We derive the effective action for superconducting fluctuations in a four-band model for pnictides, discussing the emergence of a single critical mode out of a dominant interband pairing mechanism. We then apply our model to calculate the paraconductivity in two-dimensional and layered three-dimensional systems, and compare our results with recent resistivity measurements in SmFeAsOF
We analyze the outcomes of an extended-Drude-model approach to the optical spectra of pnictides, where the multiband nature of the electronic excitations requires a careful analysis of the role of interband processes in the optical conductivity.Through a direct comparison between model calculations of the intraband optical spectra and experimental data, we show that interband transitions,whose relevance is shown by first-principle calculations,give a non negligible contribution already in the infrared region. This leads to a substantial failure of the extended-Drude-model analysis on the measu…
Recent measurements of Fermi surface with de Haas-van Alphen oscillations in LaFePO showed a shrinking of the Fermi pockets with respect to first-principle LDA calculations, suggesting an energy shift of the hole and electrons bands with respect to LDA. We show that these shifts are a natural consequence of the strong particle-hole asymmetry of electronic bands in pnictides, and that they provide an indirect experimental evidence of a dominant interband scattering in these systems.
Josephson junctions between a $FeAs$-based superconductor with antiphase s-wave pairing and a conventional s-wave superconductor are studied. The translational invariance in a planar junction between a single crystal pnictide and an aluminum metal greatly enhances the relative weight of electron pockets in the pnictide to the critical current. In a wide doping region of the pnictide, a planar and a point contact junctions have opposite phases, which can be used to design a tri-junction ring with $π$ phase to probe the antiphase pairing.
Considering model Hamiltonians that respect the symmetry properties of the pnictides, it is argued that pairing interactions that couple electrons at different orbitals with an orbital-dependent pairing strength inevitably lead to interband pairing matrix elements, at least in some regions of the Brillouin zone. Such interband pairing has not been considered of relevance in multiorbital systems in previous investigations. It is also observed that if, instead, a purely intraband pairing interaction is postulated, this requires that the pairing operator has the form $Δ^+(k)=f(k) \sum_α d^+_{k,α,…
We introduce and study an extended "t-U-J" two-orbital model for the pnictides that includes Heisenberg terms deduced from the strong coupling expansion. Including these J terms explicitly allows us to enhance the strength of the (pi, 0)-(0, pi) spin order which favors the presence of tightly bound pairing states even in the small clusters that are here exactly diagonalized. The A1g and B2g pairing symmetries are found to compete in the realistic spin-ordered and metallic regime. The dynamical pairing susceptibility additionally unveils low-lying B1g states, suggesting that small changes in pa…
A two-orbital model for Fe-pnictide superconductors is investigated using computational techniques on two-dimensional square clusters. The hopping amplitudes are derived from orbital overlap integrals, or by band structure fits, and the spin frustrating effect of the plaquette-diagonal Fe-Fe hopping is remarked. A spin 'striped' state is stable in a broad range of couplings in the undoped regime, in agreement with neutron scattering. Adding two electrons to the undoped ground state of a small cluster, the dominant pairing operators are found. Depending on parameters, two pairing operators were…
Possibility of Unconventional Pairing Due to Coulomb Interaction in Fe-Based Pnictide Superconductors: Perturbative Analysis of Multi-Band Hubbard Models
We employ the phenomenological theory of the quasiparticle relaxation based on the simplified two-band description and the spin-fluctuation induced interband coupling to analyze recent normal-state transport data in electron-doped iron pnictides, in particular the Ba(Fe_1-x Co_x)_2As_2 family. Temperature dependence of the resistivity, thermopower and the Hall constant are evaluated. It is shown that their anomalous behavior emerging from experiments can be consistently described within the same framework assuming also non-Fermi-liquid spin fluctuations.
