-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of when small momentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance . We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters. Received 12 May 2000     

Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

Charge d-wave topological insulator

Formation of a condensate of singlet electron-hole pairs in a two-dimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the self-consistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s- and d-wave channels of electron-hole pairing. Solutions with the pure orbital symmetry of s- and d-type are found, as well as solutions with the mixed s + d-symmetry. It is shown that in a wide range of values of the s- and d-wave coupling constants, the two-dimensional insulating order with the orbital symmetry $d_{x^2 - y^2 } $ can compete with pure ordered s- and d _xy -states and mixed s + d-states. Time reversal symmetry breaking under an established real order with $d_{x^2 - y^2 } $ -wave symmetry may generate the imaginary component of the order parameter with symmetry d _xy and cause a rise in topologically nontrivial d + id-wave ordering similar to the quantum Hall state in the absence of external magnetic field.     

The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.     

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.     

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

Pairing symmetry in layered BiS2 compounds driven by electron-electron correlation

We investigate the pairing symmetry of layered BiS2 compomlds by assuming that electron-electron correlation is still important so that the pairing is rather short range. We lind that the extended .s-wave pairing symmetry always wins over d-wave when the pairing is confined between two short range sites up to next nearest neighbors. The pairing strength is peaked around the doping level ：r = 0.5. which is consistent with experimental observation. The extended s-wave pairing symmetry is very robust against spin orbital coupling because it is mainly determined by the structure of Fermi surfaces, Moreover. the extended s-wave pafiring can be distinguished from conventional swave pairing by measuring and comparing superconducting gaps of different Fermi surfaces.     

SU (2N f) ⊗ O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as m_q → ∞. Our discussion involves s-wave to s-wave as well as s-wave to p-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying SU (2N_f) ? O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

SU(2N f) ⊗O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit asm _q→∞. Our discussion involvess-wave tos-wave as well ass-wave top-wave transitions. Using a constituent quark model picture for the light diquark system with an underlyingSU(2N _f)?O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

Fermion superfluid with hybridized <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-wave pairings

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized s- and p-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable s- and p-wave interactions, which is realizable in a two-component ⁴⁰K Fermi gas with close-by s- and p-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the s- and p-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.     

Possible phases of the two-dimensional Hubbard model

We present a stability analysis of the 2D t - t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed numerical calculation for the various representations under the point group C _4ν in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly large number of phases has been observed. Some of them have an order parameter with many nodes in -space. Commonly discussed types of order found by us are antiferromagnetism, d _{x2 - y2} -wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s^*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made. Received 25 July 2002 / Received in final form 28 November 2002 Published online 14 February 2003 RID="a" ID="a"Current address: Département de physique and Centre de recherche sur les propriétés électroniques de matériaux avancés, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 e-mail: vaha@physique.usherb.ca     

Electronic inhomogeneities,electron-lattice and pairing interactions in high-T c superconductors

The presence of electronic inhomogeneities strongly reduces the screening of the electron-ion interaction in high-temperature superconductors. This implies the existence of an non-totally screened long-range contribution to the electron-lattice coupling and opens an additional channel for the formation of copper pairs. We calculate the superconducting order parameter taking into account a) the longrange and the short-range parts of the electron-lattice interaction and b) the Coulomb repulsion between charge-carriers. We show that whereas the long-range electron-lattice coupling determines the anisotropy of the order parameter, the Coulomb repulsion and the short-range interactions determine its symmetry. Thus, different high-T _c superconductors may have s- or d-wave symmetry, depending on the relative strength of the interactions involved in the pairing.     

Temperature and junction-type dependency of Andreev reflection in MgB2

We studied the voltage and temperature dependency of the dynamic conductance of normal metal-MgB₂ junctions obtained either with the point-contact technique (with Au and Pt tips) or by making Ag-paint spots on the surface of MgB₂ samples. The fit of the conductance curves with the generalized BTK model gives evidence of pure s-wave gap symmetry. The temperature dependency of the gap, measured in Ag-paint junctions (dirty limit), follows the standard BCS curve with 2Δ/k_BT_c=3.3. In out-of-plane, high-pressure point-contacts we obtained almost ideal Andreev reflection characteristics showing a single small s-wave gap Δ=2.6±0.2 meV (clean limit).     

