On the origin of the shallow and “replica” bands in FeSe monolayer superconductors

We compare the electronic structures of single FeSe layer films on SrTiO₃ substrate (FeSe/STO) and K _x Fe_2-y Se₂ superconductors obtained from extensive LDA and LDA + DMFT calculations with the results of ARPES experiments. It is demonstrated that correlation effects on Fe-3d states are sufficient in principle to explain the formation of the shallow electron-like bands at the M(X)-point. However, in FeSe/STO these effects alone are apparently insufficient for the simultaneous elimination of the hole-like Fermi surface around the Γ-point which is not observed in ARPES experiments. Detailed comparison of ARPES detected and calculated quasiparticle bands shows reasonable agreement between theory and experiment. Analysis of the bands with respect to their origin and orbital composition shows, that for FeSe/STO system the experimentally observed “replica” quasiparticle band at the M-point (usually attributed to forward scattering interactions with optical phonons in SrTiO₃ substrate) can be reasonably understood just as the LDA calculated Fe-3d _xy band, renormalized by electronic correlations. The only manifestation of the substrate reduces to lifting the degeneracy between Fe-3d _xz and Fe-3d _yz bands near M-point. For the case of K _x Fe_2-y Se₂ most bands observed in ARPES can also be understood as correlation renormalized Fe-3d LDA calculated bands, with overall semi-quantitative agreement with LDA + DMFT calculations.     

Hidden Fermi Surface in K<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript>2–<Emphasis Type="Italic">y</Emphasis></Subscript>Se<Subscript>2</Subscript>: LDA + DMFT Study

In this paper we provide theoretical LDA + DMFT support of recent angle-resolved photoemission spectroscopy (ARPES) observation of the so-called hidden hole-like band and corresponding hidden Fermi surface sheet near Γ-point in the K_0.62Fe_1.7Se₂ compound. To some extent, this is a solution to the long-standing riddle of Fermi surface absence around Γ-point in the K_xFe_2–ySe₂ class of iron chalcogenide superconductors. In accordance with the experimental data, Fermi surface was found near the Γ-point within LDA + DMFT calculations. Based on the LDA + DMFT analysis in this paper it is shown that the largest of the experimental Fermi surface sheets is actually formed by a hybrid Fe-3d ( xy, xz, yz )quasiparticle band. It is also shown that the Fermi surface is not a simple circle as DFT-LDA predicts, but has (according to the LDA + DMFT) a more complicated “propeller”-like structure due to correlations and multiorbital nature of the K_xFe_2–ySe₂ materials. While the smallest experimental Fermi surface around Γ-point is in some sense fictitious, since it is formed by the summation of the intensities of the spectral function associated with “propeller” loupes and is not connected to any of quasiparticle bands.     

Fragmentation of bands and Fermi surfaces in cuprate stripe phases

The band structure and evolution of the Fermi surfaces of stripe phases were studied using the t-t′-U Hubbard model in the mean field approximation. The appearance of quasi-one-dimensional “impurity” subbands caused by the localization of particles on domain walls inside the Hubbard gap is confirmed. Among vertical stripe phases parallel to y bonds, the Y₈ and Y₄ structures with distances l = 8a and 4a between domain walls were found to be stable. Fermi surface segments in antinodal or nodal directions were shown to correspond to an “ impurity” band or the main band related to the entire antiferromagnetic domain region. This is a probable explanation of the difference in the properties of ARPES spectra at different Fermi surface regions observed for La_2?xSr_xCuO₄. It was shown for the Y₈ structure that the topology of the Fermi surface changed and an isotropic pseudogap opened at the point corresponding to a p = 1/8 doping level. Attempts at relating this property to the anomalous suppression of T _c in LSCO at p = 1/8 encountered difficulties. The low dispersion of the impurity band and the wide gap separating it from the lower Hubbard band in diagonal stripe phases formed at p < 0.05 create prerequisites for the existence of the insulating state at nonzero doping.     

The GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas*

We study the spectral function of the homogeneous electron gas using many-body perturbation theory and the cumulant expansion. We compute the angle-resolved spectral function based on the GW approximation and the “GW plus cumulant” approach. In agreement with previous studies, the GW spectral function exhibits a spurious plasmaron peak at energies 1.5ω_pl below the quasiparticle peak, ω_pl being the plasma energy. The GW plus cumulant approach, on the other hand, reduces significantly the intensity of the plasmon-induced spectral features and renormalizes their energy relative to the quasiparticle energy to ω_pl. Consistently with previous work on semiconductors, our results show that the HEG is characterized by the emergence of plasmonic polaron bands, that is, broadened replica of the quasiparticle bands, red-shifted by the plasmon energy.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

Models of spin structures in Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript>

The mean-field method is used to calculate the bands, Fermi surfaces, and spin susceptibilities of a three-band model of the RuO₄ plane of Sr₂RuO₄ rutinate for states with different spin structures. In particular, the spiral state is studied with the “incommensurate” vector Q=2π(1/3, 1/3) corresponding to the nesting of bands with the population n=4. This state proves to be the lowest with respect to energy among other (paramagnetic, ferromagnetic, antiferromagnetic, and periodic) solutions. In the spiral state, in addition to the main α, β, and γ sheets of the Fermi surface, shadow Fermi boundaries along the Γ(0, 0)-M(π, 0) line (previously observed in the ARPES experiments) are revealed and explained. This may change the interpretation of the data on dispersionless peaks in photoemission, previously ascribed to surface states. The spin susceptibilities of the spiral state exhibit peaks in the dependence Im?(q, ω) at q=Q in accordance with the observed magnetic peak in neutron scattering. The hypothesis of the presence of spin structures with q=Q in the normal state of Sr₂RuO₄ and the methods of checking this hypothesis are discussed.     

Magnetic properties of Li<Subscript>2</Subscript>RuO<Subscript>3</Subscript> as studied by NMR and LDA + DMFT calculations

We present results of the combined study of the magnetic properties of Li₂RuO₃ by means of nuclear magnetic resonance (NMR) spectroscopy and theoretical dynamical mean-field theory (LDA + DMFT) calculations. The NMR data clearly show the onset of a thermal activation process in the high temperature region, T > 560K, which is tentatively ascribed to the formation of the valence bond liquid. The LDA + DMFT calculations demonstrate that the magnetic response at these temperatures is mostly due to the xz/yz orbitals, while the xy orbitals of Ru still form molecular orbitals. Thus, Ru ions are in the orbital-selective state in the high temperature phase of Li₂RuO₃.     

From the Bose-Einstein to fermion condensation

The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M _FC ^* and M _L ^* and intersecting near the binding energy E₀, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E₀ persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as \(M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). The regime is restored at some temperature \(T^ * \propto \sqrt B \). The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Effective Hamiltonian and properties of the normal and superconducting phases of <Emphasis Type="Italic">n</Emphasis>-type cuprates

An effective low-energy Hamiltonian is derived from a microscopic multiband p-d model in the regime of strong electron correlations. The parameters of the p-d model are determined by comparison with the ARPES data for undoped Nd₂CuO₄. The Hamiltonian is the t-J* model in which hopping and exchange slowly decay with distance and are taken into account up to the fifth coordination sphere. The quasiparticle band structure is calculated as a function of the doping concentration with regard to short-range magnetic order, and the superconductivity theory with the spin-fluctuation pairing mechanism is constructed. Assuming that the parameters of the model do not depend on the doping level, we obtained quantitative agreement with the properties observed experimentally for the normal and superconducting phases without introducing fitting parameters.     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ～T^?1 appears in the expression for the spin susceptibility χ_ac(T) of the system after the transition point at finite temperatures. The behavior of χ_ac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T _f is close to zero is discussed. The results are compared with the available experimental data.     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.     

