Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

Details Calculating critical temperatures of superconductivity from a renormalized Hamiltonian Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

1997-09-16

arxiv.org/abs/cond-mat/9709175v1

Physics

Condensed Matter

Superconductivity

6 pages, LaTeX, using EuroPhys.sty, one eps figure included, accepted for publication in Europhys. Lett

Scientific paper

10.1209/epl/i1997-00445-5

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.

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