We investigate the effect of isotope substitution on the electron-phonon interaction in the multi-band superconductor MgB2 using tunable laser based Angle Resolved Photoemission Spectroscopy. The kink structure around 70 meV in the $σ$ band, which is caused by electron coupling to the E2g phonon mode, is shifted to higher binding energy by ~3.5 meV in Mg(10)B2 and the shift is not affected by superconducting transition. These results serve as the benchmark for investigations of isotope effects in known, unconventional superconductors and newly discovered superconductors where the origin of pairing is unknown.
Isotope effects in a multiband superconductor with a leading interband pairing channel are investigated. A relatively small electron-phonon contribution into the pair-transfer interaction can cause effects of observed magnitude. A multiband model which interpolates the cuprate properties is used for illustrative calculations. Isotope exponents of the transition temperature ($α$), supercarrier density ($α_n$), paired carrier effective mass ($α_m$) and of the penetration depth ($α_λ$) on the doping scale have been obtained. The known opposite trend of $α$ and $T_c$ is reflected. The trends of $α…
The impurity effects on the transition temperature Tc and the isotope effect are examined in multiband superconductors with magnetic and nonmagnetic impurities, where the effect of Coulomb repulsion is considered. It is shown that an internal transition of the superconducting state is induced by impurity doping, and that the transition is accompanied by a jump of the isotope-effect coefficient alpha. In particular, the transition is illustrated in a system with two electron bands. In some special cases, extended Abrikosov and Gor'kov (AG) equations for Tc and the expressions of the isotope-eff…
I solved the Eliashberg equations for multiband non-phononic $s\pm$ wave spin glass superconductor and I calculated the temperature dependence of the gaps and superfluid density that reveals unusual behavior as non monotonic temperature dependence and reentrant superconductivity. For particular values of input parameters the phase diagram is still more complex with two different ranges of temperature where the superconductivity appears.
We review the current situation in the theory of superconducting and transport properties of MgB2. First principle calculations of of the electronic structure and electron-phonon coupling are discussed and compared with the experiment. We also present a brief description of the multiband effects in superconductivity and transport, and how these manifest themselves in MgB2. We also mention some yet open questions.
In strontium titanate, the Froehlich electron - LO-phonon interaction dominates the electron response and can also provide superconductivity. Because of high LO-phonon frequencies in SrTiO3, the superconducting system is non-adiabatic. We demonstrate that the dielectric function approach is an adequate theoretical method for superconductivity in SrTiO3 and on the SrTiO3-LaAlO3 interface. The critical temperatures are calculated using realistic material parameters. The obtained critical temperatures are in line with experimental data both for bulk and interface superconductivity. The present me…
We examine the impact of interfacial phonons on the superconducting state of FeSe/SrTiO$_3$ developing a material's specific multiband, full bandwidth, and anisotropic Eliashberg theory for this system. Our self-consistent calculations highlight the importance of the interfacial electron-phonon interaction, which is hidden behind the seemingly weak-coupling constant λ$_m$ = 0.4, in mediating the high T$_c$, and explain other puzzling experimental observations, such as the s-wave symmetry and replica bands. We discover that the formation of replica bands has a T$_c$ decreasing effect that is ne…
Emergence of superconductivity in a two-band system coupled with breathing and Jahn-Teller phonons is discussed in a weak-coupling limit. With the use of a standard quantum mechanical procedure, the phonon-mediated attraction is derived. From the analysis of the model including such attraction, a BCS-like formula for a superconducting transition temperature $T_{\rm c}$ is obtained. When only the breathing phonon is considered, $T_{\rm c}$ is the same as that of the one-band model. On the other hand, when Jahn-Teller phonons are active, $T_{\rm c}$ is significantly enhanced by the interband att…
Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the s…
Assessing the effective relevance of multiband effects in the fullerides is of fundamental importance to understand the complex superconducting and transport properties of these compounds. In this paper we investigate in particular the role of the multiband effects on the electron-phonon (el-ph) properties of the $t_{1u}$ bands coupled with the Jahn-Teller intra-molecular $H_g$ vibrational modes in the C$_{60}$ compounds. We show that, assuming perfect degeneracy of the electronic bands, vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smaller …
We discuss the effects of anisotropy on superconducting critical temperature and order parameter in a strongly coupled regime. The multiband representation is used as a model for anisotropy. We show that strong coupling effects in multiband superconductors lead to pair-breaking due to interband coupling because soft phonon modes play the same role as usual impurities. This effect makes the order parameters in different bands equal to each other and limits the upper bound on critical temperature.
