Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

TL;DR

This paper demonstrates that accurate superconducting critical temperatures can be calculated from a renormalized Hamiltonian incorporating electron interactions, using methods like similarity renormalization, aligning well with experimental data.

Contribution

It introduces a Hamiltonian-based approach with renormalization techniques to accurately predict superconducting critical temperatures, bridging theory and experiment.

Findings

Calculated Tc matches experimental data within 10%.

Rederived McMillan formula for small coupling.

Compared results with Eliashberg theory.

Abstract

It is shown that one can obtain quantitatively accurate values for the superconducting critical temperature within a Hamiltonian framework. This is possible if one uses a renormalized Hamiltonian that contains an attractive electron-electron interaction and renormalized single particle energies. It can be obtained by similarity renormalization or using flow equations for Hamiltonians. We calculate the critical temperature as a function of the coupling using the standard BCS-theory. For small coupling we rederive the McMillan formula for Tc. We compare our results with Eliashberg theory and with experimental data from various materials. The theoretical results agree with the experimental data within 10%. Renormalization theory of Hamiltonians provides a promising way to investigate electron-phonon interactions in strongly correlated systems.