Multiple Gaps and Superfluid Density from Interband Pairing in Iron Oxypnictides
我们研究了铁氧磷属化合物的四带模型，其中的超导性质被假定为由类空穴和类电子费米面之间的带间耦合决定。我们发现，合理的参数可以解释的角度分辨的光电子能谱显示多个间隙在Ba $_{1-x}$ K $_x$ Fe $_2$ As $_2$，和超流密度的温度依赖性。同时，超流密度的零温值与载流子数呈常规的比例关系。
The nature of the pairing state in iron-based superconductors is the subject of much debate. Here we argue that in one material, the stoichiometric iron pnictide KFe2As2, there is overwhelming evidence for a d-wave pairing state, characterized by symmetry-imposed vertical line nodes in the superconducting gap. This evidence is reviewed, with a focus on thermal conductivity and the strong impact of impurity scattering on the critical temperature Tc. We then compare KFe2As2 to Ba0.6K0.4Fe2As2, obtained by Ba substitution, where the pairing symmetry is s-wave and the Tc is ten times higher. The t…
We investigate the two-orbital Hubbard model, which reproduces the electron and hole Fermi surfaces in the iron pnictide superconductors, in the presence of the Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $χ_{s}$ and $χ_{o}$, increase with $χ_{s}=χ_{o}$ because of the spin-orbital symmetry. Due to the Hund's rule coupling $J$, $χ_{s}$ is enhanced and dominates over $χ_{o}$ resulting in the repulsive local pairing intera…
We study the symmetry and strength of the superconducting pairing in a two-orbital t-J1-J2-K model for iron pnictides using the salve boson mean-field theory. We show that the nearest-neighbor biquadratic interaction -K (S_i * S_j)^2 inflences the superconducting pairing phase diagram by promoting the d_{x2-y2} B_{1g} and the s_{x^2+y^2} A_{1g} channels. The resulting phase diagram consists of several competing pairing channels, including an isotropic s_{\pm} A_{1g} channel, an anisotropic d_{x2-y2} B_{1g} channel, and two s+id pairing channels. We have investigated the evolution of supercondu…
By applying an exact unitary transformation to a two-band hamiltonian which also includes the effects due to large pnictogen polarizabilities, we show that an attractive spin-mediated Hubbard term appears in the $d_{xz}$, $d_{yz}$ nearest-neighbour channel. This pairing mechanism implies a singlet superconducting order parameter in iron pnictides.
An estimation shows that the interband pairing channel between the valence band components of doped graphane can support a superconducting transition temperature (or a contribution into this expected event) of the order of 100 K at the coupling strength near 1 eV.
We examine the nature of Josephson junction between two identical Fe-pnictides with anti-phase s-wave pairing. pi-phase shift is found if the junction barrier is thick and the two Fe-pnictides are oriented in certain directions relative to the interface. Our theory provides a possible explanation for the observed half integer flux quantum transitions in a niobium/polycrystal NdFeAsO loop, and attributes the pi-phase shift to intergrain junctions of Fe-pnictides.
Deviations of low-energy electronic structure of iron-based superconductors from density functional theory predictions have been parametrized in terms of band- and orbital-dependent mass renormalizations and energy shifts. The former have typically been described in terms of a local self-energy within the framework of dynamical mean field theory, while the latter appears to require non-local effects due to interband scattering. By calculating the renormalized bandstructure in both random phase approximation (RPA) and the two-particle self-consistent approximation (TPSC), we show that correlati…
One of the outstanding problems in Iron pnictide research is the unambiguous detection of its pairing symmetry. The most probable candidates are the two-band s$++$ and sign reversed s$\pm$ wave pairing. In this work, the Andreev conductance and shot noise are used as a probe for the pairing symmetry of Iron pnictide superconductors. Clear differences emerge in both the zero bias differential conductance and the shot noise in the tunneling limit for the two cases enabling an effective distinction between the two.
Interband pairing as the origin of the sublattice dichotomy in monolayer FeSe/SrTiO_3
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli理论科学研究所）；New Cornerstone Science Laboratory（新基石科学实验室）
Based on the five-orbital model, we study the effect of local impurity in iron pnictides, and find that the interband impurity scattering is promoted by the d-orbital degree of freedom. This fact means that the fully-gapped sign-reversing s-wave state, which is predicted by spin fluctuation theories, is very fragile against impurities. In the BCS theory, only 1% impurities with intermediate strength induce huge pair-breaking, resulting in the large in-gap state and prominent reduction in Tc, contrary to the prediction based on simple orbital-less models. The present study provides a stringent …
The origin of interband electron pairing responsible for enhancing superconductivity and the factors controlling its strength were examined. We show that the interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during the electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found and its implications were discussed.
We propose a trilayer $π$-junction that takes advantage of the unconventional $s_{x^2 y^2}=\cos k_x \cos k_y$ pairing symmetry which changes sign between electron and hole Fermi pockets in the iron pnictides. In addition, we also present theoretical results for Andreev bound states in thin superconductor-normal metal (or insulator) iron-pnictide junctions. The presence of nontrivial in-gap states, which uniquely appear in this unconventional pairing state, is a distinct feature in comparison to other singlet pairing states.
In several members of the pnictide materials, spin density wave order coexists with superconductivity over a range of dopings and temperature. In this paper we show that odd-frequency superconductivity emerges on the edges of pnictides in such a coexistence phase. In particular, the breaking of spin-rotation symmetry by SDW and translation symmetry by the edge can lead to the development of odd-frequency spin-triplet Cooper pairing on edges of superconducting pnictide samples. In this case, the odd-frequency pairing has even parity components, which are immune to disorder. Our results show tha…
The possible strong electron-phonon coupling and the pairing within the full width of the electron band and not only in a narrow sheet near the Fermi surface are taken into account. It is found that the effect of pairing of electrons belonging to different bands is crucial to the appearance of high Tc in some two-band materials. The existence of another set of the two-band high temperature materials with transition temperature Tc, not yielding Tc in cuprates, is predicted.
