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Quasiperiodically driven fermionic systems can support topological phases notrealized in equilibrium. The fermions are localized in the bulk, but supportquantized energy currents at the edge. These phases were discovered through anabstract classification, and few microscopic models exist. We develop a coupledlayer construction for tight-binding models of these phases in $d\in\{1,2\}$spatial dimensions, with any number of incommensurate drive frequencies $D$.The models exhibit quantized responses associated with synthetic two- andfour-dimensional quantum Hall effects in the steady state. A numerical study ofthe phase diagram for $(d+D) = (1+2)$ shows: (i) robust topological and trivialphases separated by a sharp phase transition; (ii) charge diffusion and ahalf-integer energy current between the drives at the transition; and (iii) along-lived topological energy current which remains present when weakinteractions are introduced.

Coupled Layer Construction for Synthetic Hall Effects in Driven Systems