You are right in a way - pinned superconductors keep their orientation as they follow the track. They will not cross magnetic field lines just like a rolling ball will not cross gravitational field lines, unless some outer force is applied to make it happen. This is all nicely summarized in Newton's first law. So…

The thinness does have a lot to do with the amazing levitation height, simply by making the superconducting disc very light. Totalnewbie's response explains the basic mechanism of superconductivity well, so I'll focus on the geometry. Until this work, all the high-temperature superconducting pellets (YBCO being the…

Small maglev trains with flux pinning (or quantum locking, if you prefer) do exist and can be quite fun: