M ar 1 99 8 Vortices in coupled planes with columnar disorder and bosonic ladders

The phase diagram of two bosonic chains coupled by interchain hopping and interchain boson boson repulsion is investigated by means of bosonization and renormalization group techniques. It comprises two types of charge density waves, a conventional superfluid phase and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localiza-tion. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase(one with entanglement and another one without entanglement) , a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vor-tex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.