The THz-TDS spectra were acquired using a commercial TeraPulse 4000 instrument across the spectral range of 0.2 -2.2 THz (TeraView, Cambridge, UK). The sample temperature (90 -360 K) was controlled using a continuous flow cryostat with liquid nitrogen as the cryogen (Janis ST-100, Wilmington MA, USA) as outlined previously. The cryostat cold finger accommodated both the reference (two z-cut quartz windows) as well as the sample (quartz/sample/quartz sandwich structure as described above). The two z-cut quartz windows for the reference (same dimensions as sample) were directly pressed to one another without any spacer in between the two windows in order to avoid internal reflections in the time-domain signal. The cold finger was moved vertically using a motorised linear stage to switch between sample and reference at each measurement temperature. For each temperature, the sample and the reference were measured at the centre position, with 2000 waveforms co-averaged for each, for approximately 2 minutes.