Does anyone know of any practical uses for a type I superconductor, where it isn't possible to use a type II (which typically have higher critical temperatures so need less cooling etc)?
I have no idea what a split Cooper-pair box is, but thanks for the clarification anyway.Most low-Tc SQUIDs are fabricated from niobium and aluminium SQUIDs are rarely used as actual magnetometers; Al SQUIDs are usually just used as "tunable Josephson junctions" since we can control the critical current (and therefore Ej) using an external magnetic field (this is used in e.g. split Cooper-pair boxes etc).
Or even a He-4 cryostat! (or was that a typo?)Aluminium also has a fairly high Tc (1.2-1.6K) meaning even a simply He-3 cryostat will often do.
Unfortunately not. A pumped He-4 cryostat will get down to 1.3-1.4K but that is still too close to Tc for most applications (the IV curve of an Al Josephson junction will be extremely smeared out at 1.3K, and it might not be superconducting at all).Or even a He-4 cryostat! (or was that a typo?)