On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Theory of dual fermion superconductivity in hole-doped cuprates

Since the discovery of the cuprate high-temperature superconductivity in 1986, a universal phase diagram has been constructed experimentally and numerous theoretical models have been proposed. However, there remains no consensus on the underlying physics thus far. Here, we theoretically investigate the phase diagram of hole-doped cuprates based on an itinerant-localized dual fermion model, with the charge carriers doped on the oxygen sites and localized holes on the copper d _{x2 ? y2} orbitals. We analytically demonstrate that the puzzling anomalous normal state or the strange metal could simply stem from a free Fermi gas of carriers bathing in copper antiferromagnetic spin fluctuations. The short-range high-energy spin excitations also act as the “magnetic glue” of carrier Cooper pairs and induce d-wave superconductivity from the underdoped to overdoped regime, distinctly different from the conventional low-frequency magnetic fluctuation mechanism. We further sketch out the characteristic dome-shaped critical temperature T _c versus doping level. The emergence of the pseudogap is ascribed to the localization of partial carriers coupled to the local copper moments or a crossover from the strange metal to a nodal Kondo-like insulator. Our work provides a consistent theoretical framework to understand the typical phase diagram of hole-doped cuprates and paves a distinct way to the studies of both non-Fermi liquid and unconventional superconductivity in strongly correlated systems.     

Ground state pairing correlation competes in the doped triangular lattice Hubbard model

By using the constrained path quantum Monte carlo method, we study the ground state paring correlations in the t ? U ? V Hubbard model on the triangular lattice. It is shown that pairings with various symmetries dominate in different electron filling regions. The pairing correlation with fn-wave symmetry dominates over other pairings around half fillings, and as the electron filling decreases away from the half filling, the d + id-wave pairing correlation tends to dominate. As the electron filling is bellow the Van Hove singularity, the f-wave pairing dominates. These crossovers are due to the interplay of electronic correlation and geometric frustration, associating with the competition between the antiferromagnetic correlations and ferromagnetic fluctuations. Our findings reveal the possible magnetic origin of superconductivity, and also provide useful information for the understanding of superconductivity in Na _x CoO₂·H₂O and the organic compounds.     

Possible universal cause of high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> superconductivity in different metals

Using the theory of high-temperature superconductivity based on the idea of the fermion-condensation quantum phase transition (FCQPT), we show that neither the d-wave pairing symmetry, the pseudogap phenomenon, nor the presence of the Cu-O₂ planes is of decisive importance for the existence of high-T _c superconductivity. We analyze recent experimental data on this type of superconductivity in different materials and show that these facts can be understood within the theory of superconductivity based on the FCQPT. The latter can be considered as a universal cause of high-T _c superconductivity. The main features of a room-temperature superconductor are discussed.     

Competing effects of Hund’s splitting and symmetry-breaking perturbations on electronic order in Pb<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te

We study the effect of a uniform external magnetization on p-wave superconductivity on the (001) surface of the crystalline topological insulator (TCI) Pb_1?xSn_xTe. It was shown by us in an earlier work that a chiral p-wave finite-momentum pairing (FFLO) state can be stabilized in this system in the presence of weak repulsive interparticle interactions. In particular, the superconducting instability is very sensitive to the Hund’s interaction in the multiorbital TCI, and no instabilities are found to be possible for the “wrong” sign of the Hund’s splitting. Here we show that for a finite Hund’s splitting of interactions, a significant value of the external magnetization is needed to degrade the surface superconductivity, while in the absence of the Hund’s interaction, an arbitrarily small external magnetization can destroy the superconductivity. This implies that multiorbital effects in this system play an important role in stabilizing electronic order on the surface.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

Band structure and the magnetic and elastic properties of SrFeO<Subscript>3</Subscript> and LaFeO<Subscript>3</Subscript> perovskites

The band structure and the magnetic and elastic characteristics of SrFeO₃ and LaFeO₃ perovskites with ferromagnetic and antiferromagnetic collinear spin configurations (of the A, C, and G types) are investigated using the ab initio pseudopotential method (the VASP program package) with the inclusion of the single-site Coulomb correlations (the LSDA + U formalism). It is shown that, in the pressure range 0–50 GPa, the most stable states are the ferromagnetic metal state for the SrFeO₃ compound and the antiferromagnetic insulator state of the G type for the LaFeO₃ compound.     

Coulomb repul sion of hole s and competition between $${d_{{x^2} - {y^2}}}$$ -wave and s-wave paring s in cuprate superconductor s

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO₂ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V _q does not appear in the kernel of the corresponding integral equation.     

