  In Thouless pumping, although non-flat band has no effects on the
quantization of particle transport, it induces wave-packet dispersion which
hinders the practical applications of Thouless pumping. Indeed, we find that
the dispersion mainly arises from the dynamical phase difference between
individual Bloch states. Here we propose two efficient schemes to suppress the
dispersion in Thouless pumping: a re-localization echo protocol and a
high-order tunneling suppression protocol. In the re-localization echo
protocol, we reverse the Hamiltonian in the second pumping cycle to cancel the
dynamical phase difference arising from non-flat band, so that the dispersed
wave-packet becomes re-localized. In the high-order tunneling suppression
protocol, we modulate the nearest-neighbor tunneling to make the Bloch band
more flat and suppress the high-order tunneling which causes wave-packet
dispersion. Our study paves a way toward the dispersionless Thouless pumping
for practical applications in matter transport, state transfer and quantum
communication.
