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_*).     

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.     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Dynamical Formation of Correlations in a Bose-Einstein Condensate

We consider the evolution of N bosons interacting with a repulsive short range pair potential in three dimensions. The potential is scaled according to the Gross-Pitaevskii scaling, i.e. it is given by N ² V(N(x _i ? x _j )). We monitor the behaviour of the solution to the N-particle Schrödinger equation in a spatial window where two particles are close to each other. We prove that within this window a short-scale interparticle structure emerges dynamically. The local correlation between the particles is given by the two-body zero energy scattering mode. This is the characteristic structure that was expected to form within a very short initial time layer and to persist for all later times, on the basis of the validity of the Gross-Pitaevskii equation for the evolution of the Bose-Einstein condensate. The zero energy scattering mode emerges after an initial time layer where all higher energy modes disperse out of the spatial window. We can prove the persistence of this structure up to sufficiently small times before three-particle correlations could develop.     

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.     

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.     

Nonlinear generation of vorticity in thin smectic films

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p_z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid ³He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d_xz + id_yz)-wave pairing state.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

Superconductivity of proximity coupled superconductor-antiferromagnetic multilayers

Nucleation of superconducting phase in proximity coupled superconductor(SC)-antiferromagnetic(AF) multilayers is studied theoretically. For SC layer we use the usual Usadel equations. As an AF layer we consider a normal metal which undergos the magnetic phase transition associated with the nesting electron and hole Fermi surfaces. The basic formalism, suitable for study of the SC phase of the SC/AF system is presented. The superconducting transition temperature,T _c , and upper critical fields,H _c2‖ (T) andH _c2⊥ (T) have been calculated.     

Magnetic susceptibility and superconductivity of (Pb<Subscript>0.2</Subscript>Sn<Subscript>0.8</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te alloys as a function of in content

Experimental data on the superconductivity of In-doped Pb_zSn_1?zTe alloys (z=0.2) are discussed. The superconducting transition was detected from simultaneous measurements of the resistivity and magnetic susceptibility of a series of samples with different indium contents (2–12 mol % InTe). The superconducting transition detected by the magnetic susceptibility was observed at a temperature which was, on the average, 0.1 K below that determined from the resistivity. The increase in the superconducting transition temperature T _c with increasing indium content is of a threshold character, with T _c being proportional to the inverse electronic density of states at the Fermi level. The observed features in the experimental data are accounted for in terms of indium impurity resonance states in the material.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

Spezifische Wärme und magnetische Suszeptibilität supraleitender,binärer komplexer Phasen von Übergangsmetallen

Measurements of the electronic specific heat in the normal and superconducting state of 15 superconducting binary complex phases of theσ- andχ-structure are presented. The alloys have been prepared under high vacuum in an electron-beam melting apparatus described in detail. In the investigated range between 6 and 7 valence-electrons, the obvious correlation betweenT _c, the superconducting critical temperature, andγ, the coefficient of the electronic specific heat, leads to agreement with the empirical rules, found byMatthias. Recently,Morel andAnderson andGarland have calculated the values of the deviation of the normal isotope-effect. With these values it is possible to relate the observedT _c-data for most of the transition metal alloys investigated so far to the density of states at the Fermi level and to a systematically varying electron-phonon interaction parameter. In the superconducting state, an exponential dependence of the electronic specific heat on 1/T is found in the range betweenT _c/2 andT _c/6. However the parameters are somewhat different from those predicted by theory. The values ofγ observed also account for the lack of any correlation between the total magnetic susceptibility and the superconducting critical temperature for these phases.     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Electronic Structure of FeSe Monolayer Superconductors: Shallow Bands and Correlations

Electronic spectra of typical single FeSe layer superconductor—FeSe monolayer film on SrTiO₃ substrate (FeSe/STO) obtained from ARPES data reveal several puzzles: what is the origin of shallow and the so called “replica” bands near the M-point and why the hole-like Fermi surfaces near the Γ-point are absent. Our extensive LDA+DMFT calculations show that correlation effects on Fe-3d states can almost quantitatively reproduce rather complicated band structure, which is observed in ARPES, in close vicinity of the Fermi level for FeSe/STO. Rather unusual shallow electron-like bands around the M-point in the Brillouin zone are well reproduced. Detailed analysis of the theoretical and experimental quasiparticle bands with respect to their origin and orbital composition is performed. It is shown that for FeSe/STO system the LDA calculated Fe-3d _xy band, renormalized by electronic correlations within DMFT gives the quasiparticle band almost exactly in the energy region of the experimentally observed “replica” quasiparticle band at the Mpoint. However, correlation effects alone are apparently insufficient to eliminate the hole-like Fermi surfaces around the Γ-point, which are not observed in most ARPES experiments. The Fermi surfaces remain here even if Coulomb and/or Hund interaction strengths are increased while overall agreement with ARPES worsens. Increase of number of electrons also does not lead to vanishing of this Fermi surface and makes agreement of LDA+DMFT results with ARPES data much worse. We also present some simple estimates of “forward scattering” electron-optical phonon interaction at FeSe/STO interface, showing that it is apparently irrelevant for the formation of “replica” band in this system and significant increase of superconducting T _c .     

