# An infinite family of 3d Floquet topological paramagnets

## TL;DR

This paper introduces an infinite family of 3d Floquet topological paramagnets exhibiting unique dynamical properties, characterized by an infinite set of topological invariants, and constructed through exactly solvable models.

## Contribution

It uncovers a new class of 3d Floquet topological phases with novel dynamical features, not captured by existing classification methods, and provides explicit models for these phases.

## Key findings

- Existence of an infinite family of 3d Floquet topological paramagnets.
- Surface states exhibit unidirectional quantum channels transferring quantized information.
- Some phases feature anomalous surface topological order with exchange of electric and magnetic excitations.

## Abstract

We uncover an infinite family of time-reversal symmetric 3d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium, and are governed by an infinite set of $Z_2$-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3d FTPMs are not captured by group cohomology methods, and cannot be obtained from equilibrium classifications simply by treating the discrete time-translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous $Z_2$ (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2d system without breaking time reversal symmetry.