The nature of the normal state and the mechanism of superconductivity in two families of high-temperature superconductors, cuprates and pnictides, remain a matter of intense discussions. According to band-structure calculations, confirmed by ARPES data, the electronic structure of pnictides differs considerably from that of cuprates. However, in spite of these differences, it looks like in both cases there exists some general and fairly "coarse" mechanism independent of fine details of the band structure and responsible for superconductive pairing in these materials. Here, we suggest a qualita…
Decoupled interband pairing in a bilayer iron-based superconductor evidenced by ultrahigh-resolution ARPES
Shanghai Jiao Tong University（上海交通大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Zhejiang University（浙江大学）
Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the symmetry properties and nodal structure of superconductors, especially for the interband gap functions. Focusing on tetragonal superconductors, we show that the interband pairing in the conventional (s-wave) channel can have features which are traditionally associated with unconventional pairing, such as triplet components and odd parity, and can produce line nodes i…
The hole-doped ground state of a recently introduced extended "t-U-J" two-orbital Hubbard model for the Fe-based superconductors is studied via exact diagonalization methods on small clusters. Similarly as in the previously studied case of electron doping, A. Nicholson et al., Phys. Rev. Lett. 106 21702 (2011), upon hole doping it is observed that there are several competing pairing symmetries including A_{1g}, B_{1g}, and B_{2g}. However, contrary to the electron-doped case, the ground state of the hole-doped state has pseudocrystal momentum k=(π,π) in the unfolded Brillouin zone. In the two …
The recent discovery of iron-based superconductors challenges the existing paradigm of high-temperature superconductivity. Owing to their unusual multi-orbital band structure, magnetism, and electron correlation, theories propose a unique sign reversed s-wave pairing state, with the order parameter changing sign between the electron and hole Fermi pockets. However, because of the complex Fermi surface topology and material related issues, the predicted sign reversal remains unconfirmed. Here we report a novel phase-sensitive technique for probing unconventional pairing symmetry in the polycrys…
Motivated by the bad metal behavior of the iron pnictides, we study a multi-orbital $\mathrm{t-J_1-J_2}$ model and investigate possible singlet superconducting pairings. Magnetic frustration by itself leads to a large degeneracy in the pairing states. The kinetic energy breaks this into a quasi-degeneracy among a reduced set of pairing states. For small electron and hole Fermi pockets, an $A_{1g}$ state dominates over the phase diagram but a $B_{1g}$ state has close-by energy. In addition to the nodeless $A_{1g}$ $s_{x^2y^2}$ channel, the nodal $A_{1g}$ $s_{x^2+y^2}$ and $B_{1g}$ $d_{x^2-y^2}$…
The discovery of high-$T_c$ superconductivity in the pnictides, materials with a Fermi surface determined by several bands, highlights the need to understand how superconductivity arises in multiband systems. In this effort, using symmetry considerations and mean-field approximations, we discuss how strong hybridization among orbitals may lead to both intra and interband pairing, and we present calculations of the spectral functions to guide the experimental search for this kind of state.
