The Misva of Sisit from the Torah applies only to wool and linen garments. Other fabrics, such as cotton and silk, are only obligated in Sisit Mdrabanan-by Rabbinic law. The Halacha states that even if one uses a cotton or silk garment for a Tallit, he may tie wool strings to it as Sisit. Wool is the universal thread for Sisit and may be tied to any fabric, except for linen, because of the prohibition of Shatnez. A cotton Tallit may have cotton Sisit, and a silk Tallit may have silk Sisit. However, silk strings may not be tied to a cotton garment and vice versa.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) raised a Halachic problem with regard to using silk strings for Sisit. Generally, non-Jews take the silk threads from the cocoon of the silk worm. This constitutes a problem since the non-Jew cannot create the string for the sake of the Misva. Therefore, silk strings should not be used. Hacham Ovadia discusses whether a similar issue exists regarding harvesting cotton for Sisit by non-Jews. He rules that a non-Jew may pick cotton for Sisit. As opposed to the silk which is drawn from the cocoon already as a thread, cotton fibers are still raw after harvesting and can later be spun into yarn by Jews for the sake of the Misva. Nevertheless, it is not common practice to use cotton string for Sisit. Even cotton Tallits use wool strings.
Leather garments are not obligated in Sisit. The Torah defines a garment as something that is woven from thread, as opposed to leather, which is one piece. The Poskim discuss whether synthetic materials are obligated in Sisit. This applies to the mesh Sisit, which are sometimes sold. The opinions differ from one end of the spectrum to the other. Some authorities rule that it is obligated; some say that is not, while others say it is obligated but not to make a Beracha. Therefore, one should avoid using synthetic material for a Talit.
SUMMARY
A Cotton Tallit may have either wool or cotton Sisit.
One should avoid using Sisit made of silk.
Leather garments are exempt from Sisit.
One should avoid using a Tallit Katan or Tallit Gadol made of synthetic fibers.
