In paper III of this series (arXiv:0901.3612) we proposed a scenario of superconductivity driven by hole "undressing" that involved a complete redistribution of the occupation of single particle energy levels: the holes near the top of the band were proposed to all condense to the bottom of the band. Here we consider a less drastic redistribution involving electrons with a definite spin chirality and show that it is in fact energetically favored by the Coulomb exchange matrix element $J$ over the scenario proposed earlier. It is shown that spin splitting with chiral states reduces the Coulomb repulsion and hence that the Coulomb repulsion promotes spin splitting. Superconductors are proposed to possess a spin-split hole `core' at the bottom of the electronic conduction band in addition to a spin-split Fermi surface. The new scenario leads naturally to the existence of a spin current in the superconducting state and is consistent with the Spin Meissner effect and negative charge expulsion discussed earlier within the theory of hole superconductivity.
Experimental evidence indicates that the superconducting transition in high $T_c$ cuprates is an 'undressing' transition. Microscopic mechanisms giving rise to this physics were discussed in the first paper of this series. Here we discuss the calculation of the single particle Green's function and spectral function for Hamiltonians describing undressing transitions in the normal and superconducting states. A single parameter, $Υ$, describes the strength of the undressing process and drives the transition to superconductivity. In the normal state, the spectral function evolves from predominantl…
In recent work, we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron-electron interaction[1], and from a single particle point of view, originating in the electron-ion interaction[2]. We proposed that superconductivity in solids only occurs when the Fermi level is close to the top of a band (hole carriers), that it originates in `undressing' of carriers from $both$ the electron-electron and the electron-ion interaction, and that as a consequence holes in the normal state behave like electrons in the sup…
Photoemission and optical experiments indicate that the transition to superconductivity in cuprates is an 'undressing' transition . In photoemission this is seen as a coherent quasiparticle peak emerging from an incoherent background, in optics as violation of the Ferrell-Glover-Tinkham sum rule indicating effective mass reduction of superconducting carriers. We propose that this is a manifestation of the fundamental electron-hole asymmetry of condensed matter described by the theory of hole superconductivity. The theory asserts that electrons in nearly empty bands and holes in nearly full ban…
Photoemission experiments in high $T_c$ cuprates indicate that quasiparticles are heavily 'dressed' in the normal state, particularly in the low doping regime. Furthermore these experiments show that a gradual undressing occurs both in the normal state as the system is doped and the carrier concentration increases, as well as at fixed carrier concentration as the temperature is lowered and the system becomes superconducting. A similar picture can be inferred from optical experiments. It is argued that these experiments can be simply understood with the single assumption that the quasiparticle …
In recent work, we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron-electron interaction, and argued that it has fundamental consequences for superconductivity. Here we discuss the fact that there is also a fundamental difference between electrons and holes already at the single particle level, arising from the electron-ion interaction. The difference between electrons and holes due to this effect parallels the difference due to electron-electron interactions: {\it holes are more dressed than electrons…
The theory of hole superconductivity proposes that superconductivity originates in the fundamental electron-hole asymmetry of condensed matter and that it is an 'undressing' transition. Here we propose that a natural consequence of this theory is that superconductors behave as giant atoms. The model predicts that the charge distribution in superconductors is inhomogeneous, with higher concentration of negative charge near the surface. Some of this negative charge will spill out, giving rise to a negative electron layer right outside the surface of the superconductor, which should be experiment…
The theoretical model for the quasiparticle self-energy in HTSC is proposed, which is based on the forward scattering peak in the electron-phonon (EPI) interaction. By assuming that EPI dominates, the model explains qualitatively and in a consistent way the recent ARPES results. The latter show a kink in the normal state quasiparticle energy at 70 meV in the nodal direction, which is (surprisingly) not shifted in the superconducting (SC) state, while the singularity at 40 meV in the anti-nodal direction is shifted by the SC gap. The model predicts a dip-hump structure in the spectral function,…
When the Fermi level is near the top of a band the carriers (holes) are maximally dressed by electron-ion and electron-electron interactions. The theory of hole superconductivity predicts that only in that case can superconductivity occur, and that it is driven by $undressing$ of the carriers at the Fermi energy upon pairing. Indeed, experiments show that dressed hole carriers in the normal state become undressed electron carriers in the superconducting state. This leads to a description of superconductors as giant atoms, where undressed time-reversed electrons are paired and propagate freely …
We predict that simple metals and early transition metals that become superconducting under high pressures will show a change in sign of their Hall coefficient from negative to positive under pressure. If verified, this will strongly suggest that hole carriers play a fundamental role in `conventional' superconductivity, as predicted by the theory of hole superconductivity.
