If you are looking for a tablet with an AMOLED screen, there are not many options. Actually, there is only one - the Samsung Galaxy Tab 7.7. However, the good news is that Verizon will offer it with an LTE connection "in the coming weeks". There is no information on pricing or exact date though.
The Verizon LTE version of the Tab 7.7 is exactly the same as the European GSM/3G model. It is SLIM at 0.31" (7.9mm) and it boasts the exact same 7.7" Super AMOLED screen with 1280x800 pixels resolution. To see more about it, please check out or Galaxy Tab 7.7 Preview.