Superconducting State in the Lagrangian Formalism of the Generalized Hubbard Model

The nonperturbative large-N expansion applied to the generalized Hubbard model describing N-fold-degenerate correlated bands is considered. Our previous results, obtained in the framework of the Lagrangian formalism for the normal-state case, are extended to the superconducting state. The standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. Our purpose is to obtain the 1/N corrections to the renormalized boson and fermion propagators when a state with Cooper-pair condensation (i.e., the superconducting state) is considered.     

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.     

Hydrostatic pressure driven spin,volume and band gap collapses in SmFeO3: a GGA + U study

The crystal structure, magnetic and electronic properties of SmFeO₃ under hydrostatic pressure have been studied by first-principles calculations within the generalized gradient approximation plus Hubbard U (GGA + U). The iso-structural phase transition with spin, volume and band gap collapses can be induced by a large enough hydrostatic pressure. The high-spin (HS) state of Fe³⁺, with the magnetic moment of ~4 μ_B, is retained at low pressure. The spin crossover occurs at a transition pressure (~68 GPa) with the magnetic moment of Fe³⁺ decreasing to ~1 μ_B in low-spin (LS) state. Meanwhile, the reductions of cell volume (by ~?5.43%) and band gap (from >2 eV to ~1.6 eV) of SmFeO₃ are obtained when the HS–LS transition happens. Finally, the critical pressure of HS–LS transition, magnetic and electronic properties are found to be Hubbard U dependent.     

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

Variational tests of current order parameters in the Hubbard model

Variational tests are performed for current order parameters as probable sources of the pseudogap normal state of cuprates. The calculations are carried out based on the states with correlations of the valence bond type whose formation can induce in principle both the superconducting order of the d symmetry and current phases. It is shown for the t-t′-U Hubbard models with a large value of U(～8t) and the Hubbard splitting of the conduction band that (1) phases of alternating charge and longitudinal spin currents cannot be realized and (2) transverse spin currents are not compatible with the superconducting order and they could exist against the normal-state background only within a very narrow doping region near the optimal one. This region does not correspond to the region of existence of a pseudogap in cuprates, which refutes the above-mentioned hypothesis of the pseudogap origin. The requirements to the parameters of models for which the consideration of correlations of the valence bond type yields a reasonable phase curve. The existence of current phases in the t-t′-U-V Hubbard models with a strong interaction (V>0.25t) of particles in neighboring sites is predicted when the d-superconductivity is completely suppressed.     

Can a Metal-Insulator Transition Induce s-Wave Superconductivity?

A recent paper of Capone et al. has studied an extended Hubbard model, in which local orbital degrees of freedom allow an even integer occupation at each site. A strong local repulsion U triggers a metal-insulator transition. Within a DMFT numerical analysis they show that when the ground state is a singlet a pocket of s-wave superconductivity appears in the vicinity of the Mott transition, with a strongly enhanced superconducting gap. A qualitative understanding of their result is proposed, and suggestions are made of possible systems in which this beautiful effect might be searched.     

Competing energy scales in high‐temperature superconductors: Ultrafast pump–probe studies

We present a review of photoexcited quasiparticle dynamics of cuprate and pnictide high‐temperature superconductors in regimes (temperature, doping) where different phases such as superconductivity, spin‐density‐wave (SDW) and pseudogap phases coexist or compete with one another. We start with the overdoped cuprate superconductor Y_1–xCa_x Ba₂Cu₃O_7–δ, where the superconducting gap and pseudogap coexist in the superconducting state. In another cuprate Tl₂Ba₂Ca₂Cu₃O_y, we ob‐ serve a competition between SDW and superconducting orders deep in the superconducting state. Finally, in the underdoped iron pnictide superconductor (Ba,K)Fe₂As₂, SDW order forms at 85 K, followed by superconductivity at 28 K. We also find the emergence of a normal‐state order that suppresses SDW at a temperature T * ～ 60 K and argue that this normal‐state order is a precursor to superconductivity. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Superconductivity in impurity bands

We present a theory of superconductivity in doped insulators. In the magnetic metal state of the compound we obtain the self-consistency equations for the superconducting state in the spin-dependent impurity bands of both extended and localized states in the initial insulator gap. A BCS-type triplet pairing field is considered. We show that the superconducting gap in which single-electron extended states do not exist is overlapped by the distribution of the localized states. The formation of a latent superconducting gap is discussed in connection with the unusual properties of high-T _c compounds. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 419–424 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Detailed study of the de Haas-van Alphen effect in the Shubnikov state of LuNi2B2C

