Unfolding the physics of URu$_{2}$Si$_{2}$ through chemical substitution (Si $\to $ P)

URu$_{2}$Si$_{2}$ features all of the major phenomena that are at the focus of current research in correlated electron metals, including an exotic ordered state (``hidden order''), unconventional superconductivity, and anomalous metallic behavior. We recently undertook to study URu$_{2}$Si$_{2}$ using the novel tuning parameter Si $\to $ P substitution which, in a simple picture, simply adds electrons to the conduction band. Substitution of high vapor pressure elements in URu$_{2}$Si$_{2}$ is unprecedented, and is enabled by our new molten metal flux technique [1]. We find a rich phase diagram that includes two quantum phase transitions that are associated with hidden order and antiferromagnetism, respectively. In the hidden order region, the superconducting transition temperature is initially enhanced with P, after which it approaches zero before hidden order is destroyed, suggesting that URu$_{2}$Si$_{2}$ might be electronically displaced from ``optimal'' doping. We also find that the hidden order and antiferromagnetic regions are distant from each other, indicating that their origins are quite different. We will discuss these results and implications for understanding hidden order, superconductivity, and quantum criticality. \\[4pt] [1] R. E. Baumbach, \textit{et. al.}, ``High purity specimens of URu$_{2}$Si$_{2}$ produced by a molten metal flux technique,'' \textit{Phil. Mag.} (2014).