We study the chiral current of non-interacting bosons in a three-leg lattice subjected to a uniform magnetic flux. The model is equivalent to a spin-1 bosonic lattice with three internal degrees of freedom or a one-dimensional lattice with a three-site synthetic dimension. By manipulating a bias field between the legs which acts as a quadratic Zeeman shift, we can effectively reverse the chiral current on the lattice. The current can also be reversed by increasing the magnetic flux or the inter-leg hopping coefficients, provided that the quadratic field is applied. Three types of current reversal, either related or unrelated to the Meissner-vortex phase transition, are revealed.
We study an extended Creutz ladder system, which supports topological phase transition as revealed by the change of topological invariant and by distinct pseudospin textures. With a linear force along the ladder, Bloch oscillation on topological bands is studied. At the topological phase transition point, the oscillation period is doubled due to band crossings and the wave packet evolves alternatively on the two bands. The magnitude of pseudospin polarizations in Bloch oscillation provide a dynamical identification of the topological feature. The local pseudospin polarizations along $y-$ and $z-$ axis are directly related to measurable inter-leg current and density difference. We also show the micromotion and non-adiabatic propagations of the Bloch wave packet. A small density oscillation beyond the description of Bloch oscillation is revealed. At avoided band crossings, the transition probability of the Landau-Zener tunneling is obtained. Our results exhibit a transparent framework to understand the properties of topological bands and of Bloch wave dynamics.
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