We present de Haas-van Alphen (dHvA) measurements in the normal and in the superconducting state of LuNi₂B₂C. Inside the superconducting state, we observe quantum oscillations of a spherical Fermi-surface sheet in all crystallographic directions. Apart from the field region close to the phase transition where a strong peak effect hampers the analysis of the dHvA signal, the additional damping of the quantum oscillations inside the superconducting state is much smaller than expected from theory. For the magnetic field aligned along the [100] direction, three different dHvA frequencies are visible in the superconducting state. In particular, the orbit related to a cushion-like Fermi surface does not show any additional damping at and below the upper critical field contrary to theoretical expectations of simple effective one-band theories. Consequently, the superconducting gap on this Fermi-surface sheet can only evolve at lower fields than the observed bulk critical field, B _c2 ≈ 8 T, which clearly points to a Fermi-surface-sheet-dependent gap opening in LuNi₂B₂C.     

Exact solution of the simplified hubbard model

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves nontrivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n=1), (ii) a preferred magnetic state atn=1 and largeU is a total spin singlet, (iii)U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t ²/U)-behavior at largeU. A phase diagram of the model is discussed.     

Spin-switch effect in a graphene d-wave superconductor spin-valve

In this paper, spin-switch effect under the influence of anisotropic pairing symmetry is investigated. It is shown that the non-local conductance is sensitive to the exchange splitting, the incident energy, and the orientation of the superconducting gap. With the increase of the exchange splitting from zero to Fermi energy, the crossed Andreev reflection conductance for parallel configuration of magnetization and the elastic co-tunneling conductance for antiparallel configuration of magnetization are suppressed to a vanishing value. When the exchange splitting equates to Fermi energy, for values of the orientation of d-wave superconducting gap in the k-space very close to π / 4, magnitude of the spin-switch effect is suppressed completely. Moreover, in contrast to the single graphene-based ferromagnet/superconductor junction case, a π / 2 periodic oscillatory behavior about the barrier is observed directly in the present spin valve. The physical origination for those phenomena has also been analyzed.     

Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

Superconductivity in a correlated two-dimensional Hubbard model: A theoretical study

In this work we study the superconductivity within an attractive two-dimensional one-band Hubbard model. We consider a d-wave superconducting gap and a Hubbard-I approximation to describe the strongly correlated superconducting regime. We use Green's function method to obtain the order parameter Δ and the superconducting critical temperature T_c. The results show that for fixed values of the superconducting attractive potential U (U<0), the gap increases for low temperatures, whereas diminishes abruptly as the temperature increases. The effect of pressure can be discussed, varying the next-nearest-neighbors hopping t₂, yielding a change in T_c, and also in Δ₀.     

“W = 0” pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C_4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have ¹ B ₂ and ¹ A ₂ symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From , we derive an integral equation for the pair eigenfunction; the binding energy of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model. Received 18 December 1998     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

d-Symmetry superconductivity as a consequence of valence-bond type correlations

It is shown that d _x ²−y ² symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T _c are of the order of 2Δ≃0.1t and 2Δ/kT _c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 350–355 (10 March 1998)     

A superconductor with 4-fermion attraction weakly perturbed by magnetic impurities

A superconductor with 4-fermion attraction, considered by Maćkowiak and Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic interaction V between conduction fermions and localized distinguishable spin 1/2 magnetic impurities. V has the form of a reduced s-d interaction. An upper and lower bound to the system’s free energy density f(H, β) is derived and the two bounds are shown to coalesce in the thermodynamic limit. The resulting mean-field equations for the gap Δ and a parameter y, characterizing the impurity subsystem are solved and the solution minimizing f is found for various values of magnetic coupling constant g and impurity concentration. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity.     

Intrinsic tunneling study of underdoped Bi2Sr2-xLaxCuO6+δ superconductors

We report on a tunneling study of underdoped submicron Bi₂Sr_2-xLa_xCuO_6+δ (La-Bi2201) intrinsic Josephson junctions (IJJs), whose self-heating is sufficiently suppressed. The tunneling spectra are measured from 4.2 K up to the pseudogap opening temperature of T^* = 260 K. The gap value found from the spectral peak position is about 35 meV and has a weak temperature dependence both below and above the superconducting transition temperature of T_c = 29 K. Since the superconducting gap should have a value of 10-15 meV, our results indicate that the pseudogap (～35 meV) plays an important role in the underdoped La-Bi2201 intrinsic tunneling spectroscopy down to the lowest temperature of 4.2 K. However, the contribution of the superconducting gap can be separated by normalizing the spectra to the one near and above T_c, which shows that the IJJs can be a useful tool for the study of the electronic properties of the La-Bi2201 cuprate superconductors.     

Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.