A theoretical overview of the classes of superconductors encompassing (a) high-Tc cuprate, (b) iron-based and (c) aromatic superconductors is given. Emphasis is put on the multiband natures of all the three classes, where the differences in the multiorbits and their manifestations in the electronic structures and pairing are clarified. From these, future directions and prospects are discussed.
We study the superconductivity in the three-dimensional multiband d-p model, in which a Cu$_2$O$_3$-ladder layer and a CuO$_2$-chain layer are alternately stacked, as a model of the superconducting spin-chain ladder cuprate. $p_z$-Wave-like triplet superconductivity is found to be the most stable, and its dependence on interlayer coupling can explain the superconducting transition temperature dependence on pressure in real superconducting spin-chain ladder cuprates. The superconductivity may be enhanced if hole transfer from the chain layer to the ladder layer can be promoted beyond the typica…
The pseudogap (PG) excitations in the framework of multiband superconductivity are analysed. Calculations for the doping phase diagram of electron-doped cuprate superconductors have been made. A nonrigid multiband model has been used. The interband pairing acts between the upper Hubbard band (UHB) and midgap states created (and shifted upwards) by doping. The appearance of two PG and two phase diagram critical points (CP) is suggested. The larger antinodal PG reflects the destruction of the long-range antiferromagnetic (AF) order. The second, smaller PG is a near-nodal event with exposed dopin…
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…
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.
Within the BCS framework a multiband model with d-wave symmetry is considered. Generalized Fermi surface topologies via band overlapping are introduced. The band overlap scale is of the order of the Debye energy. The order parameters and the pairing have d-wave symmetry. Experimental values reported for the critical temperatures $T_c(x)$ and the order parameters, $Δ_0(x)$, in terms of dopping $x$ are used. Numerical results for the coupling and the band overlapping parameters in terms of the doping are obtained for the cuprate superconductor $La_{2-x}Sr_xCuO_4$.
We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing m…
Using a doping-determined multiband model spectrum of a "typical'' cuprate the effective mass of the paired carriers is calculated on the whole doping scale. Large $m_{ab}$ values quench rapidly with leaving the very underdoped region. Further slower diminishing of $m_{ab}$ reproduces the trend towards restoring the Fermi-liquid behaviour in cuprates with progressive doping. The interband superconducting condensate density ($n_s$) shows similar behaviour to the transition temperature and superconducting gaps. The $n_s(0)/m_{ab}$ ratio has an expressed maximum close to optimal doping as also th…
We calculate the quasiparticle dispersion and spectral weight of the quasiparticle that results when a hole is added to an antiferromagnetically ordered CuO$_2$ plane of a cuprate superconductor. We also calculate the magnon contribution to the quasiparticle spectral function. We start from a multiband model for the cuprates considered previously [Nat. Phys. \textbf{10}, 951 (2014)]. We map this model and the operator for creation of an O hole to an effective one-band generalized $t-J$ model, without free parameters. The effective model is solved using the state of the art self-consistent Born…
We show that objections raised by Chakraverty $et$ $al$ (Phys. Rev. Lett. 81, 433 (1998)) to the bipolaron model of superconducting cuprates are the result of an incorrect approximation for the bipolaron energy spectrum and misuse of the bipolaron theory. The consideration, which takes into account the multiband energy structure of bipolarons and the unscreened electron-phonon interaction clearly indicates that cuprates are in the Bose-Einstein condensation regime with mobile charged bosons.
