Exchange Of Spin Fluctuations Research Articles

No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb_{10-x}10−xCu_xx(PO_44)_66O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an ab initio derived two-band model of the Cu e_geg orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin singlet d-wave superconductivity at T_cTc ≥300K if the system is put close enough to a magnetic instability.

Superconductivity in multiorbital systems with repulsive interactions: Hund's pairing versus spin-fluctuation pairing

Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange $J$. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attractions in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations are also present. We compare mean-field Hund's pairing and spin-fluctuation-mediated pairing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parameters. We find that, for systems without clear nesting features, the superconducting state generated by the Hund's mechanism agrees well with that from the full fluctuation exchange vertex when Hund's exchange and spin-orbit coupling are sufficiently large. On the other hand, for systems characterized by a peaked finite-momentum particle-hole susceptibility, spin-fluctuation pairing generally dominates over Hund's pairing. From this perspective Hund's pairing states appear unlikely to be realized in systems like ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and generic iron-based superconductors.

Parametrizations of local vertex corrections from weak to strong coupling: Importance of the Hedin three-leg vertex

In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion-spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared to the static mean-field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale $4t^2/U$. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.

Upper critical field in ferromagnetic metals with triplet pairing

The theory of triplet superconductivity in ferromagnetic metals based on electron–electron interaction by spin fluctuation exchange is developed. The equations for the upper critical field temperature dependence are derived. In contrast to the similar equations for the superconductivity in two band metals they contain the pairing amplitudes and the Fermi velocities depending on magnetic field. The critical field behaviour near the critical temperature and at T=0 is established analytically.

Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

The Fermi surface pockets that lie at the corner of the two-iron Brillouin zone in heavily electron-doped iron selenide superconductors are accounted for by an extended Hubbard model over the square lattice of iron atoms that includes the principal 3dxz and 3dyz orbitals. At half filling, and in the absence of intra-orbital next-nearest neighbor hopping, perfect nesting between electron-type and hole-type Fermi surfaces at the the center and at the corner of the one-iron Brillouin zone is revealed. It results in hidden magnetic order in the presence of magnetic frustration within mean field theory. An Eliashberg-type calculation that includes spin-fluctuation exchange finds that the Fermi surfaces undergo a Lifshitz transition to electron/hole Fermi surface pockets centered at the corner of the two-iron Brillouin zone as on-site repulsion grows strong. In agreement with angle-resolved photoemission spectroscopy on iron selenide high-temperature superconductors, only the two electron-type Fermi surface pockets remain after a rigid shift in energy of the renormalized band structure by strong enough electron doping. At the limit of strong on-site repulsion, a spin-wave analysis of the hidden-magnetic-order state finds a ‘floating ring’ of low-energy spin excitations centered at the checkerboard wavenumber . This prediction compares favorably with recent observations of low-energy spin resonances around (π, π) in intercalated iron selenide by inelastic neutron scattering.

Raising the Critical Temperature by Disorder in Unconventional Superconductors Mediated by Spin Fluctuations

We propose a mechanism whereby disorder can enhance the transition temperature T_{c} of an unconventional superconductor with pairing driven by exchange of spin fluctuations. The theory is based on a self-consistent real space treatment of pairing in the disordered one-band Hubbard model. It has been demonstrated before that impurities can enhance pairing by softening the spin fluctuations locally; here, we consider the competing effect of pair breaking by the screened Coulomb potential also present. We show that, depending on the impurity potential strength and proximity to magnetic order, this mechanism results in a weakening of the disorder-dependent T_{c}-suppression rate expected from Abrikosov-Gor'kov theory, or even in disorder-generated T_{c} enhancements.

