Anomalous superconductivity in coupled Luttinger liquids

Authors
Citation
V. Mastropietro, Anomalous superconductivity in coupled Luttinger liquids, REV MATH PH, 12(12), 2000, pp. 1627-1654
Citations number
24
Categorie Soggetti
Physics
Journal title
REVIEWS IN MATHEMATICAL PHYSICS
ISSN journal
0129055X → ACNP
Volume
12
Issue
12
Year of publication
2000
Pages
1627 - 1654
Database
ISI
SICI code
0129-055X(200012)12:12<1627:ASICLL>2.0.ZU;2-#
Abstract
According to Anderson ([1], p. 54) "the equivalent of BCS theory for a full y spin-charge separated Luttinger liquid has not been formally worked out". We consider a model for two one-dimensional spinning Luttinger liquids cou pled via a Cooper tunnelling Hamiltonian. We show that the partition functi on is the four-dimensional integral of an exponential whose exponent has an extremal point obtained solving an anomalous non-BCS self-consistence equa tion. If the extremal point is a global minimum the model is completely sol ved by the saddle point theorem and the anomalous gap generation is proved. We find that the Luttinger interaction enhances strongly T-c if the intrac hain Luttinger interaction is much bigger than the interchain interaction.