Evidence for a nematic component to the Hidden Order parameter in URu$_2$Si$_2$ from differential elastoresistance measurements

In this work, we use a novel piezo actuator technique to measure the differential elastoresistance of the unconventional heavy fermion superconductor URu$_2$Si$_2$. Prior to the onset of superconductivity ($T_c \sim 1.5$ K), URu$_2$Si$_2$ undergoes a phase transition to a novel ``Hidden Order'' state which has defied comprehensive understanding for over 30 years. By tracking the temperature dependence of various elastoresistivity coefficients (proportional to the nematic susceptibility in the limit of linear response) above the Hidden Order transition temperature ($T_{HO} \sim 17.5$ K), our measurements reveal an extended nematic fluctuation regime at high temperatures and a strong anomalous divergence (which scales as the singular contribution to the heat capacity) proximate to the Hidden Order transition. Understood within a Ginzburg-Landau framework for coupled order parameters, these measurements imply that the Hidden Order parameter is a two-component vector oriented in the [110] crystallographic direction which breaks the underlying four-fold symmetry of the lattice (in addition to other symmetries).