Unconventional anisotropic s-wave superconducting gaps of the LiFeAs iron-pnictide superconductor

We have performed high-resolution angle-resolved photoemission spectroscopy on Fe-based superconductor LiFeAs (T(c)=18 K). We reveal multiple nodeless superconducting (SC) gaps with 2Δ/k(B)T(c) ratios varying from 2.8 to 6.4, depending on the Fermi surface (FS). We also succeeded in directly observing a gap anisotropy along the FS with magnitude up to ~30%. The anisotropy is fourfold symmetric with an antiphase between the hole and electron FSs, suggesting complex anisotropic interactions for the SC pairing. The observed momentum dependence of the SC gap offers an excellent opportunity to investigate the underlying pairing mechanism.     

Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in s(±) pairing; the higher energy peak appears around the commensurate momenta due to scattering between α-FS to γ/δ-FS pockets. The second resonance is incommensurate, coming from β-FS to γ/δ-FS scatterings, and its q vector is doping-dependent and, hence, on the FS topology. Energies of both resonances ω(res)(1,2) are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.     

Probing the unconventional superconducting state of LiFeAs by quasiparticle interference

A crucial step in revealing the nature of unconventional superconductivity is to investigate the symmetry of the superconducting order parameter. Scanning tunneling spectroscopy has proven a powerful technique to probe this symmetry by measuring the quasiparticle interference (QPI) which sensitively depends on the superconducting pairing mechanism. A particularly well-suited material to apply this technique is the stoichiometric superconductor LiFeAs as it features clean, charge neutral cleaved surfaces without surface states and a relatively high T(c)～18 K. Our data reveal that in LiFeAs the quasiparticle scattering is governed by a van Hove singularity at the center of the Brillouin zone which is in stark contrast to other pnictide superconductors where nesting is crucial for both scattering and s(±) superconductivity. Indeed, within a minimal model and using the most elementary order parameters, calculations of the QPI suggest a dominating role of the holelike bands for the quasiparticle scattering. Our theoretical findings do not support the elementary singlet pairing symmetries s(++), s(±), and d wave. This brings to mind that the superconducting pairing mechanism in LiFeAs is based on an unusual pairing symmetry such as an elementary p wave (which provides optimal agreement between the experimental data and QPI simulations) or a more complex order parameter (e.g., s+id wave symmetry).     

Ultrarelativistic electron-hole pairing in graphene bilayer

We consider the ground state of an electron-hole graphene bilayer composed of two independently-doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only the conduction band of the electron-doped layer and the valence band of the hole-doped layer, thus the ground state is similar to an ordinary BCS condensate. At strong coupling, an ultrarelativistic character of the electron dynamics reveals itself and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. Analysis of the instability of the unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. The relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of a separable potential. It is shown that, if the characteristic width of the pairing region is of the order of magnitude of the chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.     

Interplay of superconductivity and magnetism in presence of inter sub-lattice effect in cuprates

In the present communication, we report a model Hamiltonian to study the interplay between the two long range orders of anti-ferromagnetism (AFM) and superconductivity (SC) in cuprate superconductors in presence of the intersite pairing effect. The BCS type but non-phonon pairing mechanism is considered among the electrons of two equivalent ‘Cu’ sites. The pairing among the electrons of two nearest neighbour non-equivalent ‘Cu’ sites is included in the Hamiltonian and its effect on the interplay of SC and AFM is investigated. The Hamiltonian is solved by the Green’s function method and the corresponding gap equations are calculated and solved selfconsistently. The influence of model parameters like AFM coupling (λ), SC couling (λ ₁) and the coupling (λ ₂) for intersite superconducting interactions on the gaps (SC and AFM) are studied numerically and the results are reported.     

Theory of the interplay between the superconductivity and the blocked antiferromagnetic order in A(y)Fe(2-x)Se(2)

Based on an effective two-orbital tight-binding model, we examine the possible superconducting states in iron-vacancy-ordered A(y)Fe(2-x)Se(2). In the presence of ordered vacancies and blocked antiferromagnetic order, it is shown that the emergent SC pairing is the nodeless next-nearest-neighbor (NNN)-pairing due to the dominant antiferromagnetic (AFM) interaction between the inter-block NNN sites. In particular, we show that due to the ordered vacancies and the associated blocked AFM order, the interplay between the superconducting and AFM states results in three distinct states in the phase diagram as doping is varied. The divergent experimental observations can be accounted for by considering the different charge carrier concentrations in their respective compounds.     