In this paper we calculate ab initially the phonon dispersion relationship of the superconductor LaFeAsO and investigate a main property in the superconductor, the oxygen isotope effect. Based on this phonon dispersion relationship, we find the fact that an important reason of the oxygen isotope effect is connected with the phonon. This result agrees well with the experimental data where the power index of the oxygen isotope effect in the superconductor LaFeAsO is small.
Using a large-N expansion we present and solve the linearized equation for the superconducting gap for a generalized t-J model which also contains phonons within a Holstein model. The leading Tc has d-wave symmetry with phonons giving a positive contribution to Tc. The corresponding isotope coefficient is very small at optimal doping and increases towards the classical value 1/2 with increasing dopings similar as in many cuprates.
The isotope effect in the superconducting transition temperature is anomalous if the isotope coefficient $α<0$ or $α>1/2$. In this work, we show that such anomalous behaviors can naturally arise within the Bardeen-Cooper-Schrieffer framework if both phonon and non-phonon modes coexist. Different from the case of the standard Eliashberg theory (with only phonon) in which $α\le1/2$, the isotope coefficient can now take arbitrary values in the simultaneous presence of phonon and the other non-phonon mode. In particular, most strikingly, a pair-breaking phonon can give rise to large isotope coeffi…
We have measured the Ca isotope effect in the newly discovered superconductor CaC6. The isotope effect coefficient is 0.50(7). If one assumes that this material is a conventional electron-phonon coupled superconductor, this result shows that the superconductivity is dominated by coupling of the electrons by Ca phonon modes and that C phonons contribute very little. Thus, in contrast to MgB2, where phonons in the B layers are responsible for the superconductivity, in CaC6 the phonons are primarily modes of the intercalated Ca.
Superconducting transition temperature $T_C$ of some of the cubic $β$-phase Mo$_{1-x}$Re$_x$ alloys with x > 0.10 is an order of magnitude higher than that in the elements Mo and Re. We investigate this rather enigmatic issue of the enhanced superconductivity with the help of experimental studies of the temperature dependent electrical resistivity ($ρ$(T)) and heat capacity (C$_P$(T)), as well as the theoretical estimation of electronic density of states (DOS) using band structure calculations. The $ρ$(T) in the normal state of the Mo$_{1-x}$Re$_x$ alloys with x > 0.15 is distinctly different …
We show that recent ARPES results on the "unusual" oxygen isotope shift in the real part of the self-energy in the optimally doped $Bi2212$ samples can be qualitatively (and semi-quantitatively) explained by the theory of the electron-phonon interaction (EPI) elaborated few decades ago. However, for a quantitative analysis of the ARPES spectra it is necessary to know the momentum dependence of the EPI, the Coulomb contribution at high energies and the background due to impurities and defects.
We report the boron isotope effect on the E2g phonon mode by micro-Raman spectroscopy on the ternary Mg1-xAlxB2 system, synthesized with pure isotopes 10B and 11B. The isotope coefficient on the phonon frequency is near 0.5 in the full range decreasing near x = 0. The intraband electron-phonon (e-ph) coupling, for the electrons in the sigma band, has been extracted from the E2g line-width and frequency softening. Tuning the Fermi energy near the electronic topological transition (ETT), where the sigma Fermi surface changes from 2D to 3D topology the E2g mode, shows the known Kohn anomaly on th…
The exact formula of Tc's equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of interband interaction. The paring interaction in each band consisted of 2 parts : the electron-phonon interaction and non-phonon interaction are included in our model. The isotope effect exponent of MgB2 equal to 0.3 with Tc 40 K can be found in the weak coupling regime and interband interaction of electron-phonon interaction show more effect on isotope effect exponent than of non-phonon interaction.
