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arXiv:cond-mat/0406367

A Hydrodynamic Approach to Superconductivity

Girish S. Setlur

Published Jun 16, 2004• 0 citations
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Abstract

Recently Tsai et.al. (cond-mat/0406174) have used the renormalization group approach to study strong coupling superconductors without assuming a broken symmetry phase. We use the hydrodynamic formulation to study the same problem with the same intention. We recast the electron-phonon + electron-electron problem in the hydrodynamic language and compute the one-particle electron Green function at finite temperature. From this we extract the dynamical density of states at finite temperature and look for sign of a gap.

DOI
10.48550/arxiv.cond-mat/0406367

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Recently Tsai et.al. (cond-mat/0406174) have used the renormalization group approach to study strong coupling superconductors without assuming a broken symmetry phase. We use the hydrodynamic formulation to study the same problem with the same intention. We recast the electron-phonon + electron-electron problem in the hydrodynamic language and compute the one-particle electron Green function at finite temperature. From this we extract the dynamical density of states at finite temperature and look for sign of a gap.
We present the numerical solution of the renormalization group (RG) equations derived in Tsai, Castro Neto, Shankar, et al. [Phys. Rev. B to appear], for the problem of superconductivity in the presence of both electron–electron and electron–phonon coupling at zero temperature. We study the instability of a Fermi liquid to a superconductor and the RG flow of the couplings in the presence of retardation effects and the crossover from weak to strong coupling. We show that our numerical results provide an ansatz for the analytic solution to the problem in the asymptotic limits of weak and strong coupling.
It is shown that gauge theories with fermions are most naturally studied via a polar decomposition of the field variable. This is the fermionic analog of the preprint cond-mat/0210673. The hope is that these two put together will enable the treatment of neutral nonrelativisitc matter composed of electrons and nuclei in a nonperturbative manner with nuclei and electrons treated on an equal footing. We recast the electron-phonon (superconductivity) problem in the hydrodynamic language and indicate how it is solved. In particular we focus on the a.c. conductivity.
"En esta tesis hemos aplicado el método de renormalización de grupo de la matriz densidad a un Hamiltoniano que introduce grados de libertad fonónicos, con el fin de entender al acoplamiento electrón-fonón que ocurre en los superconductores cerámicos de alta temperatura. El trabajo se basa en resultados previos publicados en el campo [27, 28, 32, 34]. La investigación se enfoca en la energía de estado base y se exploran varios regímenes del acoplamiento electrón-fonón. Los sistemas físicos considerados aquí son cadenas de iones de oxígeno y cobre. Las cadenas de menor tamaño consisten de tres sitios que aparecen como cadenas aisladas en el cerámico YBa2Cu3O7. Aquí se han explorado dos aproximaciones al estudio de sistemas bosónicos, la base fonónica óptima y el método de pseudositios. Como complemento, se ha investigado el caso simple del modelo de Hubbard unidimensional."
This thesis deals with the Hubbard model as prototypical model to describe the physics of electrons in the two-dimensional copper-oxide planes of high-TcT_cTc​ cuprates. To get approximate solutions, we employ functional renormalization group (fRG) and dynamical mean-field theory (DMFT) methods. We deal with the problem of identifying bosonic fluctuations in the vertex function, exhibiting an intricate dependence on momenta and frequencies already at moderate coupling. In the normal, paramagnetic phase, the goal is achieved by employing the recently introduced single-boson exchange decomposition. In the symmetry-broken phases, we reformulate the previously introduced combination of fRG with mean-field theory by explicitly introducing a bosonic field. A widely discussed and challenging problem is the emergence of a pseudogap in the Hubbard model. In this thesis we assume this phase to be characterized by strong magnetic fluctuations. Following previous works, we fractionalize the electron in a chargon, carrying the electron's charge, and a charge neutral spinon, which represents local fluctuations of the spin orientation. The chargons undergo Néel or spiral magnetic order below a density-dependent transition temperature T∗T^*T∗. We compute DC charge transport coefficients for the chargons, and obtain a pronounced drop in the charge carrier density across the magnetic-to-paramagnetic transition. Directional fluctuations of the spin orientation are described by a non-linear sigma model and prevent long-range ordering of the electrons at any finite temperature. The phase where the chargon degrees of freedom are magnetically ordered shares many features with the pseudogap regime observed in high-TcT_cTc​ cuprates: a strong reduction of the charge carrier density, a spin gap, Fermi arcs, and electronic nematicity.