  It was recently experimentally proved that the superconducting counterpart of
a diode, i.e., a device that realizes nonreciprocal Cooper pairs transport, can
be realized by breaking the spatial and time-reversal symmetry of a system
simultaneously. Here we report the theory, fabrication, and operation of a
monolithic dc superconducting quantum interference device (dc-SQUID) that
embedding three-dimensional (3D) Dayem nanobridges as weak links realizes an
efficient and magnetic flux-tunable supercurrent diode. The device is entirely
realized in Al and achieves a maximum rectification efficiency of $\sim 20\%$,
which stems from the high harmonic content of its current-to-phase relation
only without the need of any sizable screening current caused by a finite loop
inductance. Our interferometer can be easily integrated with state-of-the-art
superconducting electronics, and since it does not require a finite loop
inductance to provide large rectification its downsizing is not limited by the
geometrical constraints of the superconducting ring.
