Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

Institut für Theoretische Physik, Ruprecht-Karls-Universität Philosophenweg 19, 69120 Heidelberg, Germany

Received: 25 July 1997
Accepted: 11 September 1997

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 T_c. 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.