We examine the isotope effect of superconductivity in systems with coexisting interactions of phonon and nonphonon mechanisms in addition to the direct Coulomb interaction. The interaction mediated by the spin fluctuations is discussed as an example of the nonphonon interaction. Extended formulas for the transition temperature Tc and the isotope-effect coefficient alpha are derived for cases (a) omega_np < omega_D and (b) omega_np > omega_D, where omega_np is an effective cutoff frequency of the nonphonon interaction that corresponds to the Debye frequency omega_D in the phonon interaction. In…
Oxygen-isotope effect has been investigated in a recently discovered superconductor Sr_{0.4}K_{0.6}BiO_{3}. This compound has a distorted perovskite structure and becomes superconducting at about 12 K. Upon replacing ^{16}O with ^{18}O by 60-80%, the T_c of the sample is shifted down by 0.32-0.50 K, corresponding to an isotope exponent of alpha_{O} = 0.40(5). This isotope exponent is very close to that for a similar bismuthate superconductor Ba_{1-x}K_{x}BiO_{3} with T_c = 30 K. The very distinctive doping and T_c dependencies of alpha_{O} observed in bismuthates and cuprates suggest that bism…
A short review of the optical and far-infrared measurements on MgB$_{2}$ is given. Multiband and multigap effects are analyzed by comparing optical properties with other experiments and {\em ab initio} calculations. The covered topics are: the plasma frequency, electron-phonon interaction, impurity scattering, the effects of C and Al substitution, interband transitions and the far-infrared signatures of the superconducting gaps.
We present Raman measurements on the iron-pnictide superconductors CeFeAsO_{1-x}F_{x} and NdFeAsO{1-x}F_{x}. Modeling the Fe-As plane in terms of harmonic and a cubic anharmonic Fe-As interaction we calculate the temperature dependence of the energy and lifetime of the Raman active Fe B_{1g} mode and fit to the observed energy shift. The shifts and lifetimes are in good agreement with those measured also in other Raman studies which demonstrate that the phonon spectrum is well represented by phonon-phonon interactions without any significant electronic contribution. We also estimate the anharm…
The results of first principles calculations of the electronic structure and the electron-phonon interaction in MgB2 are used to study theoretically the temperature dependence and anisotropy of the magnetic field penetration depth. The effects of impurity scattering are essential for a proper description of the experimental results. We compare our results with experimental data and we argue that the two-band model describes the data rather well.
We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurit…
The role of electron-phonon interactions in iron-based superconductor is currently under debate with conflicting experimental reports on the isotope effect. To address this important issue, we employ the renormalization-group method to investigate the competition between electron-electron and electron-phonon interactions in these materials. The renormalization-group analysis shows that the ground state is a phonon-dressed unconventional superconductor: the dominant electronic interactions account for pairing mechanism while electron-phonon interactions are subdominant. Because of the phonon dr…
The recent discovery of superconductivity at ~39 K in MgB2, by Nagamatsu et al. establishes this simple binary compound as having the highest bulk superconducting transition temperature, Tc, of any non-copper-oxide material. Much of the initial research has focused on whether MgB2 is a conventional BCS, electron-phonon mediated superconductor, and, if it is, why Tc is so high. Isotope effect measurements, in which the atom masses are manipulated to systematically change the phonon frequencies, are one of the fundamental experimental tests of electron-phonon mediated superconductivity. One woul…
Enhanced superconductivity in palladium hydrides by non-perturbative electron-phonon effects
Centro de Física de Materiales (CFM-MPC), CSIC-UPV/EHU（材料物理中心）；Ruđer Bošković Institute（鲁杰尔·博什科维奇研究所）；Università di Modena e Reggio Emilia（摩德纳和雷焦艾米利亚大学）；Istituto Nanoscienze-CNR（国家研究委员会纳米科学研究所）；University of the Basque Country (UPV/EHU)（巴斯克大学）
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 shi…
