  Chiral $d$-wave superconductivity has recently been proposed in a wide range
of materials based on both experiment and theoretical works. Chiral
superconductors host a finite Chern number set by the winding of the
superconducting order parameter and associated topologically protected chiral
edge modes. However, the chiral edge currents and orbital angular momentum
(OAM) generated by the edge modes are not topologically protected and another,
more robust, experimental probe is therefore needed to facilitate experimental
verification of chiral $d$-wave superconductors. We have recently shown the
appearance of quadruply quantized coreless vortices (CVs) in chiral $d$-wave
superconductors, consisting of a closed domain wall decorated with eight
fractional vortices, and generating a smoking-gun signature of the Chern
number, chirality, and the superconducting pairing symmetry [P. Holmvall and A.
M. Black-Schaffer, arXiv:2212.08156 (2023)]. Specifically, the CV spontaneously
breaks axial symmetry for parallel chirality and vorticity, with a signature
appearing directly in the local density of states (LDOS) measurable with
scanning-tunneling spectroscopy (STS). In this work, we first demonstrate a
strong tunability of the CV size and shape directly reflected in the LDOS and
then show that the LDOS signature is robust in the presence of regular
Abrikosov vortices, strong confinement, system and normal-state anisotropy,
different Fermi surfaces (FSs), non-degenerate order parameters, and even
non-magnetic impurities. In conclusion, our work establishes CVs as a tunable
and robust signature of chiral $d$-wave superconductivity.
