  Circulators are non-reciprocal circuit elements integral to technologies
including radar systems, microwave communication transceivers, and the readout
of quantum information devices. Their non-reciprocity arises from the
interference of microwaves over the centimetre-scale of the signal wavelength
in the presence of bulky magnetic media that break time-reversal symmetry. Here
we realize a completely passive on-chip microwave circulator with size
one-thousandth the wavelength by exploiting the chiral, slow-light response of
a 2-dimensional electron gas (2DEG) in the quantum Hall regime. For an
integrated GaAs device with 330 um diameter and 1 GHz centre frequency, a
non-reciprocity of 25 dB is observed over a 50 MHz bandwidth. Furthermore, the
direction of circulation can be selected dynamically by varying the magnetic
field, an aspect that may enable reconfigurable passive routing of microwave
signals on-chip.