We calculate the isotope coefficients $α$ and $α^\ast$ for the superconducting critical temperature $T_c$ and the pseudogap temperature $T^\ast$ in a mean-field treatment of the t-J model including phonons. The pseudogap phase is identified with the $d$-charge-density wave ($d$-CDW) phase in this model. Using the small electron-phonon coupling constant $λ_d \sim 0.02$ obtained previously in LDA calculations in YBa$_2$Cu$_3$O$_7$, $α^{\ast}$ is negative but negligible small whereas $α$ increases from about 0.03 at optimal doping to values around 1 at small dopings in agreement with the general …
We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the coupling to electron dynamic response in the form of a damped oscillator and explore the possibility to reconstruct the spectrum of the latter from the phonon measurements. Preliminary estimates point to its location in the mid infrared region and we show how the required additional information can be extracted from the oxygen isotope effect on the phonon spectrum. The model predicts a significant measurable deviation from the "standard value" of the isotope effect even if the phonon frequency is far…
We studied the isotope effect of phonon in the Fe-based superconductors using a phenomenological two band model for the sign-changing s-wave ($\pm$s-wave) state. Within this mean-field model, we showed that the large isotope effect is not inconsistent with the $\pm$s-wave pairing state and its high transition temperature. In principle, a large phonon isotope coefficient $α$ implies a large phonon coupling constant. However, the asymmetric density of states (DOS) between two bands substantially enhances the value of $α$, so that a moderate value of the phonon coupling constant ($λ_{\rm ph} \app…
Palladium hydrides display the largest isotope effect anomaly known in literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largel…
It is shown that the translation-invariant bipolaron theory of superconductivity can explain the dependence of the isotope coefficient in high-temperature superconductors on the critical temperature of a superconducting transition: in the case of strong electron-phonon interaction, the isotope coefficient is low when doping is optimal and high when it is weak. It is demonstrated that in the case of London penetration depth, the absolute value of the isotope coefficient behaves in the opposite way. A conclusion of the great role of non-adiabaticity in the case of weak doping is made. The criter…
We use a tunable laser ARPES to study the electronic properties of the prototypical multiband BCS superconductor MgB2. Our data reveal a strong renormalization of the dispersion (kink) at ~65 meV, which is caused by coupling of electrons to the E2g phonon mode. In contrast to cuprates, the 65 meV kink in MgB2 does not change significantly across Tc. More interestingly, we observe strong coupling to a second, lower energy collective mode at binding energy of 10 meV. This excitation vanishes above Tc and is likely a signature of the elusive Leggett mode.
Point-contact spectroscopy was originally developed for the determination of the electron-phonon spectral function in normal metals. However, in the past 20 years it has become an important tool in the investigation of superconductors. As a matter of fact, point contacts between a normal metal and a superconductor can provide information on the amplitude and symmetry of the energy gap that, in the superconducting state, opens up at the Fermi level. In this paper we review the experimental and theoretical aspects of point-contact spectroscopy in superconductors, and we give an experimental surv…
Using the large-$N$ limit of the $t$-$J$ model and allowing also for phonons and the electron-phonon interaction we study the isotope effect $α$ for coupling constants appropriate for YBCO. We find that $α$ has a minimum at optimal doping and increases strongly (slightly) towards the underdoped (overdoped) region. Using values for the electron phonon interaction from the local density approximation we get good agreement for $α$ as a function of $T_c$ and doping $δ$ with recent experimental data in YBCO. Our results strongly suggest that the large increase of $α$ in the underdoped region is (a)…
Recently, the discovery of room-temperature superconductivity (SC) was experimentally realized in the fcc phase of LaH$_{10}$ under megabar pressure. Specifically, the isotope effect of $T_{\rm c}$ was measured by the replacement of hydrogen (H) with deuterium (D), demonstrating a driving role of phonons in the observed room-temperature SC. Herein, based on the first-principles calculations within the harmonic approximation, we reveal that (i) the identical electron-phonon coupling constants of fcc LaH$_{10}$ and LaD$_{10}$ decrease monotonously with increasing pressure and (ii) the isotope ef…