Knight shift in superconducting oxides BaPb<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Bi<Subscript>x</Subscript>O<Subscript>3</Subscript> (<Emphasis Type="Italic">x</Emphasis> < 0.35)

The Knight shift ²⁰⁷K_s for the ²⁰⁷Pb nuclei in the metal phase of the oxides BaPb_1?xBi_xO₃ (x < 0.35) has been analyzed as a function of the concentration. The shift, which is proportional to the density of states near the Fermi energy: ²⁰⁷K_s ～ N(E_F), reaches a maximum for an oxide with the maximum superconducting transition temperature T_c(x ≈ 0.25) = 12 K. A significant increase in the width of the shift distribution with the Bi concentration testifies to the formation of a nonuniform state of the electronic system in the conduction band of superconducting oxides, which is accompanied by an increase in short-wavelength contributions to the spin susceptibility. To detect the ²⁰⁷Pb NMR spectra in superconducting oxides with x > 0.2, the ¹⁷O-²⁰⁷Pb spin-echo double-resonance method is used, which provides successful detection of the ²⁰⁷Pb NMR signal with an anomalously high rate of spin-spin relaxation T ₂ ^?1 > 500 ms^?1. Thus, fundamental restrictions arising in investigations of rapidly relaxing ²⁰⁷Pb nuclei, which are “unobservable” in superconducting oxides BaPb_1?xBi_xO₃ when they are studied by traditional single-resonance methods of pulse NMR spectroscopy, have been overcome.     

Phase diagram and transport properties of Sb-doped Ca0.88La0.12Fe2As2 single crystals

The effects of isovalent Sb substitution on the superconducting properties of the Ca_0.88La_0.12Fe₂(As_1-ySb_y)₂ system have been studied through electrical resistivity measurements. It is seen that the antiferromagnetic or structural transition is suppressed with Sb content, and a high-T_c superconducting phase, accompanied by a low-T_c phase, emerges at 0.02 ≤ y ≤ 0.06. In this intermediate-doping regime, normal-state transport shows non-Fermi-liquid-like behaviors with nearly T-linear resistivity above the high-T_c phase. With further Sb doping, this high-T_c phase abruptly vanishes for y > 0.06 and the conventional Fermi liquid is restored, while the low-T_c phase remains robust against Sb impurities. The coincidence of the high-T_c phase and non-Fermi liquid transport behaviors in the intermediate Sb-doping regime suggests that AFM fluctuations play an important role in the observed non-Fermi liquid behaviors, which may be intimately related to the unusual nonbulk high-T_c phase in this system.     

Robustness of <Emphasis Type="Italic">s</Emphasis>-wave pairing symmetry in iron-based superconductors and its implications for fundamentals of magnetically driven high-temperature superconductivity

Based on the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we propose that the pairing symmetry in all measured iron-based superconductors is generally consistent with the A _1g s-wave. 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: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-T _c superconductivity and determine pairing symmetries; (ii) the magnetic-selection pairing rule: superconductivity is only induced by the magnetic-exchange couplings from the super-exchange mechanism through cation-anion-cation chemical bonding. These principles explain why unconventional high-T _c superconductivity appears to be such a rare but robust phenomena, with its strict requirements regarding the electronic environment. The results will help us to identify new electronic structures that can support high-T _c superconductivity.     

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.     

Analytical assessment of some characteristic ratios for <Emphasis Type="Italic">s</Emphasis>-wave superconductors

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ? T_c are discussed using the method of successive approximations. The equation for the ratio R₁, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R₂, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-T_c superconductors. The prospect of application of the presented model in studies of high-T_c superconductors and other superconducting systems of the new generation is also discussed.     

Meissner effect in superconductors with a finite pair momentum

The features of the Meissner effect in superconductors with a finite pairing momentum are analyzed. Response to a weak magnetic field is calculated for various cases covering a pair momentum range from q ? Δ/v ₀ to q ～ p ₀, including q = Δ₀/v ₀ (v ₀ is the velocity on the Fermi surface and Δ₀ is the order parameter at zero temperature; the system of units where ? = 1 is used). The response of a superconductor carrying the transport current at a temperature close to the critical temperature T _c is determined. It is shown that, at a certain critical momentum (current), the response parallel to the momentum vanishes and the London length is infinite. The response perpendicular to the momentum remains unchanged. The response of the superconductor in the current state at zero temperature is calculated. A new contribution to the paramagnetic current is found, and its mechanism is determined. This contribution can be large for high momenta q ～ p ₀. The Meissner effect is analyzed in detail for the state proposed by Larkin and Ovchinnikov, Zh. Éksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP 20, 762 (1964)], as well as by Fulde and Ferrel, Phys. Rev. A 135, 550 (1964). It is shown that the response parallel to the vector q is nonzero and diamagnetic. On the contrary, the response perpendicular to the momentum vanishes at the optimal momentum q ₀. The sensitivity of the Meissner effect to the fine features of the superconducting state such as the quasiparticle spectrum, coherent factors, etc. is demonstrated.