Unlike the parent phases of the iron-arsenide high Tc superconductors, undoped FeSe is not magnetically ordered and exhibits superconductivity with Tc~9K. Equally surprising is the fact that applied pressure dramatically enhances the modest Tc to ~37K. We investigate the electronic properties of FeSe using 77Se NMR to search for the key to the superconducting mechanism. We demonstrate that the electronic properties of FeSe are very similar to those of electron-doped FeAs superconductors, and that antiferromagnetic spin fluctuations are strongly enhanced near Tc. Furthermore, applied pressure e…
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 underdoped 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 \textit{why the quasiparticle dispersion is so flat in the anti-nodal region}, a be…
It is natural for a Mott antiferromagnetism in RVB description to become a superconductor in doped metallic regime. But the issue of superconducting transition temperature is highly nontrivial, as the AF fluctuations in the form of RVB pair-breaking are crucial in determining the phase coherence of the superconductivity. Underestimated AF fluctuations in a fermionic RVB state are the essential reason causing an overestimate of T_c in the same system. We point out that by starting with a {\it bosonic} RVB description where both the long-range and short-range AF correlations can be accurately de…
We have identified ferromagnetic- and superconducting-like magnetization hysteresis loops in highly oriented pyrolytic graphite samples below and above room temperature. We also found that both behaviors are very sensitive to low-temperature -- as compared to the sample synthesis temperature -- heat treatment. The possible contribution of magnetic impurities and why these do not appear to be the reason for the observed phenomena is discussed.
The experimental observation of superconductivity in LaFeAsO appearing on doping is analyzed with the group-theoretical approach that evidently led in a foregoing paper (J. Supercond 24:2103, 2011) to an understanding of the cause of both the antiferromagnetic state and the accompanying structural distortion in this material. Doping, like the structural distortions, means also a reduction of the symmetry of the pure perfect crystal. In the present paper we show that this reduction modifies the correlated motion of the electrons in a special narrow half-filled band of LaFeAsO in such a way that…
In rare-earth doped single crystalline CaFe2As2, the mysterious small volume fraction which superconducts up to 49 K, much higher than the bulk Tc ~ 30s K, has prompted a long search for a hidden variable that could enhance the Tc by more than 30% in iron-based superconductors of the same structure. Here we report a chemical, structural, and magnetic study of CaFe2As2 systematically doped with La, Ce, Pr, and Nd. Coincident with the high Tc phase, we find extreme magnetic anisotropy, accompanied by an unexpected doping-independent Tc and equally unexpected superparamagnetic clusters associated…
The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what is that, even less so of why it should be used and next to nothing of how it can be applied. These what, why and mainly how are the subject of the present lectures. In the first part, after a short description of why to be bothered, the NLSM is derived from scratch in a relatively simple (but still rather mathematical) way for non-interacting electrons in th…
Despite being the oldest known superconductor, solid mercury is mysteriously absent from all current computational databases of superconductors. In this work, we present a critical study of its superconducting properties based on state-of-the-art superconducting density-functional theory. Our calculations reveal numerous anomalies in electronic and lattice properties, which can mostly be handled, with due care, by modern ab-initio techniques. In particular, we highlight an anomalous role of (i) electron-electron correlations on structural properties (ii) spin-orbit coupling on the dynamical st…
We apply the staggered-pairing Ginzburg-Landau phenomenology to describe superconductivity in UPd_2Al_3 and UNi_2Al_3. The phenomenology was applied successfully to UPt_3 so it explains why these materials have qualitatively different superconducting phase diagrams although they have the same point-group symmetry. UPd_2Al_3 and UNi_2Al_3 have a two-component superconducting order parameter transforming as an H-point irreducible representation of the space group. Staggered superconductivity can induce charge-density waves characterized by new Bragg peaks suggesting experimental tests of the phe…
