Author: Vieri Mastropietro
Title: Anomalous superconductivity in coupled Luttinger liquids
Abstract:
According to Anderson ([A], pag. 54) "the equivalent
of BCS theory for a fully spin-charge separated Luttinger liquid
has not been formally worked out". We
consider a model for two one dimensional spinning Luttinger liquids
coupled via a Cooper tunnelling hamiltonian.
We show that the partition function
is the four dimensional integral of an exponential whose
exponent has
an extremal point obtained solving an anomalous
non-BCS self-consistence equation.
If the extremal point is a global minimum the model
is completely solved by the saddle point theorem and the anomalous gap
generation is proved.
We find that the Luttinger
interaction enhances strongly $T_c$ if the intrachain
Luttinger interaction is much bigger than the interchain interaction.
Keywords: Renormalization group, BCS theory, one dimensional Fermi systems
Vieri Mastropietro tel 0672594698
Matematica, Universita' Tor Vergata
Via della Ricerca Scientifica, Roma
vieri@ipparco.roma1.infn.it
http://ipparco.roma1.infn.it