Where can you get that tooth powder that dental hygenists use for teeth cleaning?

I use a herbal tincture that I rub on my gums to keep them tight and prevent periodontal disease. The tincture leaves some discoloring on my teeth near the gum line.

The only thing that gets my teeth clean is the quarterly cleaning I get at the dentist. I have tried brushing my teeth with baking soda, and with Dr. Bronner's soap as recommended on this forum. They both do a good job of cleaning off bacteria, but neither remove the discoloring.

What homemade remedies are there to remove the discoloring or is there a source for that tooth powder the dental hygenist uses? I have a herbal tooth powder from Dr. Christopher's herbs but it's not the same thing; when I use it to brush my teeth it leaves them more discolored than with the tincture!