The Ginzburg sandwich is a superconducting film coated with a dielectric layer containing Bose-type exitations, i.e. exitons. Using spatially inhomogeneous Eliashberg equations in the local interaction limit, an exact result for the superconducting transition temperature of the Ginzburg sandwich has been obtained in the first order in a/L (where a is interatomic distance and L is the film thickness). The result has been found to be independent of the exiton frequency. The exitonic mechanism appears only in the second order in a/L since both partners of the Cooper pair should enter a layer of t…
Starting from a spin-fermion model for the cuprate superconductors, we obtain an effective interaction for the charge carriers by integrating out the spin degrees of freedom. Our model predicts a quantum critical point for the superconducting interaction coupling, which sets up a threshold for the onset of superconductivity in the system. We show that the physical value of this coupling is below this threshold, thus explaining why there is no superconducting phase for the undoped system. Then, by including doping, we find a dome-shaped dependence of the critical temperature as charge carriers …
The Z = 12.67 family of materials includes CaBeSi and NaAlSi which have been reported as non-superconducting and superconducting respectively. We show with an algorithm how to generate other members of this family. We discover through the material specific characterization dataset (MSCD) scheme and the symmetry conditions for superconductivity, why some are superconducting and others may not be superconducting.We estimate too the Tcs of members of this interesting family of materials.
Superconducting nickelates appear to be difficult to synthesize. Since the chemical reduction of ABO3 (A: rare earth; B transition metal) with CaH2 may result in both, ABO2 and ABO2H, we calculate the topotactic H binding energy by density functional theory (DFT). We find intercalating H is energetically favorable for LaNiO2 but not for Sr-doped NdNiO2. This has dramatic consequences for the electronic structure as determined by DFT+dynamical mean field theory: that of 3d9 LaNiO2 is similar to (doped) cuprates, 3d8 LaNiO2H is a two-orbital Mott insulator. Topotactical H might hence explain why…
We report a 29Si-NMR study on the pressure-induced superconductivity (SC) in an antiferromagnetic (AFM) heavy-fermion compound CeIrSi3 without inversion symmetry. In the SC state at P=2.7-2.8 GPa, the temperature dependence of the nuclear-spin lattice relaxation rate 1/T_1 below Tc exhibits a T^3 behavior without any coherence peak just below Tc, revealing the presence of line nodes in the SC gap. In the normal state, 1/T_1 follows a \sqrt{T}-like behavior, suggesting that the SC emerges under the non-Fermi liquid state dominated by AFM spin fluctuations enhanced around quantum critical point …
Using the full potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure-dependence of superconductivity in the two metallic phases of Boron: bct and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to stiffening of phonons with an accompanying decrease in electron-phon…
Motivated by the recent observations of possible p-wave superconductivity in the bismuth-nickel (Bi/Ni) bilayer, we explore theoretically the possibilities of realizing p-wave superconductivity in this bilayer. We begin with a literature survey on this system and related materials which have similar superconducting transition temperature. From the survey, the superconducting mechanism in this bilayer system is suggested to be phonon mediated type II superconductivity. A simple model is proposed to explain why the p-wave like Andreev reflection signals are likely to be observed in the surface p…
It is well established that the superconductivity in the recently discovered superconducting compound MgB$_{2}$ resides in the quasi-two-dimensional band ($σ$-band) and three-dimensional band ($π$-band). We demonstrate that, due to such band structure, the anisotropic Ginzburg-Landau theory practically does not have region of applicability, because gradient expansion in the $c$ direction breaks down. In the case of dirty $π$-band we derive the simplest equations which describe properties of such superconductors near $T_{c}$ and explore some consequences of these equations.