Many-electron model of band structure and metal-insulator transition under pressure in FeBO<Subscript>3</Subscript>

A many-electron model is proposed for the band structure of FeBO₃ with regard to strong electron correlations in the d⁴, d⁵, and d⁶ configurations. Under normal conditions, FeBO₃ is characterized by a dielectric charge-transfer gap in the strong correlation regime U?W. With increasing pressure, not only does the d-band W width grow but simultaneously the effective Hubbard parameter U_eff sharply drops, which is due to the crossover of high-spin and low-spin ground state terms of the Fe²⁺, Fe³⁺, and Fe⁴⁺ ions. It is predicted that a transition from the semiconducting antiferromagnetic state to the metallic paramagnetic state will occur in the high-pressure phase with increasing temperature.     

Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

It has been shown that the strong coupling model taking into account a rise in the spin antiferromagnetic insulating state explains the doping dependence of the topology and shape of the Fermi contour of superconducting cuprates. Hole pockets with shadow bands in the second Brillouin zone form the Fermi contour with perfect ordinary and mirror nesting, which ensures the coexistence of orbital antiferromagnetism and superconductivity with a large pair momentum for T < T_C. The weak pseudogap region (T_* < T < T*) corresponds to the orbital antiferromagnetic ordering, which coexists with the incoherent state of superconducting pairs with large momenta in the strong pseudogap region (T_C < T < T_*).     

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A₁(x)T at doping levels x below the critical value x _c ^h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x _c ^h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A₁(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.     

Thermodynamics of a Magnetic Transition in MnS<Subscript>2</Subscript> at High Pressures

The behavior of the specific heat of MnS₂ at high pressures has been studied. A significant increase in the transition temperature T_N to an antiferromagnetic state with the pressure from 48.2 K at atmospheric pressure to 76 K at a pressure of 5.3 GPa has been revealed. The initial pressure derivative is dT _N /dP = 4.83 K/GPa. It has been found that the parameter α = d(logT _N )/d(logV ) = ?6.6 ± 0.1 is significantly different from the value α = ?10/3 ≈ ?3.3 (Bloch relation), which is typical of numerous antiferromagnetic insulators—transition- metal oxides and fluorides. The volume jump at the magnetic transition point has been estimated. The necessity of direct dilatometric measurements of the volume has been justified.     

High-pressure magnetic properties and <Emphasis Type="Italic">P-T</Emphasis> phase diagram of iron borate

The high-pressure magnetic states of iron borate ⁵⁷FeBO₃ single-crystal and powder samples have been investigated in diamond anvil cells by nuclear forward scattering (NFS) of synchrotron radiation at different temperatures. In the low-pressure (0 < P < 46 GPa) antiferromagnetic phase, an increase of the Neél temperature from 350 to 595 K induced by pressure was found. At pressures 46–49 GPa, a transition from the antiferromagnetic to a new magnetic state with a weak magnetic moment (magnetic collapse) was discovered. It is attributed to the electronic transition in Fe³⁺ ions from the high-spin 3d⁵ (S = 5/2, ⁶A_1g) to the low-spin (S = 1/2, ²T_2g) state (spin crossover) due to the insulator-semiconductor-type transition with extensive suppression of strong d-d electron correlations. At low temperatures, NFS spectra of the high-pressure phase indicate magnetic correlations in the low-spin system with a magnetic ordering temperature of about 50 K. A tentative magnetic P-T phase diagram of FeBO₃ is proposed. An important feature of this diagram is the presence of two triple points where magnetic and paramagnetic phases of the high-spin and low-spin states coexist.     

Unconventional superconductivity in two-dimensional electron systems with long-range correlations

Properties of superfluid states of two-dimensional electron systems with critical antiferromagnetic fluctuations are investigated. These correlations are found to result in the emergence of rapid variation in the momentum space terms in all components of the mass operator, including the gap function Δ(p). It is shown that the domain where these terms reside shrinks with temperature, leading to a significant difference between the temperature T _c , at which superconductivity is terminated, and the temperature T*, where the gap in the single-particle spectrum vanishes.     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J _H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J _H and high conduction electron density but a chiral \(d_{x^2 - y^2 } + id_{xy}\)-wave for large J _H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.     

Theoretical studies of superconductivity in doped BaCoSO

We investigate superconductivity that may exist in the doped BaCoSO, a multi-orbital Mott insulator with a strong antiferromagnetic ground state. The superconductivity is studied in both t-J type and Hubbard type multi-orbital models by mean field approach and random phase approximation (RPA) analysis. Even if there is no C₄ rotational symmetry, it is found that the system still carries a d-wave like pairing symmetry state with gapless nodes and sign changed superconducting order parameters on Fermi surfaces. The results are largely doping insensitive. In this superconducting state, the three \({t_{{2_g}}}\) orbitals have very different superconducting form factors in momentum space. In particular, the intra-orbital pairing of the \({d_{{x^2} - {y^2}}}\) orbital has an s-wave like pairing form factor. The two methods also predict very different pairing strength on different parts of Fermi surfaces. These results suggest that BaCoSO and related materials can be a new ground to test and establish fundamental principles for unconventional high temperature superconductivity.