Background: Shape coexistence in the $Z\approx 82$ region has been established in mercury, lead, and polonium isotopes. For even-even mercury isotopes with $100\le N\le 106$ multiple fingerprints of this phenomenon are observed, which seems to be no longer present for $N\ge 110$. According to a number of theoretical calculations, shape coexistence is predicted in the ${}^{188}\mathrm{Hg}$ isotope.

The electromagnetic structure of ${}^{66}\mathrm{Zn}$ at low excitation energy was investigated via low-energy Coulomb excitation at INFN Legnaro National Laboratories, using the Gamma Array of Legnaro Infn Laboratories for nuclEar spectrOscopy (GALILEO) $\gamma$-ray spectrometer coupled to the SPIDER (Silicon PIe DEtectoR). A set of reduced $E2, E3$, and $M1$ matrix elements was extracted from the collected data using the gosia code, yielding 12 reduced transition probabilities between the low-spin states and the spectroscopic quadrupole moment of the ${2_1}^{+}$ state. The $B\left(E2\right)$ values for transitions depopulating the ${0_2}^{+}$ state have been determined for the first time, allowing for the lifetime of this state to be deduced and, consequently, the ${\rho }^2(E0;{0_2}^{+}\to {0_1}^{+})$ monopole transition strength to be extracted. In addition, the $B(E3;{3_1}^{-}\to {0_1}^{+})$ value has been determined for the first time in a Coulomb excitation experiment. The obtained results resolve the existing discrepancies between literature lifetimes and demonstrate that ${}^{66}\mathrm{Zn}$ cannot be described by using simple collective models. Therefore, new state-of-the-art beyond-mean-field and large-scale shell-model calculations were performed in order to interpret the structure of this nucleus. Both the experimental and theoretical results suggest that the triaxial degree of freedom has an important impact on electromagnetic properties of ${}^{66}\mathrm{Zn}$, while the unique features of the ${0_2}^{+}$ state indicate its distinct and rather isolated structure.