  Recent theoretical investigations have revealed unconventional transport
mechanisms within high Brilliouin zones of two-dimensional superlattices.
Electrons can navigate along channels we call superwires, gently guided without
brute force confinement. Such dynamical confinement is caused by weak
superlattice deflections, markedly different from the static or energetic
confinement observed in traditional wave guides or one-dimensional electron
wires. The quantum properties of superwires give rise to elastic dynamical
tunneling, linking disjoint regions of the corresponding classical phase space,
and enabling the emergence of several parallel channels. This paper provides
the underlying theory and mechanisms that facilitate dynamical tunneling
assisted by chaos in periodic lattices. Moreover, we show that the mechanism of
dynamical tunneling can be effectively conceptualized through the lens of a
paraxial approximation. Our results further reveal that superwires
predominantly exist within flat bands, emerging from eigenstates that represent
linear combinations of conventional degenerate Bloch states. Finally, we
quantify tunneling rates across various lattice configurations, and demonstrate
the tunneling can be suppressed in a controlled fashion, illustrating potential
implications in future nanodevices.
