'\tab' is not a character, so that will never work - a character hold just a single letter, or an escaped letter such as '\n' or '\\'
If your string is separated by TAB characters, then '\t' will work fine - that is the C# character for a TAB.
If it's separated by the sequence '\', 't', 'a', 'b', then you would need to use a string array:
string[] stringSeparators = new string[] {@"\tab"};
string[] result = source.Split(stringSeparators, StringSplitOptions.None);