# C4

## Periodically driven many-body systems and topological stabilization of transport

### Johann Kroha

We theoretically investigate directed transport in systems of ultracold atomic gases in optical lattices in the presence of strong many-body interactions. In particular, the conditions for topological stabilization of current-carrying states will be investigated. Since static electric fields cannot be applied to neutral atoms, transport currents must be induced by a time-periodic modulation of the hopping matrix elements and of the on-site energies of the atoms in the lattice (ratchet potentials). In the stationary state, the current as well as the excitation energy density imposed on the system by the hopping and the on-site driving fields are constant on time-average. This is due to the finite energy density of the driving fields and the balance of energy absorption and emission between the atomic gas system and the driving fields. These driving fields thus act as a reservoir, structured in space and time, which controls the current-carrying non-equilibrium state of the system.

As a current-carrying system is in a highly excited non-equilibrium state, possible topological stabilization of this state is an important issue. In one spatial dimension, the spatio-temporal modulation necessary for transport currents induces a bi-partite lattice, described by the Su-Schrieffer-Heeger (SSH) model, whose band structure has a non-trivial topology. While a static, spatial modulation of the on-site energies excludes a non-trivial topological phase by breaking chiral symmetry, the time-periodic modulation adds time as an additional, effective dimension and makes a non-trivial topological phase possible: a Floquet topological insulator. We exploit this fact to investigate the possibility of topologically stabilized, current-carrying edge states extended in position space, but localized along the Floquet frequency axis (Floquet space).