Evidence for two superconducting gaps in MgB2

We have measured the Raman spectra of polycrystalline MgB2 from 25 to 1200 cm(-1). A superconductivity-induced redistribution in the electronic Raman continuum was observed. Two pair-breaking peaks appear in the spectra, suggesting the presence of two superconducting gaps. The measured spectra were analyzed using a quasi-two-dimensional model in which two s-wave superconducting gaps open on two sheets of Fermi surface. For the gap values we have obtained Delta(1) = 22 cm(-1) ( 2.7 meV) and Delta(2) = 50 cm(-1) ( 6.2 meV). Our results suggest that a conventional phonon-mediated pairing mechanism occurs in the planar boron sigma bands and is responsible for the superconductivity of MgB2.     

Angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3: strong coupling behavior and the universality of interband scattering

We have performed angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3 to investigate the electronic structure relevant to superconductivity. We observed a holelike Fermi surface (FS) and an electronlike FS at the Brillouin zone center and corner, respectively, which are nearly nested by the Q～(π,π) wave vector. We do not find evidence for the nesting instability with Q～(π+δ,0) reminiscent of the antiferromagnetic order in the parent compound Fe1+yTe. We have observed an isotropic superconducting (SC) gap along the holelike FS with the gap size Δ of ～4 meV (2Δ/kBTc ～ 7), demonstrating the strong-coupling superconductivity. The observed similarity of low-energy electronic excitations between iron-chalcogenides and iron-arsenides strongly suggests that common interactions which involve Q～(π,π) scattering are responsible for the SC pairing.     

Commensurate spin dynamics in the superconducting state of an electron-doped cuprate superconductor

We report neutron scattering studies on two single crystal samples of the electron-doped (n-type) superconducting (SC) cuprate Nd2-xCexCuO4 (x=0.15) with T(c)=18 and 25 K. Unlike the hole-doped (p-type) SC cuprates, where incommensurate magnetic fluctuations commonly exist, the n-type cuprate shows commensurate magnetic fluctuations at the tetragonal (1/2 1/2 0) reciprocal points both in the SC and in the normal state. A spin gap opens up when the n-type cuprate becomes SC, as in the optimally doped p-type La2-xSrxCuO4. The gap energy, however, increases gradually up to about 4 meV as T decreases from T(c) to 2 K, which contrasts with the spin pseudogap behavior with a T-independent gap energy in the SC state of p-type cuprates.     

Effects of competing orders and quantum phase fluctuations on the low-energy excitations and pseudogap phenomena of cuprate superconductors

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green’s function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, “dichotomy” in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole- (electron-) type cuprates depending on the relative scale of the CO and SC energy gaps.     

Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz-Thouless transition.     

Full t-matrix approach to quasiparticle interference in non-centrosymmetric superconductors

We develop the full t-matrix theory of quasiparticle interference (QPI)for non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling. We give aclosed solution for the QPI spectrum for arbitrary combination and strength of nonmagnetic(V _c ) and magnetic(V _m ) impurity scattering potentials interms of integrated normal and anomalous Green’s functions. The theory is applied to arealistic 2D model of the Ce-based 131-type heavy fermion superconductors. We discuss theQPI dependence on frequency, composition and strength of scattering and compare with Bornapproximation results. We show that the QPI pattern is remarkably stable against changesin the scattering model and can therefore give reliable information on the properties ofRashba-split Fermi surface sheets and in particular on the accidental nodal position ofthe mixed singlet-triplet gap function in NCS superconductors.     

Mechanism for explaining differences in the order parameters of FeAs-based and FeP-based pnictide superconductors

We put forward a scenario that explains the difference between the order-parameter character in arsenide (As) and phosphorous (P) iron-based superconductors. Using functional renormalization group to analyze it in detail, we find that nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the hole pocket at (π,π) in the unfolded Brillouin zone is absent, as is the case in LaOFeP. There, electron-electron interactions render the gap on the electron pockets softly nodal (of s(±) form). When the pocket of d(xy) orbital character is present, intraorbital interactions with the d(xy) part of the electron Fermi surface drives the superconductivity nodeless.     