A phenomenological theory of tunneling spectroscopy for Fe-pnictide superconductors is developed by taking into consideration of asymmetric interface scattering between particle and holes. It is shown that in consistent with anti-phase $s^{\pm}$-wave pairing, appreciable zero-energy surface bound states exist on the [100] surface of Fe-pnictide superconductors. However, in contrast to the [110] bound states in $d$-wave cuprate superconductors, these bound states arise as a result of non-conservation of momentum perpendicular to the interface for tunneling electrons and the $s^{\pm}$ pairing, a…
Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we calculate the effective pairing interactions in the singlet and triplet channels by summing the bubble and ladder diagrams taking the reconstructed band structure into account. The leading pairing instabilities and the corresponding superconducting gap structures are then obtained from the superconducting gap equation. We illustrate this approach for a mini…
We show that the competition between magnetism and superconductivity can be used to determine the pairing state in the iron arsenides. To this end we demonstrate that the itinerant antiferromagnetic phase (AFM) and the unconventional $s^{+-}$ sign-changing superconducting state (SC) are near the borderline of microscopic coexistence and macroscopic phase separation, explaining the experimentally observed competition of both ordered states. In contrast, conventional $s^{++}$ pairing is not able to coexist with magnetism. Expanding the microscopic free energy of the system with competing orders …
In this paper we investigate the effects of the band shifts induced by the interband spin-fluctuation coupling on the optical sum rule in pnictides. We show that, despite the shrinking of the Fermi surfaces with respect to first-principle calculations, the charge-carrier concentration in each band is almost unchanged, with a substantial conservation of the total optical sum rule. However, a significant transfer of spectral weight occurs from low-energy coherent processes to incoherent ones, with practical consequences on the experimental estimate of the sum rule, that is carried out integratin…
We suggest that an inhomogeneous (non-zero momentum) paired phase can appear in the absence of an external magnetic field in the system with a predominant interband pairing and with separate Fermi-surface sheets. The Fermi wave vector mismatch which appears in such situation can be compensated by nonzero center-of-mass momentum of the Cooper pairs, what can lead to a spontaneous appearance of the Fulde-Ferrell type of superconducting state. The idea is examined using a tight-binding model which emulates the hole-like and the electron-like bands of iron based superconductor. The state can appea…
We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like fermi surface. In this pairing scenario, driven by the interplay between interband $V_{i,j}$ and intraband $V_{i,i}$ pairing terms, we have solved the two gap equations at the critical temperature $T = T_c$ and calculate $T_c$ and the chemical potential $μ$ as a function of the number of carriers $n$ for various values of pairing interactions, $V_{1,1}$, $V_{2,2}$, and $V_{1,2}$. The results …
We study the orbital-dependent superconducting pairing in a five-orbital t-J1-J2 model for iron pnictides. Depending on the orbital selectivity of electron correlations and the orbital characters along the Fermi surface, the superconducting gap in an A_{1g} pairing state may exhibit anisotropy. This anisotropy varies with the degree of J1-J2 magnetic frustration. We have also calculated the dynamical spin susceptibility in the superconducting state. The frequency dependence of the susceptibility at the antiferromagnetic wavevector (π,0) shows a resonance, whose width is enhanced by the orbital…
One of the major themes in the physics of condensed matter is unconventional superconductivity in correlated electronic systems. The symmetry structure of Cooper pairs is thought to be the key to the understanding of the pairing mechanism of their superconductivity. In iron pnictide superconductors, the precise symmetry of the order parameter as well its evolution with doping remains highly controversial. There is no general consensus on the nature of pairing in iron-based superconductors leaving the perspectives ranging from $s^{++}$ wave, to $s^{\pm}$, and $d$ wave. Here we show that doping …
We investigate the electronic state and the superconductivity in the 5-orbital Hubbard model for iron pnictides by using the dynamical mean-field theory in conjunction with the Eliashberg equation. The renormalization factor exhibits significant orbital dependence resulting in the large change in the band dispersion as observed in recent ARPES experiments. The critical interactions towards the magnetic, orbital and superconducting instabilities are suppressed as compared with those from the random phase approximation (RPA) due to local correlation effects. Remarkably, the s++-pairing phase due…
The rich variety of iron-based superconductors and their complex electronic structure lead to a wide range of possibilities for gap symmetry and pairing components. Here we solve in the 2-Fe Brillouin zone the full frequency-dependent linearized Eliashberg equations for LiFeAs with spin-fluctuation mediated pairing interactions. The magnetic excitations are calculated with the random phase approximation on a correlated electronic structure obtained with density functional theory and dynamical mean field theory. Correlations induce long-lived local moments with orbital-dependent dynamics. The i…
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in …
The key feature of the Fe-based superconductors is their quasi 2D multiband Fermi surface. By relating the problem to a negative U Hubbard model and its superconducting ground state, we show that the defining instability of such a Fermi surface is the valley density-wave (VDW), a combined spin/charge density-wave at the wavevector connecting the electron and hole valleys. As the valley parameters change by doping or pressure, the fictitious superconductor experiences "Zeeman splitting", eventually going into a non-uniform "Fulde-Ferrell-Larkin-Ovchinikov" (FFLO) state, an itinerant and often i…
We use the functional renormalization group method to analyze the phase diagram of a 4-band model for the iron-pnictides subject to band interactions with certain A_{1g} momentum dependence. We determine the parameter regimes where an extended s-wave pairing instability with and without nodes emerges. On the electron-doped side, the parameter regime in which a nodal gap appears is found to be much narrower than recently predicted in arXiv:0903.5547. On the hole-doped side, the extended s-wave pairing never becomes nodal: above a critical strength of the intra-band repulsion, the system favors …
We have performed high-resolution angle-resolved photoemission spectroscopy on Fe-based superconductor LiFeAs (Tc = 18 K). We reveal multiple nodeless superconducting (SC) gaps with 2D/kBTc 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 four-fold 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 invest…