Orbital-dependent Fermi surface shrinking as a fingerprint of nematicity in FeSe

The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electronic structure of FeSe across the nematic transition. We show that the self-energy corrections due to the exchange of spin fluctuations between hole and electron pockets are responsible for an orbital-dependent shrinking of the Fermi Surface that affects mainly the $xz/yz$ parts of the Fermi surface. This result is consistent with our experimental observation of the Fermi Surface in the high-temperature tetragonal phase, that includes the $xy$ electron sheet that was not clearly resolved before. In the low-temperature nematic phase, we experimentally confirm the appearance of a large ($\sim$ 50meV) $xz/yz$ splittings. It can be well reproduced in our model by assuming a moderate splitting between spin fluctuations along the $x$ and $y$ crystallographic directions. Our mechanism shows how the full entanglement between orbital and spin degrees of freedom can make a spin-driven nematic transition equivalent to an effective orbital order.

Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

We analyze the interplay between charge-density-wave (CDW) orders with axial momenta $(Q, 0)$ and $(0,Q)$ ($\Delta_x$ and $\Delta_y$ respectively), detected in the underdoped cuprates. The CDW order in real space can be uni-directional (either $\Delta_x$ or $\Delta_y$ is non-zero) or bi-directional (both $\Delta_x$ and $\Delta_y$ are non-zero). To understand which of the two orders develop, we adopt the magnetic scenario, in which the CDW order appears due to spin-fluctuation exchange, and derive the Ginzburg-Landau action to the sixth order in $\Delta_x$ and $\Delta_y$. We argue that, at the mean-field level, the CDW order is bi-directional at the onset, with equal amplitudes of $\Delta_x$ and $\Delta_y$, but changes to uni-directional inside the CDW phase. This implies that, at a given temperature, CDW order is uni-directional at smaller dopings, but becomes bi-directional at larger dopings. This is consistent with recent x-ray data on YBCO, which detected tendency towards bi-directional order at larger dopings. We discuss the role of discrete symmetry breaking at a higher temperature for the interplay between bi-directional and uni-directional CDW orders and also discuss the role of pair-density-wave (PDW) order, which may appear along with CDW. We argue that PDW with the same momentum as CDW changes the structure of the bi-directional charge order by completely replacing either $\Delta_x$ or $\Delta_y$ CDW components by PDW. However, if an "Amperean" PDW order, which pairs fermions with approximately the same momenta, is also present, both $\Delta_x$ and $\Delta_y$ remain non-zero in the bi-directional phase, albeit with non-equal amplitudes. This is again consistent with x-ray experiments, which at larger doping found non-equal $\Delta_x$ and $\Delta_y$ in every domain.

Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates.

We analyze incommensurate charge-density-wave (CDW) and pair-density-wave (PDW) orders with transferred momenta (±Q,0)/(0,±Q) in underdoped cuprates within the spin-fermion model. Both orders appear due to an exchange of spin fluctuations before magnetic order develops. We argue that the ordered state with the lowest energy has nonzero CDW and PDW components with the same momentum. Such a state breaks C_{4} lattice rotational symmetry, time-reversal symmetry, and mirror symmetries. We argue that the feedback from CDW/PDW order on fermionic dispersion is consistent with ARPES data. We discuss the interplay between the CDW/PDW order and d_{x^{2}-y^{2}} superconductivity and make specific predictions for experiments.

Superconducting and charge-density-wave orders in the spin-fermion model: A comparative analysis

We present comparative analysis of superconducting and charge-density-wave orders in the spin-fluctuation scenario for the cuprates. That spin-fluctuation exchange gives rise to d-wave superconductivity is well known. Several groups recently argued that the same spin-mediated interaction may also account for charge-density-wave order with momenta $(Q,0)$ or $(0,Q)$, detected in underdoped cuprates. This has been questioned on the basis that charge-density-wave channel mixes fermions from both nested and anti-nested regions on the Fermi surface, and fermions in the anti-nested region do not have a natural tendency to form a bound state, even if the interaction is attractive. We show that anti-nesting is not an obstacle for charge order, but to see this one needs to go beyond the conventional Eliashberg approximation. We show that in the prefect nesting/antinesting case, when the velocities of hot fermions are either parallel or antiparallel, the onset temperatures in superconducting and charge-density-wave channels are of comparable strength for any magnetic correlation length $\xi$. The superconducting $T_{\rm sc}$ is larger than $T_{\rm cdw}$, but only numerically. When the velocities of hot fermions are not strictly parallel/antiparallel, $T_{\rm cdw}$ progressively decreases as $\xi$ decreases and vanishes at some critical $\xi$.