Nodeless d-wave superconducting pairing due to residual antiferromagnetism in underdoped Pr2-xCexCuO4-delta

We investigate the doping dependence of the penetration depth versus temperature in electron-doped Pr(2-x)Ce(x)CuO(4-delta) using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a d(x2-y2) pairing gap in the underlying spectrum, we find nodeless behavior of the low-T penetration depth in the underdoped case, in accord with experimental results. As doping increases, a linear-in-T behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.     

Superfluid pairing gap in strong coupling

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.     

From high resolution spectroscopy to the modeling of potential energy surfaces

Methods and recipes used to establish potential energy surfaces in condensed molecular phases are discussed. The reliability of calculations is tested by confrontation with spectroscopic measurements in crystals. Optical spectroscopy, in particular, hole burning as a line-narrowing technique, as well as high resolution inelastic neutron scattering (INS), are used to resolve tunneling level structures corresponding to large-amplitude atomic and molecular motions. Rotational tunneling of methyl groups is discussed, and new measurements by INS are presented for crystals that are proposed as suitable candidates for optical studies. Translational tunneling in benzoic acid crystals and the role of promoting modes are reviewed, and new measurements of vibrational spectra by inelastic x-ray scattering are compared with INS and Raman spectra.     

Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of a much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin (RG) model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground-state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.     

Dispersion and damping of zone-boundary magnons in the noncentrosymmetric superconductor CePt3Si

Inelastic neutron scattering (INS) is employed to study damped spin-wave excitations in the noncentrosymmetric heavy-fermion superconductor CePt3Si along the antiferromagnetic Brillouin zone boundary in the low-temperature magnetically ordered state. Measurements along the (1/2 1/2 L) and (H H 1/2 - H) reciprocal-space directions reveal deviations in the spin-wave dispersion from the previously reported model. The broad asymmetric shape of the peaks in energy signifies strong spin-wave damping by interactions with the particle-hole continuum. Their energy width exhibits no evident anomalies as a function of momentum along the (1/2 1/2 L) direction which could be attributed to Fermi surface nesting effects, implying the absence of pronounced commensurate nesting vectors at the magnetic zone boundary. In agreement with a previous study, we find no signatures of the superconducting transition in the magnetic excitation spectrum, such as a magnetic resonant mode or a superconducting spin gap, either at the magnetic ordering wavevector (0 0 1/2) or at the zone boundary. However, the low superconducting transition temperature in this material still leaves the possibility of such features being weak and therefore hidden below the incoherent background at energies ? 0.1 meV, precluding their detection by INS.     

铁基超导体FeSe0.5Te0.5表面隧道谱的研究

用扫描隧道显微镜/谱仪仔细研究了铁基超导单晶FeSe_0.5Te_0.5样品的表面形貌和隧道谱, 测量到了清晰的表面原子形貌和在空间比较稳定的隧道谱结构．在样品中测量的隧道谱零能态密度比较高, 说明样品里面有比较强的非弹性准粒子散射. 在正能5 mV附近有个较大的背景鼓包, 这一背景在很高温度也未消失. 空间中Se和Te集中的位置会带来高能背景的变化, 超导能隙附近谱的形状大致相同. 较强的非弹性准粒子散射破坏了超导的准粒子散射, 因此没有在二维微分电导图中发现超导准粒子相干散射的特征亮斑.     

Multiband nodeless superconductivity near the charge-density-wave quantum critical point in ZrTe_(3-x)Se_x

It was found that selenium doping can suppress the charge-density-wave(CDW) order and induce bulk superconductivity in ZrTe_3. The observed superconducting dome suggests the existence of a CDW quantum critical point(QCP) in ZrTe_3-xSex near x ≈ 0.04. To elucidate the superconducting state near the CDW QCP, we measure the thermal conductivity of two ZrTe_(3-x)Se_x single crystals(x = 0.044 and 0.051) down to 80 m K. For both samples, the residual linear term κ_0/T at zero field is negligible, which is a clear evidence for nodeless superconducting gap. Furthermore, the field dependence of κ_0/T manifests a multigap behavior. These results demonstrate multiple nodeless superconducting gaps in ZrTe_(3-x)Se_x,which indicates conventional superconductivity despite of the existence of a CDW QCP.