We have measured the effect of oxygen isotope substitution on the ab-plane reflectance of underdoped YBCO. The frequency shift of the transverse optic phonons due to the substitution of O-16 by O-18 yields an isotope effect of the expected magnitude for copper-oxygen stretching modes with alpha=0.5 +- 0.1. The reflectance shoulder at 400 - 500 cm^-1 shows a much smaller exponent of alpha=0.1 +- 0.1 in the normal state and alpha=0.23+- 0.1 in the superconducting state. These observations suggest that the shoulder is of electronic origin and not due to a phonon mode as has been suggested recentl…
Strong electron-phonon interactions in cuprates and other high-temperature superconductors have gathered support over the last decade in a large number of experiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong on-site repulsive correlations and the long-range Coulomb and electron-phonon (e-ph) interactions. Our extension of the BCS theory to the strong-coupling regime with the long-range \emph{unscreened} electron-phonon interaction could naturally explain the isotope effects, unconventional thermomagnetic tr…
We investigate the isotope effect on the London penetration depth of a superconductor which measures $n_S/m^*$, the ratio of superfluid density to effective mass. We use a simplified model of electrons weakly coupled to a single phonon frequency $ω_E$, but assume that the energy gap $Δ$ does not have any isotope effect. Nevertheless we find an isotope effect for $n_S/m^*$ which is significant if $Δ$ is sufficiently large that it becomes comparable to $ω_E$, a regime of interest to high $T_c$ cuprate superconductors and possibly other families of unconventional superconductors with relatively h…
Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which…
The isotope effects for Fe based superconductors are considered by including the phonon and magnetic fluctuations within the two band Eliashberg theory. We show that the recently observed inverse isotope effects of Fe, $α_{Fe} \approx -0.18 \pm 0.03 $,\cite{Shirage0903.3515} as well as the large positive isotope exponent ($α\approx 0.35$) can naturally arise for the magnetically induced sign revered s-wave pairing state within reasonable parameter range. Either experimental report can not be discarded from the present analysis based on the parameter values they require. The inverse and positiv…
Angle-resolved photoemission spectroscopy with low-energy tunable photons along the nodal direction of oxygen isotope substituted Bi2Sr2CaCu2O8+delta reveals a distinct oxygen isotope shift near the electron-boson coupling "kink" in the electronic dispersion. The magnitude (a few meV) and direction of the kink shift are as expected due to the measured isotopic shift of phonon frequency, which are also in agreement with theoretical expectations. This demonstrates the participation of the phonons as dominant players, as well as pinpointing the most relevant of the phonon branches.
The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping whereas the AF susceptibility at inte…
From the observed oxygen-isotope shift of the mid-infrared two-magnon absorption peak of YBa$_{2}$Cu$_{3}$O$_{6}$, we evaluate the oxygen-isotope effect on the in-plane antiferromagnetic exchange energy $J$. The exchange energy $J$ in YBa$_{2}$Cu$_{3}$O$_{6}$ is found to decrease by about 0.9% upon replacing $^{16}$O by $^{18}$O, which is slightly larger than that (0.6%) in La$_{2}$CuO$_{4}$. From the oxygen-isotope effects, we determine the lower limit of the polaron binding energy, which is about 1.7 eV for YBa$_{2}$Cu$_{3}$O$_{6}$ and 1.5 eV for La$_{2}$CuO$_{4}$, in quantitative agreement …
I present the results of first principles calculations of the phonon dispersions and electron-phonon coupling for BaTi$_2$Sb$_2$O. The phonon dispersions show a weak lattice instability near the zone corners that leads to a charge-density wave phase. The calculations of the electron-phonon coupling reveal strong coupling, especially to the in-plane Ti modes. The total coupling is large enough to readily explain the superconductivity in this compound. As the Fermi surfaces are disconnected with different orbital character weights, this compound is likely to host a multiband superconductivity.