Pairing glue in the two-dimensional Hubbard model

Cluster dynamical mean field calculations are used to construct the superconducting gap function of the two dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element $t$ and one at a much lower scale. The lower frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to available information on the spin fluctuation spectrum of the model suggests that the superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from time-resolved optical conductivity data.

Impurity effects on the superconducting transition temperatures of Fe pnictides and superconducting symmetry of the order parameter

We focus on effects of nonmagnetic impurities on the superconducting transition temperatures Tc and point out, using various experimental evidences obtained for LnFe1−y MyAsO0.89−xF0.11+x (Ln=La and Nd; M=Co, Ni, Mn, Ru) systems, that the sign reversal of the order parameters Δ pointed out theoretically at the early stage of the study does not exist between disconnected Fermi surfaces around Γ and M points. The results imply that a new pairing mechanism different from the spin-fluctuation exchange and possibly related to the orbital degrees of freedom, should be considered seriously.

Superconductivity enhanced by d-density wave: A weak-coupling theory

Making a revision of mistakes in Ref. [19], we present a detailed study of the competition and interplay between the d-density wave (DDW) and d-wave superconductivity (DSC) within the fluctuation-exchange (FLEX) approximation for the two-dimensional (2D) Hubbard model. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearest-neighbor Coulomb repulsion is included within the Hartree–Fock approximation. We solve the coupled gap equations for the DDW, DSC, and π-pairing as the possible order parameters, which are caused by exchange of spin fluctuations, together with calculating the spin fluctuation pairing interaction self-consistently within the FLEX approximation. We show that even when nesting of the Fermi surface is perfect, as in a square lattice with only nearest-neighbor hopping, there is coexistence of DSC and DDW in a large region of dopings close to the quantum critical point (QCP) at which the DDW state vanishes. In particular, we find that in the presence of DDW order the superconducting transition temperature T c can be much higher compared to pure superconductivity, since the pairing interaction is strongly enhanced due to the feedback effect on spin fluctuations of the DDW gap. π-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small. In the present work, we have developed a weak-coupling theory of the competition between DDW and DSC in 2D Hubbard model, using the static spin fluctuation obtained within FLEX approximation and ignoring the self-energy effect of spin fluctuations. For our model calculations in the weak-coupling limit we have taken U/ t=3.4, since the antiferromagnetic instability occurs for higher values of U/ t.

Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0, 0) and ( π, π) in the folded Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is A 1 g in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.

Optical sum in nearly antiferromagnetic Fermi liquid model

We calculate the optical sum (OS) and the kinetic energy (KE) for a tight binding band in the Nearly Antiferromagnetic Fermi Liquid (NAFFL) model which has had some success in describing the electronic structure of the high $T_c$ cuprates. The interactions among electrons due to the exchange of spin fluctuations profoundly change the probability of occupation $(n_{{\bf k},\sigma})$ of states of momentum {\bf k} and spin $\sigma$ which is the central quantity in the calculations of OS and KE. Normal and superconducting states are considered as a function of temperature. Both integrals are found to depend importantly on interactions and an independent electron model is inadequate.