The conventional theory of superconductivity says that charge carriers in a metal that becomes superconducting can be either electrons or holes. I argue that this is incorrect. In order to satisfy conservation of mechanical momentum and of entropy of the universe in the superconductor to normal transition in the presence of a magnetic field it is necessary that the normal state charge carriers are holes. I will also review the empirical evidence in favor of the hypothesis that all superconductors are hole superconductors, and discuss the implications of this for the search for higher $T_c$ sup…
We propose a novel mechanism for the photo-induced superconducting-like response recently reported in cuprates and other strongly correlated materials. This mechanism relies on quantum-fluctuating bosons consisting of electron pairs. With periodic drive, the electron pairs and vacancies of pairs form a coherent non-equilibrium condensate, different from conventional superconductors, yet showing superconducting-like response in some regimes even with dissipation. Unlike the case of driven fermionic bands which results in the familiar Floquet bands with hybridization gaps, for driven bosons the …
We develop a correlated-electron minimal model for the normal state of charged phenanthrene ions in the solid state, within the reduced space of the two lowest antibonding molecular orbitals of phenanthrene. Our model is general and can be easily extended to study the normal states of other polycyclic aromatic hydrocarbon superconductors. The main difference between our approach and previous correlated-electron theories of phenacenes is that our calculations are exact within the reduced basis space, albeit for finite clusters. The enhanced exchange of electron populations between these molecul…
We propose a minimum single-band model for the newly discovered iron-based superconducting K$_x$Fe$_2$Se$_2$. Our model is found to be numerically consistent with the five-orbital model at low energies. Based on our model and the random phase approximation, we study the spin fluctuation and the pairing symmetry of superconducting gap function. The $(π/2,π/2)$ spin excitation and the $d_{x^2-y^2}$ pairing symmetry are revealed. All of the results can well be understood in terms of the interplay between the Fermi surface topology and the local spin interaction, providing a sound picture to expla…
Magnetic properties of TaB$_{2}$ were studied by means of DC and AC susceptibility measurements. It has been found that the compound becomes superconducting at T$_{c}$ = 9.5 K. From upper critical field measurements the superconducting parameters have been evaluated, which indicated that TaB$_{2}$ is a hard type-II superconductor. Possible reasons why superconductivity has not been discovered in previous studies are briefly discussed.
Ted Geballe has contributed enormously to the knowledge of superconducting materials during an illustrious scientific career spanning seven decades, encompassing groundbreaking discoveries and studies of both so-called conventional and unconventional superconductors. On the year of his 100th birthday I would like to argue that all superconducting materials that Ted investigated, as well as those he did not, have one thing in common that is not generally recognized: hole carriers. This includes $PbTe$ doped with $Tl$, for which Ted has proposed that superconductivity is driven by negative-U pai…
Many issues concerning the origin of high-temperature superconductivity (HTS) are still under debate. For example, how the magnetic ordering varies with doping and its relationship with the superconducting temperature; and why the maximal Tc always occurs near the quantum critical point. In this paper, taking hole-doped La2CuO4 as a classical example, we employ the first-principles band structure and total energy calculations and Monte Carlo simulations to explore how the symmetry-breaking magnetic ground state evolves with hole doping and the origin of a dome-shaped superconductivity region i…
We show that for a thin superconducting strip placed in a transverse dc magnetic field - the typical geometry of experiments with high-Tc superconductors - the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field.…
We report a detailed study of specific heat, electrical resistivity and thermal expansion in combination with inelastic neutron and inelastic X-ray scattering to investigate the origin of superconductivity in the two silicon clathrate superconductors Ba8Si46 and Ba24Si100. Both compounds have a similar structure based on encaged barium atoms in oversized silicon cages. However, the transition temperatures are rather different: 8 K and 1.5 K respectively. By extracting the superconducting properties, phonon density of states, electron-phonon coupling function and phonon anharmonicity from these…
Based on the recent developed real-space picture of superconductivity, we study the stability of the superconducting vortex lattices in layered superconductors. It is shown that the effective c-axis lattice constant play a significant role in promoting the superconducting transition temperature in these materials. An unified expression Tc(max)=10c*-28 can be applied to estimate the highest possible Tc(max) for a given layered superconductor with an effective c-axis lattice constant c*. For the newly discovered iron-based superconductors, our results suggest that their Tc cannot exceed 60K, 50K…
An antiferromagnetic (AF) spin fluctuation induced pairing model is proposed for the electron-doped cuprate superconductors. It suggests that, similar to the hole-doped side, the superconducting gap function is monotonic d_{x^2-y^2}-wave and explains why the observed gap function has a nonmonotonic d_{x^2-y^2}-wave behavior when an AF order is taken into account. Dynamical spin susceptibility is calculated and shown to be in good agreement with the experiment. This gives a strong support to the proposed model.