Recent discovery of high T_c superconductivity in Fe-based compounds may have opened a new pathway to the room temperature superconductivity. The new materials feature FeAs layers instead of the signature CuO_2 planes of much-studied cuprates. A model Hamiltonian describing FeAs layers is introduced, highlighting the crucial role of puckering of As atoms in promoting d-electron itinerancy and warding off large local-moment magnetism of Fe ions, the main enemy of superconductivity. Quantum many-particle effects in charge, spin and multiband channels are explored and a nesting-induced spin densi…
The three-component ab-plane optical conductivity of the high-T_c cuprates is derived using the gauge invariant response theory, and compared to the data previously obtained from the optical reflectivity measurements in the La_2CuO_4 based families. The valence electrons are described by the Emery three-band model with the antiferromagnetic correlations represented by an effective single-particle potential. In the 0 < delta < 0.3 doping range, it is shown that the total spectral weight of the three-band model is shared between the intra- and interband channels nearly in equal proportions. At o…
Emerging in the 1950s, the multiband superconductivity has been considered for a long time as an approximate model in the form of a generalization of the BCS theory to the case of two bands for a more accurate quantitative description of the properties and characteristics of such superconductors as cuprates, heavy fermions compounds, metal boron carbides, fullerides, strontium ruthenate etc. due to their complex piecewise-continuous Fermi surfaces. However the discovery of the multiband structure of the superconducting state in magnesium diboride in 2001 and iron oxypnictides and chalcogenides…
Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal $d$-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized…
We analyze how the coherence peaks observed in Scanning Tunneling Spectroscopy (STS) of cuprate high temperature superconductors are transferred from the cuprate layer to the oxide layers adjacent to the STS microscope tip. For this purpose, we have carried out a realistic multiband calculation for the superconducting state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) assuming a short range d-wave pairing interaction confined to the nearest-neighbor Cu $d_{x^2-y^2}$ orbitals. The resulting anomalous matrix elements of the Green's function allow us to monitor how pairing is then induced not only w…
The detailed optical properties of the multiband iron-chalcogenide superconductor FeTe$_{0.55}$Se$_{0.45}$ have been reexamined for a large number of temperatures above and below the critical temperature $T_c=14$ K for light polarized in the a-b planes. Instead of the simple Drude model that assumes a single band, above $T_c$ the normal-state optical properties are best described by the two-Drude model that considers two separate electronic subsystems; we observe a weak response ($ω_{p,D;1}\simeq 3000$ cm$^{-1}$) where the scattering rate has a strong temperature dependence ($1/τ_{D,1}\simeq 3…
High-$T_c$ superconductors with CuO$_2$ layers, manganites La$_{1-x}$Sr$_x$MnO$_3$, and cobaltites LaCoO$_3$ present several mysteries in their physical properties. Most of them are believed to come from the strongly-correlated nature of these materials. From the theoretical viewpoint, there are many hidden rocks in making the consistent description of the band structure and low-energy physics starting from the Fermi-liquid approach. Here we discuss the alternative method -- multielectron approach to the electronic structure calculations for the Mott insulators -- called LDA+GTB (local density…
Pressure effect is overviewed for the cuprates and carbon-based superconductors, with an emphasis on how their orbital characters are modified by pressure. For the high-Tc cuprates, we start from an observation for ambient pressure that, on top of the main orbital (dx2-y2), a hybridization with the second (dz2) orbital around the Fermi energy significantly affects Tc in the spin-fluctuation mediated pairing, where the hybridization is dominated by material parameters. We can then show that applying pressures along a, b axes enhances Tc while a c axis pressure suppresses Tc, where not only the …
High Tc superconductivity in FeAs-based multilayers (pnictides), evading temperature decoherence effects in a quantum condensate, is assigned to a Feshbach resonance (called also shape resonance) in the exchange-like interband pairing. The resonance is switched on by tuning the chemical potential at an electronic topological transition (ETT) near a band edge, where the Fermi surface topology of one of the subbands changes from 1D to 2D topology. We show that the tuning is realized by changing i) the misfit strain between the superconducting planes and the spacers ii) the charge density and iii…
The minimal ingredients to explain the essential physics of layered copper-oxide (cuprates= materials remains heavily debated. Effective low energy single-band models of the copper-oxygen orbitals are widely used because there exists no strong experimental evidence supporting multiband structures. Here we report angle-resolved photoelectron spectroscopy experiments on La-based cuprates that provide direct observation of a two-band structure. This electronic structure, qualitatively consistent with density functional theory, is parametrised by a two-orbital ($d_{x^2-y^2}$ and $d_{z^2}$) tight-b…
Optical spectral weight transfer associated with the onset of superconductivity at high energy scales compared with the superconducting gap has been observed in several systems such as high-$T_c$ cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. We discuss applying this idea to the cuprates and twisted multilayer graphene.
