Laboratoire de Physique Théorique
Toulouse - UMR 5152

We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit (t-J model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust but immediately acquires algebraic transverse (i.e. along rungs) current correlations which are commensurate with the density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interactions ratio J/t : we found strong anomalies only in the vicinity of the commensurate fillings and 1/2 and low J/t. However, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different : while for a charge density wave is confirmed, the phase is shown to be a bond order wave.