THz Second and Third Harmonic Generation in PdCoO$_2$ Thin Films

Terahertz high harmonic generation (THz HHG) is a common property of nonlinear systems. Recently it has been used to investigate fundamental principles that govern transport and nonlinear dynamics in novel quantum materials like graphene, Dirac semimetals or high-temperature superconductors. Here, we report on the observation of exceptionally large THz second harmonic and third harmonic generation in thin films of the highly conducting delafossite PdCoO$_2$ down to low temperatures. The growth of this material on offcut substrate allows for a significant enhancement of the third harmonic intensity compared to ordinary $c$-axis grown thin films. Furthermore, it appears to be a necessity for the observation of THz second harmonic generation. We model the temperature dependence of the third harmonic generation by means of Boltzmann transport theory and provide an explanation for the second harmonic generation by comparing the system to the electric field induced second harmonic generation. The present investigation thus provides an important contribution to the ongoing discussion of low temperature origins of THz HHG and might serve as a new platform for THz high harmonic applications.