  Over sixty years ago, it was hypothesized that specially designed acoustic
systems that leveraged the acoustoelectric effect between phonons and charge
carriers could revolutionize radio frequency electronic systems by allowing
nonlinear and nonreciprocal functionalities such as gain and isolation to be
achieved in the acoustic domain. Despite six decades of work, no
acoustoelectric amplifier has been produced that can achieve a large net
(terminal) gain at microwave frequencies with low power consumption and noise
figure. Here we demonstrate a novel three-layer acoustoelectric heterostructure
that enables the first-ever continuously operating acoustoelectric amplifier
with terminal gain at gigahertz frequencies. We achieve a terminal gain of
11.25 dB in a 500 micron long device, operating at 1 GHz with a DC power
dissipation of 19.6 mW. We also realize broadband gain from 0.25-3.4 GHz and
nonreciprocal transmission exceeding 44 dB at 1 GHz. Our acoustic noise figure
is 2.8 dB, which is the lowest-ever demonstrated noise figure for an
acoustoelectric amplifier. We discuss generally how to optimize these
acoustoelectric heterostructures and show that it should be immediately
achievable to produce devices with even larger gain in shorter lengths while
simultaneously having lower power consumption and noise figure.
