Dear friend Md. Jahid Hasan Sagor

To obtain the temperature-dependent dielectric constant for materials like Au, Si, Graphene, or any other material, you typically need experimental data or theoretical models that describe the temperature dependence of the dielectric constant. Here are a few approaches you can consider:

1. Experimental data: Look for published experimental studies that provide temperature-dependent dielectric constant data for the specific materials of interest. These studies often involve measurements using techniques such as spectroscopic ellipsometry, capacitance measurements, or other relevant characterization methods. Research papers, scientific journals, and materials science databases like the Materials Project or NIST (National Institute of Standards and Technology) databases can be valuable sources for such information.

2. Empirical models: Certain empirical models exist that can estimate the temperature dependence of the dielectric constant for specific materials. These models are typically derived from fitting experimental data and can provide reasonable approximations over a given temperature range. One example is the Debye model, which describes the temperature-dependent dielectric response of materials. Published research papers and materials science textbooks may contain information on these models.

3. Theoretical calculations: If you're unable to find experimental or empirical data, you can explore theoretical calculations based on first principles methods or density functional theory (DFT) calculations. Quantum Espresso, as you mentioned, is one such software package that can perform DFT calculations. While Quantum Espresso provides output at 0 K (absolute zero temperature), you can use the calculated electronic structure data to estimate the temperature-dependent dielectric constant through additional calculations or models. However, it's important to note that the accuracy of these calculations relies on the validity of the underlying assumptions and the chosen theoretical approach.

Regarding finding the dielectric constant at room temperature using Quantum Espresso, it might be challenging to directly obtain the temperature-dependent dielectric constant from the software itself. However, you can potentially perform calculations at different temperatures and then extrapolate the results to estimate the dielectric constant at room temperature. Alternatively, you can consider post-processing the calculated electronic structure data using other software or analysis tools to derive the dielectric constant.

Remember that the accuracy and reliability of the temperature-dependent dielectric constant estimation depend on various factors, including the quality of the experimental data or theoretical models used. It's always recommended to consult relevant literature, collaborate with experts in the field, and validate the results through experimental measurements whenever possible.

Here are a few references that can provide further information on finding the temperature-dependent dielectric constant for materials:

1. Beier, C. W., Cuevas, M. A., & Brutchey, R. L. (2010). Effect of surface modification on the dielectric properties of BaTiO3 nanocrystals. Langmuir, 26(7), 5067-5071.

2. Taylor, T. R., Hansen, P. J., Acikel, B., Pervez, N., York, R. A., Streiffer, S. K., & Speck, J. S. (2002). Impact of thermal strain on the dielectric constant of sputtered barium strontium titanate thin films. Applied Physics Letters, 80(11), 1978-1980.

3. Soares, B. G., Leyva, M. E., Barra, G. M., & Khastgir, D. (2006). Dielectric behavior of polyaniline synthesized by different techniques. European Polymer Journal, 42(3), 676-686.

4. Parker, R. A. (1961). Static dielectric constant of rutile (ti o 2), 1.6-1060 k. Physical Review, 124(6), 1719.

5. Rumble, J. (Ed.). (2017). CRC handbook of chemistry and physics.

These references cover a range of topics related to the temperature-dependent dielectric constant, including experimental measurements, theoretical models, and specific material systems. They can serve as starting points for further exploration and provide additional references within their respective fields.