Abstract:The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In th… Show more
“…Hence, our results provide evidence against a generic antiferromagnetic quantum critical point in cuprates. Instead, evidence points to a crossover with p from stronger to weaker correlations [6,33]. While subtracting the high-temperature phonon contribution does a reasonably good job of isolating the magnetic response, the differences between χ (ω) below and near T c , as shown in Fig.…”
Motivated by recent attention to a potential antiferromagnetic quantum critical point at xc ∼ 0.19, we have used inelastic neutron scattering to investigate the low-energy spin excitations in crystals of La2−xSrxCuO4 bracketing xc. We observe a peak in the normal-state spin-fluctuation weight at ∼ 20 meV for both x = 0.21 and 0.17, inconsistent with quantum critical behavior. The presence of the peak raises the question of whether low-energy spin fluctuations limit the onset of superconducting order. Empirically evaluating the spin gap ∆spin in the superconducting state, we find that ∆spin is equal to the coherent superconducting gap ∆c determined by electronic spectroscopies. To test whether this is a general result for other cuprate families, we have checked through the literature and find that ∆c ≤ ∆spin for cuprates with uniform d-wave superconductivity. We discuss the implications of this result.
“…Hence, our results provide evidence against a generic antiferromagnetic quantum critical point in cuprates. Instead, evidence points to a crossover with p from stronger to weaker correlations [6,33]. While subtracting the high-temperature phonon contribution does a reasonably good job of isolating the magnetic response, the differences between χ (ω) below and near T c , as shown in Fig.…”
Motivated by recent attention to a potential antiferromagnetic quantum critical point at xc ∼ 0.19, we have used inelastic neutron scattering to investigate the low-energy spin excitations in crystals of La2−xSrxCuO4 bracketing xc. We observe a peak in the normal-state spin-fluctuation weight at ∼ 20 meV for both x = 0.21 and 0.17, inconsistent with quantum critical behavior. The presence of the peak raises the question of whether low-energy spin fluctuations limit the onset of superconducting order. Empirically evaluating the spin gap ∆spin in the superconducting state, we find that ∆spin is equal to the coherent superconducting gap ∆c determined by electronic spectroscopies. To test whether this is a general result for other cuprate families, we have checked through the literature and find that ∆c ≤ ∆spin for cuprates with uniform d-wave superconductivity. We discuss the implications of this result.
“…In metals, such effects result in strong deviations from the Fermi-liquid behavior or unconventional superconductivity for instance [2,3]. Quantum criticality is being investigated in various materials including high-T c superconductors, insulating magnets, or heavy-fermion systems [1,4]. The latter are mainly Yb-or Ce-based intermetallics where low-energy scales give access to the QCP using nonthermal control parameters such as chemical doping, pressure, and magnetic field [2,3].…”
“…In what follows we provide a largely incomplete list of past and contemporary research subfields in the realm of superconductivity: i) Unconventional superconductors. Huge efforts have been devoted to investigate unconventional superconductivity [17][18][19][20][21][22][23][24][25], i.e. superconductivity unrelated to EPIs but arising from other pairing glues, originating microscopically solely from repulsive electron-electron interactions (EEIs).…”
We use a Luttinger-Ward functional approach to study the problem of phononmediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowledge, have never been discussed in the literature. Our approach is applicable to (and in fact designed to tackle superconductivity in) strongly correlated electron systems described by generic lattice models, as long as the glue for electron pairing is provided by phonons. solid-state system. No approximations are made, except for the truncation of the LWF (such a truncation is necessary to develop any practical theory). Our main general results can be found in Eqs. (87)-(89), (92), and (93).Sect. 8 is specific to the problem of phonon-mediated superconductivity. Here, we apply the previously developed general formalism to derive a set of extended Eliashberg equations. Our aim is to provide a way to compute the anomalous components of the electronic self-energy, accounting as much as possible for the EEI effects derived in Sections 3-6. This task requires some approximations. Most importantly, we need to adopt a tractable, explicit expression for the electronic self-energy functional; this cannot be done exactly, because the functional corresponding to the EEI self-energy is not known analytically (and even if it was, it would be overwhelmingly complicated). In Sect. 8 we therefore: 1) neglect the EEI vertices appearing in the EPI self-energy functionals and 2) confine ourselves to the regime of temperatures close to the critical temperature, where the expressions can be linearized in the anomalous self-energy. We then assume that the EEI self-energy functional in the normal state can be obtained via other theoretical/computational means [71][72][73], and plugged into the resulting extended Eliashberg equations, (135)-(140). These equations include the vertex corrections arising from the EEI self-energy functional, which are not captured by the Tolmachev-Morel-Anderson pseudopotential method [74,75] and the McMillan formula [76].A brief set of conclusions and future perspectives are reported in Sect. 9. Numerous technical details are reported in Appendix A-Appendix G.
Model HamiltonianWe consider a system of electrons and phonons, in the presence of EEIs and EPIs. The Hamiltonian has the following general formwhere the independent-electron (IE) term iŝthe electron-electron interaction (EEI) iŝthe independent-phonon (IP) term iŝ
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