We investigate the interplay of the electron-phonon and the spin fluctuation interaction for the superconducting state of YBa$_2$Cu$_3$O$_{7}$. The spin fluctuations are described within the nearly antiferromagnetic Fermi liquid theory, whereas the phonons are treated using a shell model calculation of all phonon branches. The electron-phonon coupling is calculated using rigidly displaced ionic potentials screened by a background dielectric constant $ε_\infty$ and by holes within the CuO$_2$ planes. Taking into account both interactions we get a superconducting state with $d_{x^2-y^2}$-symmetr…
Starting from the three-band $p-d$ Hubbard Hamiltonian we derive an effective $t-J$ model including electron-phonon interaction of quasiparticles with optical phonons. Within the effective Hamiltonian we analyze the influence of electronic correlations and electron-phonon interaction on the dynamical spin susceptibility in layered cuprates. We find a huge isotope effect on the resonance peak in the magnetic spin susceptibility, ${Im}χ({\bf q},ω)$, seen by inelastic neutron scattering. It results from both the electron-phonon coupling and the electronic correlation effects taken into account be…
Superconductivity in high-Tc cuprates is unconventional and there is a growing acceptance that carrier pairing in these strongly correlated electronic materials is mediated mainly by bosons of electronic origin rather than the phonons. Still, a significant isotope exponent (IE) (in certain cases, much larger than 0.5, the canonical BCS value) is observed experimentally. This has led to the assumption that phonons are also involved up to a certain extent. The magnitude of the IE in cuprates depends strongly on the number of doped holes, p, in the CuO2 planes and therefore, may indicate that pho…
The weak-coupling quantum phase diagrams of the one-dimensional (1D) Holstein-Hubbard and Peierls-Hubbard models are computed near half-filling, using a multi-step renormalization group technique. If strong enough, the electron-phonon interaction induces a spin gap. The spin gap, which determines the superconducting pairing energy, depends strongly on the band filling and decreases monotonically as the system is doped away from half-filling. However, the superconducting susceptibility exhibits a different doping dependence; it can vary non-monotonically with doping and exhibit a maximum at an …
In this paper, we reexamine the results of isotope effect experiments of the conventional monoatomic superconductor (Hg). It is shown clearly that the isotopic coefficients of mercury can be largely deviated from $α=0.5$, the standard value suggested by the phonon-mediated BCS pairing theory. According to the reported experimental results of various mercury isotopes, a giant isotope effect ($α=2.896$) is numerically found in the data. This study indicates that the validity of the conventional BCS theory cannot be verified by the isotope effect.
The exact formula of Tc's equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of two kinds of density of state : constant and van Hove singularity. The pairing interaction in each band consisted of 2 parts : the electron-phonon interaction and non-electron-phonon interaction are included in our model. We find that the interband interaction of electron-phonon show more effect on isotope exponent than the intraband interaction and the isotope effect exponent with constant density of state can fit to an experi…
Looking for superconductors with higher transition temperature requires a guiding principle. In conventional superconductors, electrons pair up into Cooper pairs via the retarded attraction mediated by electron-phonon coupling. Higher-frequency phonon (or smaller atomic mass) leads to higher superconducting transition temperature, known as the isotope effect. Furthermore, superconductivity is the only instability channel of the metallic normal state. In correlated systems, the above simple scenario could be easily violated. The strong local interaction is poorly screened, and this conspires wi…
We have prepared oxygen isotope exchanged crystals of impurity-free YBCO with various oxygen concentents, and examined pure doping ($p$) dependance of isotope effect on superconducting transition temperature. With decreasing oxygen contents, the isotope exponent $α$ monotonously increases without any anomaly around $p = 1/8$. The monotonous increase in $α$ indicates that phonons are involved in the mechanism which causes the monotonous $T_c$ suppression with underdoping.
We reconsider the long-standing problem of the effect of spin fluctuations on the critical temperature and isotope effect in a phonon-mediated superconductor. Although the general physics of the interplay between phonons and paramagnons had been rather well understood, the existing approximate formulas fail to describe the correct behavior of $% T_{c}$ for general phonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formula for $T_{c}$ which agrees well with exact numerical solutions of the Eliashberg equations for a broad range of parameters. Based on bot…
In the present paper, the impact of small Fermi energy on the selected parameters of the superconducting state in Ba$_{1-x}$K$_{x}$BiO$_{3}$ (BKBO) is studied at $x \in (0.3, 0.4, 0.5)$. This is done by employing the adiabatic and non-adiabatic Eliashberg equations in context of the available experimental data. It is found that the retardation, strong-coupling and the non-adiabatic effects notably influence superconducting phase in BKBO. In particular, the electron-electron interaction, approximated here by the Coulomb pseudopotential, is argued to be reduced by the non-adiabatic effects that …
