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In a series of recent articles, Liu, Yang, Pan, et al. claim to have determined the exact dressed electron-boson vertex for a number of very general interacting many-body problems by inverting certain Ward-Takahashi identities. Here, we…
Electron-phonon interaction plays an important role in metals and can lead to superconductivity and other instabilities. Previous theoretical studies on superconductivity are largely based on the Migdal-Eliashberg theory, which neglects all…
Studying the strong correlation effects in interacting Dirac fermion systems is one of the most challenging problems in modern condensed matter physics. The long-range Coulomb interaction and the fermion-phonon interaction can lead to a…
It is well-known that following summing Feynman graphs, the fermion-boson coupling vertex is modified according to gamma^u-->Gamma^u=gamma^u+Delta^u, with Delta^u representing non-divergent perturbative corrections. Here, we calculate the…
We propose an approach for investigating the many body effects on phonon spectrum in an electron-phonon coupled system by taking into account the electron self-energy and vertex corrections which respect the Ward identity representing the…
We study bulk photovoltaic effects in electron-phonon coupled systems. The conservation of current or gauge invariance, manifested as the Ward-Takahashi identity, plays an essential role in the analysis of the Feynman diagrams, and the…
In previous theoretical studies of phonon-mediated superconductors, the electron-phonon coupling is treated by solving the Migdal-Eliashberg equations under the bare vertex approximation, whereas the effect of Coulomb repulsion is…
In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $\lambda$ as well as the Coulomb pseudopotential $\mu^*$ are important to determine the transition temperature $T_c$ and other properties.…
As discovered in the quantum Hall effect, a very effective way for strongly-repulsive electrons to minimize their potential energy is to aquire non-zero relative angular momentum. We pursue this mechanism for interacting two-dimensional…
We study the electron-phonon interaction in the strongly correlated superconducting cuprates. Two types of the electron-phonon interactions are introduced in the $t-J$ model; the diagonal and off-diagonal interactions which modify the…
More than a century after discovery, the theory of conventional superconductivity remains incomplete. While the importance of electron-phonon coupling is understood, a controlled first-principles treatment of Coulomb interaction is lacking.…
An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this non-perturbative…
We include the treatment of quadrupolar fields beyond the Fr\"ohlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for…
The strong coupling Eliashberg theory plus vertex correction is used to calculate maps of transition temperature (Tc) in parameter-space characterizing superconductivity. Based on these Tc maps, crossover behaviors are found when…
We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view: the strong interaction is responsible for vertex corrections, which are strongly dependent on the…
The Ward-Takahashi identity, reflecting local gauge invariance, is perturbatively verified for a boson model in light front field theory. A careful integration over the light front energy, corresponding to exactly taking into account pair…
Based on the path integral formalism, we rederive and extend the transverse Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible…
The McMillan-Rowell tunneling inversion program, which extracts the electron-phonon spectral function $\alpha^2F(\Omega)$ and the Coulomb pseudopotential $\mu^*$ from experimental tunneling data, is generalized to include the lowest-order…
The Coulomb pseudo-potential $\mu^*$ is extracted by fitting the numerically calculated transition temperature $T_c$ of the Eliashberg-Nambu equation which is extended to incorporate the narrow-band effects, that is, the vertex correction…
We address the outstanding problem of electron pairing in the presence of strong Coulomb repulsion at small to moderate values of the Coulomb parameter, $r_s \lesssim 2$, and demonstrate that the pseudopotential framework is fundamentally…