Inhomogeneously doped two-leg ladder systems

A chemical potential difference between the legs of a two-leg ladder is found to be harmful for the Cooper pairing. The instability of superconductivity in such systems is analyzed by compairing results of various analytical and numerical methods. Within a strong-coupling approach for the t-J model, supplemented by exact numerical diagonalization, hole binding is found unstable beyond a finite, critical chemical potential difference. The spinon-holon mean field theory for the t-J model shows a clear reduction of the BCS gaps upon increasing the chemical potential difference leading to a breakdown of superconductivity. Based on a renormalization group approach and an Abelian bosonization, the doping dependent phase diagram for the weakly interacting Hubbard model with different chemical potentials was determined.