Under the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we argue that the pairing symmetry in all measured iron-based superconductors is universally consistent with the A_{1g} s-wave. The robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high T_c superconducting mechanisms: (1) the correspondence principle: the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high T_c superconduc…
We report beta-NMR investigations of polarized 8Li implanted in thin Pb and Ag/Nb films. At the critical superconducting temperature, we observe a singular peak in the spin relaxation rate in small longitudinal magnetic fields, which is attributed to fluctuations in the superconducting order parameter. However, the peak is more than an order of magnitude larger than the prediction based on the enhancement of the dynamic electron spin susceptibility by superconducting fluctuations and reflects the presence of unexpected slow fluctuations. Furthermore the fluctuations are rapidly suppressed in a…
In cuprate superconductors, a pronounced maximum of superconducting Tc is observed in compounds that have an in-plane Cu-O distance close to ~1.92 Angstroms. On the other hand, direct measurements of the electron-phonon coupling lambda as a function of Cu-O distance show a clear linear correlation, implying that Tc is a strongly non-linear function of lambda. Conventional superconductivity theories based on the electron-phonon interaction predict a monotonic dependence of Tc on electron phonon coupling constant, which makes them incompatible with the observed behaviour. The observed cross-over…
Doping bismuth selenide (Bi2Se3) with elements such as copper and strontium (Sr) can induce superconductivity, making the doped materials interesting candidates to explore potential topological superconducting behaviors. It was thought that the superconductivity of doped Bi2Se3 was induced by dopant atoms intercalated in van der Waals gaps. However, several experiments have shown that the intercalation of dopant atoms may not necessarily make doped Bi2Se3 superconducting. Thus, the structural origin of superconductivity in doped Bi2Se3 remains an open question. Herein, we combined material syn…
Magnetism and nematic order are the two non-superconducting orders observed in iron-based superconductors. To elucidate the interplay between them and ultimately unveil the pairing mechanism, several models have been investigated. In models with quenched orbital degrees of freedom, magnetic fluctuations promote stripe magnetism which induces orbital order. In models with quenched spin degrees of freedom, charge fluctuations promote spontaneous orbital order which induces stripe magnetism. Here we develop an unbiased approach, in which we treat magnetic and orbital fluctuations on equal footing…
In this contribution to the J. Phys. memorial issue in honor of Sandro Massidda I reflect on a phenomenon Sandro had been a part of. While theoretical condensed matter physicists have made, over the years, exciting and most elegant contributions to the theory of superconductivity (which, in and by itself, is one of the most beautiful constructs in theoretical physics), some of them of utmost importance, they have had less success in predicting and explaining superconducting states and mechanisms in specific materials. More down-to-earth computational materials scientists, who often go by the m…
We investigate the effect of strong disorder on a system with strong electronic repulsion. In absence of disorder, the system has a d-wave superconducting ground-state with strong non-BCS features due to its proximity to a Mott insulator. We find that, while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. The suppression of charge motion in regions of strong potential fluctuation leads to formation of Mott insulating patches, which anchor a larger non-s…
We report on a microscopic study of the noncentrosymmetric superconductor W$_3$Al$_2$C (with $T_c$ = 7.6 K), mostly by means of $^{27}$Al- and $^{13}$C nuclear magnetic resonance (NMR). Since in this material the density of states at the Fermi level is dominated by the tungsten's 5$d$ orbitals, we expect a sizeable spin-orbit coupling (SOC) effect. The normal-state electronic properties of W$_3$Al$_2$C resemble those of a standard metal, but with a Korringa product $1/(T_{1}T)$ significantly smaller than that of metallic Al, reflecting the marginal role played by $s$-electrons. In the supercon…
