy technique is used. Published data on HgBa2Ca2Cu3O8 (Tc = 130 K) are also inverted and these new results are put in the context of other known cases. All spectra (with two notable exceptions) show a peak at an energy (Omega_r) proportional to the superconducting transition temperature Omega_r ~= 6.3 kB.Tc. This charge channel relationship follows closely the magnetic resonance seen by polarized neutron scattering, Omega_r^{neutron} ~= 5.4 kB.Tc. The amplitudes of both peaks decrease strongly with increasing temperature. In some cases, the peak at Omega_r is weak and the spectrum can have additional maxima and a background extending up to several hundred meV.

cond-mat.supr-con↗

arXiv2008

Multiple bosonic mode coupling in the charge dynamics of the electron-doped superconductor (Pr$_{2-x}$Ce$_x$)CuO$_4$

We analyze optical spectroscopy data of the electron-doped superconductor (Pr$_{2-x}$Ce$_x$)CuO$_4$ (PCCO) to investigate the coupling of the charge carriers to bosonic modes. The method of analysis is the inversion of the optical scattering rate $τ^{-1}_{\rm op}(ω,T)$ at different temperatures $T$ by means of maximum entropy technique combined with Eliashberg theory. We find that in the superconducting state the charge carriers couple to two dominant modes one at $\sim 10 $meV and a second one at $\sim 45 $meV. The low energy mode shows a strong temperature dependence and disappears at or slightly above the critical temperature $T_c$. The high energy mode exists above $T_c$ and moves towards higher energies with increasing temperatures. It also becomes less prominent at temperatures $> 100 $K above which it evolves into a typical spin-fluctuation background. In contrast to the hole-doped High-$T_c$ superconductors PCCO proves to be a superconductor close to the dirty limit.

cond-mat.supr-con↗

arXiv2008

Bosonic spectral density of epitaxial thin-film La1.83Sr0.17CuO4 superconductors from infrared conductivity measurements

We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La1.83Sr0.17CuO4. Using Eliashberg formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La2-xSrxCuO4 with another high temperature superconductor Bi2Sr2CaCu2O8+d. The bosonic spectral functions of the two materials account for the low Tc of LSCO as compared to Bi-2212.

cond-mat.supr-con↗

arXiv2008

Finite band inversion of ARPES in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in comparison with optics

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.

cond-mat.supr-con↗

arXiv2006

Optical Sum Rule in Finite Bands

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high $T_c$ oxides, both theoretical and experimental.

cond-mat.supr-con↗

arXiv2006

Inversion techniques for optical conductivity data

Optical data is encoded with information on the microscopic interaction between charge carriers. For an electron-phonon system, the Eliashberg equations apply and a Kubo formula can be used to get the infrared conductivity. The task of extracting the electron-phonon spectral density $α^2F(ω)$ from data is rather complicated and, thus, simplified but approximate expressions for the conductivity have often been used. We test the accuracy of such simplifications and also discuss the advantages and disadvantages of various numerical methods needed in the inversion process. Normal and superconducting state are considered as well as boson exchange mechanisms which might be applicable to the High-$T_c$ oxides.

cond-mat.supr-con↗

arXiv2005

Optical sum in Nearly Antiferromagnetic Fermi Liquid Model

We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the Nearly Antiferromagnetic Fermi Liquid (NAFFL) model which has had some success in describing the electronic structure of the high $T_c$ cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation $(n_{{\bf k},σ})$ of states of momentum {\bf k} and spin $σ$ which is the central quantity in the calculations of OS and KE. Normal and superconducting states are considered as a function of temperature. Both integrals are found to depend importantly on interactions and an independent electron model is inadequate.

cond-mat.supr-con↗