There are a few I looked into.
1) TT blower, basically a variable geared centrifugal apparently feels almost as good as a pure NA.
2) Screw blower. Low down power like roots, top end like centrifugal, but more efficient than both. Expensive! Thinnk Merc use these on the AMG cars, mazda used them on something.
3) Roots, good low end power, dying off at the top. Very inefficient compared to the other two.