Basic experimental facts related to ARPES, tunnelling, optics ad neutron scattering measurements are discussed. They give evidence for the relevance of the electron-phonon interaction (EPI) in pairing mechanism of HTSC cuprates. A controllable theory for strong correlations and their effects on EPI is discussed which is based on the 1/N expansion method in the t-J model. Strong correlations renormalize EPI and other charge-fluctuation properties (by including nonmagnetic impurity scattering) and the forward scattering peak (FSP) appears in the effective interactions. Pronounced FSP in EPI of H…
To date, several experimental groups reported measurements of the thickness dependence of T_c of atomically uniform single-crystalline Pb nanofilms. The reported amplitude of the T_c-oscillations varies significantly from one experiment to another. Here we propose that the reason for this unresolved issue is an interplay of the quantum-size variations in the single-electron density of states with thickness-dependent oscillations in the phonon mediated electron-electron coupling. Such oscillations in the coupling depend on the substrate material, the quality of the interface, the protection cov…
We study the superconducting phase transition, both in a graphene bilayer and in graphite. For that purpose we derive the mean-field effective potential for a stack of graphene layers presenting hopping between adjacent sheets. For describing superconductivity, we assume there is an on-site attractive interaction between electrons and determine the superconducting critical temperature as a function of the chemical potential. This displays a dome-shaped curve, in agreement with previous results for two-dimensional Dirac fermions. We show that the hopping between adjacent layers increases the cr…
Chevrel ternary superconductors show an intriguing coexistence of molecular aspects, large electron-phonon and electron-electron correlations, which to some extent still impedes their quantitative understanding. We present a first principles study on the prototypical Chevrel compound PbMo$_{6}$S$_{8}$, including electronic, structural and vibrational properties at zero and high pressure. We confirm the presence of an extremely strong electron-phonon coupling, linked to the proximity to a R$\overline{3}$-P$\overline{1}$ structural phase transition, which weakens as the system, upon applied pres…
Much remains unknown of the microscopic origin of superconductivity when it materializes in atomically disordered systems as in amorphous alloys (1) or in crystals riddled with defects(2). A manifestation of this conundrum is envisaged in the highly defective iron chalcogenide superconductors of KxFe2-ySe2 (3-6). How can superconductivity survive under such crude conditions that call for strong electron localization (7)? With vacancies present both at the K and Fe sites, superconductivity is bordering a semi-metallic region below x ~ 0.7 and an insulating and antiferromagnetic region above x ~…
Why Bi2Sr2CaCu2Ox (Bi2212) allows high critical current density Jc in round wires rather than only in the anisotropic tape form demanded by all other high temperature superconductors is important for future magnet applications. Here we compare the local texture of state-of-the-art Bi2212 and Bi2223 ((Bi,Pb)2Sr2Ca2Cu3O10), finding that round wire Bi2212 generates a dominant a-axis growth texture that also enforces a local biaxial texture (FWHM <15°) while simultaneously allowing the c-axes of its polycrystals to rotate azimuthally along and about the filament axis so as to generate macroscopica…
It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of superconducting $MgB_2$ is due to a bound state caused by the electron-phonon coupling. Our theory explains why this peak appears only in the spectra with $E_{2g}$ symmetry and only in the $σ$ but not $π$ bands. The properties of the bound state and the Raman spectrum are investigated, also in the presence of impurity scattering.
