Eur. Phys. J. B 72, 503-507 (2009)
https://doi.org/10.1140/epjb/e2009-00373-2

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

¹ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, 5600 12, India
² Poornaprajna Institute of Scientific Research, 4 Sadashiva Nagar, Bangalore, 5600 80, India

Corresponding author: ^a manoranjan@sscu.iisc.ernet.in

Received: 10 May 2009
Revised: 26 September 2009
Published online: 3 November 2009

Abstract

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.