  Time-reversal invariance and inversion symmetry are responsible for the
topological band structure in Dirac semimetals. These symmetries can be broken
by applying an external magnetic or electric field, resulting in fundamental
changes to the ground state Hamiltonian and a topological phase transition. We
probe these changes via the magnetic-field dependence and gate
voltage-dependence of universal conductance fluctuations in top-gated nanowires
of the prototypical Dirac semimetal Cd3As2. As the magnetic field is increased
beyond the phase-breaking field, we find a factor of sqrt(2) reduction in the
magnitude of the universal conductance fluctuations, in agreement with
numerical calculations that study the effect of broken time reversal symmetry
in a 3D Dirac semimetal. In contrast, the magnitude of the fluctuations
increases monotonically as the chemical potential is gated away from the charge
neutrality point. This effect cannot be attributed to broken inversion
symmetry, but can be explained by Fermi surface anisotropy. The concurrence
between experimental data and theory in our study provides unequivocal evidence
that universal conductance fluctuations are the dominant source of intrinsic
transport fluctuations in mesoscopic Cd3As2 devices and offers a promising
general methodology for probing the effects of broken symmetry in topological
quantum materials.
