How to make authentic black Russian bread?
There are two elements responsible for the darkness of “black bread”, which is a term used for different breads all over East, North and Central Europe

Whole grain flour, typically rye, but sometimes with a part wheat or spelt.
A low and slow bake, the probably most extreme example is Pumpernickel, which needs almost a day at 100-120 C and is more steamed than baked. Other recipes aim for 2.5 hours at 150 C. Above that, you will still get a good and dark bread, but more brown-grey than dark “black”.

The lower and slower, the darker will the bread turn out. Some sources claim that the darkness is caused by the Maillard reaction, but I am not sure whether this is the whole truth. Considering the temperature range, other factors like enzymes out of the grain are at least involved. The only “traditional” colorant I could find at a quick research was molasses or similar, which is used in some recipes.