Doping dependence of correlation effects in K1 − x Fe2 − y Se2 superconductors: LDA’ + DMFT investigation

We present a detailed LDA’ + DMFT investigation of the doping dependence of correlation effects in the novel K_{1 ? x} Fe_{2 ? y} Se₂ superconductor. Calculations are performed at four different hole doping levels, starting from a hypothetical stoichiometric composition with the total number of electrons equal to 29 per unit cell through 28 and 27.2 electrons toward the case of 26.52, which corresponds to the chemical composition K_0.76Fe_1.72Se₂ studied in recent ARPES experiments. In the general case, the increase in hole doping leads to quasiparticle bands in a wide energy window ±2 eV around the Fermi level becoming more broadened by lifetime effects, while correlation-induced compression of Fe-3d LDA’ bandwidths stays almost the same, of the order of 1.3 for all hole concentrations. However, close to the Fermi level, the situation is more complicated. In the energy interval from ?1.0 eV to 0.4 eV, the bare Fe-3d LDA’ bands are compressed by significantly larger renormalization factors up to 5 with increased hole doping, while the value of Coulomb interaction remains the same. This fact manifests the increase in correlation effects with hole doping in the K_{1 ? x} Fe_{2 ? y} Se₂ system. Moreover, in contrast to typical pnictides, K_{1 ? x} Fe_{2 ? y} Se₂ does not have well-defined quasiparticle bands on the Fermi levels, but has a “pseudogap”-like dark region instead. We also find that with the growth of hole doping, Fe-3d orbitals of various symmetries are affected by correlations differently in different parts of the Brillouin zone. To illustrate this, we determine the quasiparticle mass renormalization factors and energy shifts that transform the bare Fe-3d LDA’ bands of various symmetries into LDA’ + DMFT quasiparticle bands. These renormalization factors effectively mimic more complicated energy-dependent self-energy effects and can be used to analyze the available ARPES data.     

Memory-function conductivity formula and transport coefficients in underdoped cuprates

The two-band memory-function conductivity formula is derived from the quantum kinetic equation in the pseudogap state of underdoped cuprates. The conduction electrons are described by using the adiabatic version of the nested Fermi liquid model, and the effects of Mott correlations are taken into account phenomenologically. The linear dependence of the low-temperature effective number of conduction electrons on the doping level δ (for not too large δ) is found to be in agreement with experimental observation. The momentum distribution function turns out to play an important role in describing temperature effects. The closing of the antiferromagnetic pseudogap at temperatures of the order of room temperature is shown to be a direct consequence of a relatively large width of the quasiparticle peak in this distribution function. The coupling of conduction electrons to external magnetic fields is included in the two-band transport equations in the usual semiclassical way. It is shown that the low-temperature Hall number is proportional to δ as well (again for not too large δ) and that it exhibits singular behaviour when the Fermi surface changes from the hole-like shape into the electron-like shape.     

Fermi Surface Topology in the Case of Spontaneously Broken Rotational Symmetry

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p ? p'| = q₀. It is shown that, in the case of attraction and q₀ = 2p_F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q₀, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ? π(p_F/q₀ ? 1) small hole pockets at the distance p_F ? q₀ from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q₀ → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Dependence of the upper critical field on the defect concentration in MgB<Subscript>2</Subscript> and the electronic structure parameters

The upper critical field H _c 2 (H ‖ c) of the two-band superconductor MgB₂ is studied as a function of the residual resistivity ρ_n. It is found that the superconductor follows the standard trend: the slope-dH_c2/dT of the temperature dependence of H_c2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of H_c2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dH_c2/dT on ρ_n and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.     

Effect of spin structures and nesting on the shape of the fermi surface and pseudogap anisotropy in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">t</Emphasis>′-<Emphasis Type="Italic">U</Emphasis> Hubbard models

The effect of two types of spin structures on the shape of the Fermi surface and on the map of photoemission intensities for the t-t′-U Hubbard model is investigated. The stripe phase with a period of 8α and the spiral spin structure are calculated in the mean field approximation. It is shown that, in contrast to electron-type doping, hole-doped models are unstable to the formation of such structures. Pseudogap anisotropy is different for h-and e-doping and is determined by the spin structure. In accordance with ARPES data for La_2?xSr_xCuO₄, the stripe phase is characterized by quasi-one-dimensional FS segments in the vicinity of points M(±π, 0) and by suppression of the spectral density for k _x =k _y . It is shown that spiral structures exhibit polarization anisotropy: different segments of the FS correspond to electrons with different spin polarizations.