We report the discovery of superconductivity in Nb$_3$Pd$_{x}$Se$_7$ with a $x$-dependent superconducting transition-temperature as high as $T_c \simeq 2.1 $ K for $x \simeq0.7$ (middle point of the resistive transition). Needle-like single crystals display anisotropic upper-critical fields with an anisotropy $γ= H^{b}_{c2}/H^{a}_{c2}$ as large as 6 between fields applied along their needle axis (or $b-$axis) or along the $a-$axis. As for the Fe based superconductors $γ$ is temperature-dependent suggesting that Nb$_3$Pd$_{0.7}$Se$_7$ is a multi-band superconductor. This is supported by band st…
We report a systematic investigation, together with a theoretical analysis, of the resistivity and Hall effect in single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$, over a wide doping range. We find a surprisingly great disparity between the relaxation rates of the holes and the electrons, in excess of an order of magnitude in the low-doping, low-temperature regime. The ratio of the electron to hole mobilities diminishes with temperature and doping (away from the magnetically ordered state) and becomes more conventional. We also find a straightforward explanation of the large asymmetry (…
The Fe-based superconductors (FBS) are an important new class of superconducting materials. As with any new superconductor with a high transition temperature and upper critical field, there is a need to establish what their applications potential might be. Applications require high critical current densities, so the usefulness of any new superconductor is determined both by the capability to develop strong vortex pinning and by the absence or ability to overcome any strong current-limiting mechanisms of which grain boundaries in the cuprates are a cautionary example. In this review we first co…
Motivated by the recent experimental determination of the three-dimensional Fermi surface of overdoped La-based cuprate superconductors [Horio et al., Phys. Rev. Lett. 2018, 121, 077004], we revisit the tight-binding parameterization of their conduction band. We construct a minimal tight-binding model entailing eight orbitals, two of them involving apical oxygen ions. Parameter optimization allows to almost perfectly reproduce the three-dimensional conduction band as obtained from density functional theory (DFT). We discuss how each parameter entering this multiband model influences it, and sh…
Intermetallic R$_3$T$_4$X$_{13}$ series consists of cage like structure and have been in focus due to their unconventional electronic ground states. In this work, we report the normal and superconducting state properties of a high quality single crystal of Lu$_3$Os$_4$Ge$_{13}$. Lu$_3$Os$_4$Ge$_{13}$ belongs to the above mentioned series and crystallizes in a cubic crystal structure with the space group $\it{Pm\bar{3}n}$. Using electrical transport, magnetization and heat capacity measurements, we show that Lu$_3$Os$_4$Ge$_{13}$ is a type-II multi-band superconductor ($T{_c} =3.1$~K) with unus…
CeCoIn5 is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism, and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low temperature microwave spectroscopy to study the charge dynamics of the CeCoIn5 superconducting state. The similarities to cuprates, in particular to ul…
After the reward of more than two decades of pursuit on the high-Tc cuprate analog with the hope to obtain a better understanding of the mechanism of high-Tc superconductivity, the discovery of superconductivity in the infinite-layer nickelate brings more mystery to the picture than expected. Tops in the list of questions are perhaps (1) absence of superconductivity in the bulk nickelate and limited thickness of the infinite-layer phase in thin film, (2) absence of superconductivity in the La-nickelate despite it being the earliest studied rare-earth nickelate, and the role of 4f orbital in th…
FeSe is an iron-based superconductor of immense current interest due to the large enhancements of Tc that occur when it is pressurized or grown as a single layer on an insulating substrate. Here we report precision measurements of its superconducting electrodynamics, at frequencies of 202 and 658 MHz and at temperatures down to 0.1 K. The quasiparticle conductivity reveals a rapid collapse in scattering on entering the superconducting state that is strongly reminiscent of unconventional superconductors such as cuprates, organics and the heavy fermion material CeCoIn5. At the lowest temperature…
The ongoing search for new superconductors has recently yielded a new family of oxypnictides composed of alternating La_2O_{2-x}F_x and Fe_2As_2 layers [1-4] with transition temperatures T_c of 25-28 K, which can be raised to 40-43 K by replacing La with Ce [5] or Sm [6] or to 52 K by replacing La with Nd and Pr [7, 8]. Recent experiments and band structure calculations have suggested an unconventional multiband superconductivity in the layers of paramagnetic Fe ions, which would normally destroy superconductivity in the traditional mechanism of the s-wave Cooper pairing. Here we report very h…
We present a detailed study of the electrical transport properties of a recently discovered iron-based superconductor: Sm$_4$Fe$_2$As$_2$Te$_{0.72}$O$_{2.8}$F$_{1.2}$. We followed the temperature dependence of the upper critical field by resistivity measurement of single crystals in magnetic fields up to 16 T, oriented along the two main crystallographic directions. This material exhibits a zero-temperature upper critical field of 90 T and 65 T parallel and perpendicular to the Fe$_2$As$_2$ planes, respectively. An unprecedented superconducting magnetic anisotropy $γ_H=H_{c2}^{ab}/H_{c2}^c \si…
Photo-excitation is a very powerful way to instantaneously drive a material into a novel quantum state without any fabrication, and variable ultrafast techniques have been developed to observe how electron-, lattice-, and spin-degrees of freedom change. One of the most spectacular phenomena is photo-induced superconductivity, and it has been suggested in cuprates that the transition temperature Tc can be enhanced from original Tc with significant lattice modulations. Here we show another photo-induced high-Tc superconducting state in the iron-based superconductor FeSe with semi-metallic hole a…