Van Hove scenario for a high Tc superconductor having a (s+d)-wave symmetry order parameter

The effects of having a van Hove singularity in the density of states on a high temperature superconductors having an (s+d)-wave symmetry order parameter (OP) are studied. It is assumed that superconductivity is due to the exchange of spin fluctuations. It is found that the two (s-wave and d-wave) components of the OP are determined by a set of coupled equations. Close to T c′ these equations are linear in Δ s and Δ d while at T=0 K, they form a set of non-linear equations in the two components of the OP. The equations for T close to T c are solved analytically to yield an expression for the transition temperature T c. The equations for T=0 K are solved numerically for different values of ω b (the cutoff frequency of the magnetic excitation responsible for superconductivity in the system). The dependence of the ratio 2 Δ(0)/ k B T c (with Δ(0)=Δ s (0) (1+ R 2) and R being the ratio of the two components of the OP at T=0 K) on ω b is shown.

Phase diagram of underdoped cuprate superconductors: Effects of Cooper-pair phase fluctuations

In underdoped cuprates fluctuations of the phase of the superconducting order parameter play a role due to the small superfluid density. We consider the effects of phase fluctuations assuming the exchange of spin fluctuations to be the predominant pairing interaction. Spin fluctuations are treated in the fluctuation-exchange approximation, while phase fluctuations are included by Berezinskii-Kosterlitz-Thouless theory. We calculate the stiffness against phase fluctuations, ns(omega)/m*, as a function of doping, temperature, and frequency, taking its renormalization by phase fluctuations into account. The results are compared with recent measurements of the high-frequency conductivity. Furthermore, we obtain the temperature T*, where the density of states at the Fermi energy starts to be suppressed, the temperature Tc*, where Cooper pairs form, and the superconducting transition temperature Tc, where their phase becomes coherent. We find a crossover from a phase-fluctuation-dominated regime with Tc proportinal to ns for underdoped cuprates to a BCS-like regime for overdoped materials.

Coupling to spin fluctuations from conductivity scattering rates

A recent analysis of optical conductivity data which has provided strong evidence for coupling of the charge carriers to the 41 meV spin resonance, seen in the superconducting state of optimally doped Y123, is extended to other systems. We find that the corresponding spin resonance is considerably broader in Tl2201 and Y124 than it is in Bi2212. On the other hand, in overdoped Tl2201 with T_c = 23 K no resonance forms. A more specific interpretation of the optical data in terms of a spin fluctuation exchange mechanism of superconductivity gives an underlying effective spectral density which is strongly temperature dependent and which contains important feedback effects that further stabilize superconductivity as the temperature is reduced.

Isotope effect in the presence of a pseudogap

We investigate the question whether the unusual doping dependence of the isotope exponent observed in underdoped high-Tc superconductors might be related to another unusual phenomenon observed in these systems: the pseudogap phenomenon. Within different approximations we study the influence of a phenomenological pseudogap on the isotope exponent and find that it generally strongly increases the isotope exponent, in qualitative agreement with experiments on underdoped high-Tc compounds. This result is stable against strong-coupling self-energy corrections and also holds for recently proposed spinfluctuation exchange models, if a weak additional electron-phonon coupling is considered.

Effect of a normal-state pseudogap on optical conductivity in underdoped cuprate superconductors

We calculate the c-axis infrared conductivity $\sigma_c(\omega)$ in underdoped cuprate superconductors for spinfluctuation exchange scattering within the CuO$_2$-planes including a phenomenological d-wave pseudogap of amplitude $E_g$. For temperatures decreasing below a temperature $T^* \sim E_g/2$, a gap for $\omega < 2E_g$ develops in $\sigma_c(\omega)$ in the incoherent (diffuse) transmission limit. The resistivity shows 'semiconducting' behavior, i.e. it increases for low temperatures above the constant behavior for $E_g=0$. We find that the pseudogap structure in the in-plane optical conductivity is about twice as big as in the interplane conductivity $\sigma_c(\omega)$, in qualitative agreement with experiment. This is a consequence of the fact that the spinfluctuation exchange interaction is suppressed at low frequencies as a result of the opening of the pseudogap. While the c-axis conductivity in the underdoped regime is described best by incoherent transmission, in the overdoped regime coherent conductance gives a better description.