## 2 Materials and Methods  
We selected the bare fused silica (~1 mm thick) as substrates to fabricate all the devices. All substrates were washed in acetone, isopropyl alcohol, and deionized water under ultrasonic agitation, then dried by using a nitrogen gun and hotplate, and subjected to cooling for half an hour. Three sets of samples were used in this investigation. The details of the fabrication process for all sets of samples are presented in the following paragraphs. First set: pristine PEDOT: PSS (Agfa-S300, Taipei, Taiwan), with sheet resistance 216 \(\mathrm{ohm}\)/square) with three different thicknesses were coated on substrates by spin coating and baked at approximately 130 \({}^{\circ}\)C for 12 min. One clean bare substrate was used for the reference to investigate the THz transmittance properties. The thickness of the pristine PEDOT: PSS films was controlled by the spin coater with a rotation speed 3000 rpm for 30 s.  
Second set: we prepared two types of LC cells (thickness \(\sim\)250 \(\mathrm{\SIUnitSymbolMicro m}\)), one with MDA-00-3461 and another with mixture 1825. A polyimide (PI) \(\sim\)2 \(\mathrm{\SIUnitSymbolMicro m}\) thin layer was spin coated on the TCE-coated substrates and baked for solvent evaporation. The mechanical rubbing process was applied on top of the PI layer after cooling. The two substrates for each LC cell were assembled together in anti-parallel orientation to form a cell with a homogeneous alignment. The cell gap was controlled by a Mylar film with a thickness of 250 \(\mathrm{\SIUnitSymbolMicro m}\). The details of a homogeneously aligned LC cell structure can be found in Figure 1a. In addition, we prepared an empty cell as reference cell \(-1\). Third set: we prepared three types of LC THz phase shifters using the optimized thickness of pristine PEDOT: PSS films as TCEs. In this case, the pristine PEDOT: PSS layer was prepared on the substrate using the spin coating method. Substrate preparation was the same as that described for set 2. The two substrates were then assembled together with the rubbing direction in perpendicular orientation to each other, corresponding to the rubbing directions to form a cell with TN molecule alignment. Here, two TN-LC cells with thicknesses of 250 and 550 \(\mathrm{\SIUnitSymbolMicro m}\), respectiv  
Figure 1: Schematic illustration of device structures for (**a**) a homogeneously aligned liquid crystal (LC) cell to carry out the optical constant measurement of both types of LC and (**b**) a twisted nematic (TN)-LC phase shifter with pristine poly(3,4-ethylenedioxythiophene):polystyrenesulfonate) (PEDOT: PSS) as transparent electrodes. with injected MDA-00-3461 LC molecules. Another 250 \(\upmu\)m thick TN-LC sample was fabricated with injected mixture 1825 LC molecules. The thickness of each cell was controlled by the thickness of the Mylar film. Moreover, we prepared an empty cell as reference cell \(-\)2. We defined the identity of the three types of TN-LC phase shifters as shown in Table 1. A schematic illustration of the TN-LC THz phase shifter is shown in Figure 1b. A photoconductive antenna (PCA)-based transmission-type THz time-domain spectrometer (THz-TDS) as described in our previous works in the frequency range of 0.2-1.2 THz was used for characterization of the materials and devices in the THz frequency band [23; 24]. For measurement of the THz optical constants of both types of LCs, the transmitted THz signal of the extraordinary wave was measured while the LC alignment direction of the sample was placed parallel to the THz field polarization, whereas the ordinary wave was measured by simply rotating the sample by 90\({}^{\circ}\). In addition, we measured the transmitted THz signals from the reference cell. For the details of the techniques and procedures used to extract all the parameters, please refer to our previous work [23; 24]. In this study, the critical parameters such as the thickness of the sample and the reference were well taken into account.