Rare earth ion size dependence of the Tc of the “RE-123” HTSC within the (d + s)-wave description of their superconducting state

The dependence of the T_c's on the radius of the rare earth ions in the rare earth “123” high temperature superconductors (HTSC) is explained within the framework of a (d + s)-wave model of superconductivity. The appearance of a s-wave symmetry component in the order parameter of a spin fluctuation mediated d-wave superconductor is taken to be due to the orthorhombic distortion which occurs in these HTSC. It is assumed that the structural (orthorhombic) distortion induces a corresponding anisotropy in the pairing interaction, resulting in a nonseparable anisotropic interaction. It is shown that the T_c's are affected by the orthorhombic distortion which in turn is observed to depend on the size of the RE ions.     

Sign reversal of the order parameter near <Emphasis Type="Italic">s</Emphasis><Subscript>±</Subscript>-superconductor surface

The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of self-consistent calculations for a two band superconductor with nodeless extended s-wave order parameter symmetry, as possibly realized in Fe-based high-temperature superconductors. It is found that for a wide range of parameters the spatial behavior of the order parameter at a surface is not reduced to a trivial suppression. If the interband scattering at a surface is of the order of the intraband one or dominates it, it can be energetically favorable to change the symmetry of the superconducting state near the surface from s _± to conventional s-wave. The range of existing of this surface conventional superconductivity is very sensitive to the relative values of interband and intraband pairing potentials. It is shown that the LDOS spectra near the surface can qualitatively differ upon calculating with and without taking into account the self-consistency of the order parameter.     

Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p_x+ip_y. Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p_x+ip_y-wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a “nonrelativistic defect conformal field theory (CFT)”. The reduced Schrödinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.     

Nuclear spin-lattice relaxation rate in electron-doped Pr0.91LaCe0.09CuO4 − y: Constraint on the gap symmetry

We present numerical calculations of the nuclear spin-lattice relaxation (Rs) rate in the superconducting state of pure indium and slightly underdoped n-type cuprate Pr_0.91LaCe_0.09CuO_4 − y. By properly taking into account electron-phonon coupling, our calculated Rs for the conventional s-wave superconductor, indium, is in quantitative agreement the experimental data with a clear Hebel-Slichter peak. In contrast, the absence of the Hebel-Slichter peak in the Rs data of Pr_0.91LaCe_0.09CuO_4 − y can be explained by either d-wave or highly anisotropic s-wave gap symmetry. Thus, the absence of the Hebel-Slichter peak does not necessarily argue against an s-wave gap symmetry in this electron-doped cuprate.     

Influence of s± symmetry on unconventional superconductivity in pnictides above the Pauli limit – two-band model study

The theoretical analysis of the Cooper pair susceptibility shows the two-band Fe-based superconductors (FeSC) to support the existence of the phase with nonzero Cooper pair momentum (called the Fulde-Ferrel-Larkin-Ovchinnikov phase or shortly FFLO), regardless of the order parameter symmetry. Moreover this phase for the FeSC model with s _± symmetry is the ground state of the system near the Pauli limit. This article discusses the phase diagram h-T for FeSC in the two-band model and its physical consequences. We compare the results for the superconducting order parameter with s-wave and s _±-wave symmetry – in first case the FFLO phase can occur in both bands, while in second case only in one band. We analyze the resulting order parameter in real space – showing that the FeSC with s _±-wave symmetry in the Pauli limit have typical properties of one-band systems, such as oscillations of the order parameter in real space with constant amplitude, whereas with s-wave symmetry the oscillations have an amplitude modulation. Discussing the free energy in the superconducting state we show that in absence of orbital effects, the phase transition from the BCS to the FFLO state is always first order, whereas from the FFLO phase to normal state is second order.     

The scattering of the Manning-Rosen potential with centrifugal term

In this Letter the approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Manning-Rosen potential are carried out by a proper approximation to the centrifugal term. The normalized radial wave functions of l-wave scattering states are presented and the calculation formula of phase shifts is derived. It is well shown that the poles of the S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.     

Positron-hydrogen-like-ion scattering

Scattering of positrons by hydrogen-like-ions (He⁺, Li²⁺, Be³⁺ and B⁴⁺) has been studied using two variants of the polarized orbital method. The positronium formation channel has not been included in the calculations,s-wave phase shifts obtained using the two variants differ appreciably from each other. Moreover, the polarized orbitals-wave phase shifts fore ⁺-B⁴⁺ scattering differ from the corresponding variational results qualitatively in the low energy region. The differential cross sections are reported.