1) This is simulation result using density functional theory. While a standard method for understanding the electronic structure of materials it often does not do so accurately when correlations (electronic interactions) are strong. In this kind of context (where strong interactions are expected to be necessary to give something like high temperature superconductivity) what one is looking for from a DFT simulation is an indication of what kind of starting point to extend further and include interactions.
2) What is seen here are features called "flat bands". Essentially, the kinetic energy of the electrons relevant at low energies is only weakly dependent on the (crystal) momentum of the particle. Having lots of different states (different momenta) at similar energy usually means the interactions are more important than in materials where the kinetic energy is larger and more dispersive (depends more strongly on momentum). Here the partially filled d-shells of the Cu atoms appear to make a flat band at low energy. This flat band is partially filled and thus is potentially susceptible to interaction induced instabilities.
3) Flat bands can come from trivial features of a crystal as well. If you've got isolated atoms far apart enough that their atomic orbitals barely overlap their bands will be flat. Some of this may be at play here since the Cu atoms seem to be quite distant (7-9 Angstroms or so).
4) Flat bands appear in many many kinds of systems (at the level of DFT, even at the level of experiments, etc, etc) and do not necessarily imply superconductivity, let alone high temperature superconductivity. Even if the presence of flat bands is pointing towards stronger and more important interaction effects these interaction effects can stabilize other kinds of order instead (magnetism, charge order, etc).
5) Predicting what instability is realized is hard and can be quite delicate. There are materials where this can be debated (theoretically and sometimes experimentally) for years. Predicting the onset temperature of the order that is produced is hard. I.e. Don't necessarily expect a reliable estimate of the critical temperature from theory.
> and do not necessarily imply superconductivity, let alone high temperature superconductivity
That's true, but are there superconductors that do not have those flat bands?
If not then it wouldn't be evidence that it is superconducting but it would at least check one more expected property (based on the evidence obtained about superconductors so far).
> That's true, but are there superconductors that do not have those flat bands?
Yes, many. Most (all?) conventional superconductors. High-Tc iron arsenide superconductors discovered ~15 years ago. DFT (without including Hubbard "U" type corrections) for the cuprate high-Tc superconductors also doesn't indicate show flat bands.
Examples that do have flat bands (or similar physics) include the recently discovered twisted bilayer graphene (still very much actively studied), as well as (morally speaking at least) heavy-fermion superconductors (too many to list).
Superconductivity is a phase of matter than can arise in a variety of different ways depending on the details of the underlying physics. So at least when talking about the microscopic mechanism that stabilizes the superconducting state there isn't any single theory or one set of predictions/properties.
1) This is simulation result using density functional theory. While a standard method for understanding the electronic structure of materials it often does not do so accurately when correlations (electronic interactions) are strong. In this kind of context (where strong interactions are expected to be necessary to give something like high temperature superconductivity) what one is looking for from a DFT simulation is an indication of what kind of starting point to extend further and include interactions.
2) What is seen here are features called "flat bands". Essentially, the kinetic energy of the electrons relevant at low energies is only weakly dependent on the (crystal) momentum of the particle. Having lots of different states (different momenta) at similar energy usually means the interactions are more important than in materials where the kinetic energy is larger and more dispersive (depends more strongly on momentum). Here the partially filled d-shells of the Cu atoms appear to make a flat band at low energy. This flat band is partially filled and thus is potentially susceptible to interaction induced instabilities.
3) Flat bands can come from trivial features of a crystal as well. If you've got isolated atoms far apart enough that their atomic orbitals barely overlap their bands will be flat. Some of this may be at play here since the Cu atoms seem to be quite distant (7-9 Angstroms or so).
4) Flat bands appear in many many kinds of systems (at the level of DFT, even at the level of experiments, etc, etc) and do not necessarily imply superconductivity, let alone high temperature superconductivity. Even if the presence of flat bands is pointing towards stronger and more important interaction effects these interaction effects can stabilize other kinds of order instead (magnetism, charge order, etc).
5) Predicting what instability is realized is hard and can be quite delicate. There are materials where this can be debated (theoretically and sometimes experimentally) for years. Predicting the onset temperature of the order that is produced is hard. I.e. Don't necessarily expect a reliable estimate of the critical temperature from theory.