Hidden Order Transition in URu$_2$Si$_2$: Evidence for the Emergence of a Coherent Anderson Lattice from Scanning Tunneling Spectroscopy

The heavy-fermion compound URu$_2$Si$_2$ exhibits an onset of Kondo screening around T $\approx$ 55K and undergoes a second order phase transition at T$_0$ = 17.5K into a state with a still unknown hidden order parameter. Recent scanning tunneling spectroscopy experiments have provided insight into the temperature evolution of the electronic structure. Above the hidden order transition, the differential conductance, dI/dV, exhibits a characteristic Fano lineshape. In contrast, below T$_0$, a soft gap opens up in dI/dV and a quasi-particle interference (QPI) analysis reveals a band structure similar to that expected in a screened Kondo lattice. We demonstrate that the experimental dI/dV and QPI results below T$_0$ are consistent with the formation of a coherent Anderson lattice (CAL). In particular, dI/dV exhibits characteristic signatures of the Anderson lattice band structure, such as an asymmetric gap and a peak inside the gap which arises from the van Hove singularity of the heavy f-electron band. We identify several branches of the QPI pattern arising from intra- and interband scattering. Finally, the temperature evolution of dI/dV suggests that the formation of the CAL below the HOT is primarily driven by a strong increase of the lifetime of the heavy quasi-particles.