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Register a new userInfluence of Electron-Phonon Interaction on Spin Fluctuation Induced Superconductivity
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We investigate the interplay of the electron-phonon and the spin fluctuation interaction for the superconducting state of YBa$_2$Cu$_3$O$_{7}$. The spin fluctuations are described within the nearly antiferromagnetic Fermi liquid theory, whereas the phonons are treated using a shell model calculation of all phonon branches. The electron-phonon coupling is calculated using rigidly displaced ionic potentials screened by a background dielectric constant $epsilon_infty$ and by holes within the CuO$_2$ planes. Taking into account both interactions we get a superconducting state with $d_{x^2-y^2}$-symmetry, whose origin are antiferromagnetic spin fluctuations. The investigation of all phonon modes of the system shows that the phononic contribution to the d-wave pairing interaction is attractive. This is a necessary prerequisite for a positive isotope effect. The size of the isotope exponent depends strongly on the relative strength of the electron-phonon and spin fluctuation coupling. Due to the strong electronic correlations no phononic induced superconducting state, which is always of s-wave character, is possible.
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A microscopic Hamiltonian reflecting the correct symmetry of $f$-orbitals is proposed to discuss superconductivity in heavy fermion systems. In the orbitally degenerate region in which not only spin fluctuations but also orbital fluctuations develop considerably, cancellation between spin and orbital fluctuations destabilizes $d_{x^{2}-y^{2}}$-wave superconductivity. Entering the non-degenerate region by increasing the crystalline electric field, $d_{x^{2}-y^{2}}$-wave superconductivity mediated by antiferromagnetic spin fluctuations emerges out of the suppression of orbital fluctuations. We argue that the present scenario can be applied to recently discovered superconductors CeTIn$_{5}$ (T=Ir, Rh, and Co).
Laser control of solids was so far mainly discussed in the context of strong classical nonlinear light-matter coupling in a pump-probe framework. Here we propose a quantum-electrodynamical setting to address the coupling of a low-dimensional quantum material to quantized electromagnetic fields in quantum cavities. Using a protoypical model system describing FeSe/SrTiO$_3$ with electron-phonon long-range forward scattering, we study how the formation of phonon polaritons at the 2D interface of the material modifies effective couplings and superconducting properties in a Migdal-Eliashberg simulation. We find that through highly polarizable dipolar phonons, large cavity-enhanced electron-phonon couplings are possible but superconductivity is not enhanced for the forward-scattering pairing mechanism due to the interplay between coupling enhancement and mode softening. An analysis of critical temperature dependencies on couplings and mode frequencies suggests that that cavity-enhanced superconductivity is possible for more conventional short-range pairing mechanisms. Our results demonstrate that quantum cavities enable the engineering of fundamental couplings in solids paving the way to unprecedented control of material properties.
Unconventional superconductivity is commonly linked to electronic pairing mechanisms, since it is believed that the conventional electron-phonon interaction (EPI) cannot cause sign-changing superconducting gap symmetries. Here, we show that this common understanding needs to be revised when one considers a more elaborate theory of electron-phonon superconductivity beyond standard approximations. We selfconsistently solve the full-bandwidth, anisotropic Eliashberg equations including vertex corrections beyond Migdals approximation assuming the usual isotropic EPI for cuprate, Fe-based and heavy-fermion superconductors with nested Fermi surfaces. In case of the high-$T_c$ cuprates we find a $d$-wave order parameter, as well as a nematic state upon increased doping. For Fe-based superconductors, we obtain $s_{pm}$ gap symmetry, while for heavy-fermion CeCoIn$_5$ we find unconventional $d$-wave pairing. These results provide a proof-of-concept that EPI cannot be excluded as a mediator of unconventional and of high-$T_c$ superconductivity.
We discuss the possibility of superconductivity in graphene taking into account both electron-phonon and electron-electron Coulomb interactions. The analysis is carried out assuming that the Fermi energy is far away from the Dirac points, such that the density of the particles (electrons or holes) is high. We derive proper Eliashberg equations that allow us to estimate the critical superconducting temperature. The most favorable is pairing of electrons belonging to different valleys in the spectrum. Using values of electron-phonon coupling estimated in other publications we obtain the critical temperature T_c as a function of the electron (hole) density. This temperature can reach the order of 10 K at the Fermi energy of order 1-2 eV. We show that the dependence of the intervalley pairing on the impurity concentration should be weak.
The effect of the resonance of electron scattering energy difference and phonon energy on the electron-phonon-electron interaction (EPEI) is studied. Results show that the resonance of electron transition energy and phonon energy can enhance EPEI by a magnitude of 1 to 2. Moreover, the anisotropic S-wave electron or dx2-y2 electron can enhance resonance EPEI, and the self-energy correction of the electron will weaken resonance EPEI. Particularly, the asymmetrical spin-flip scattering process in k space can reduce the effect of electronic self-energy to enhance resonance EPEI
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