Flat bands as a route to high-temperature superconductivity in graphite

Superconductivity is traditionally viewed as a low-temperature phenomenon. Within the BCS theory this is understood to result from the fact that the pairing of electrons takes place only close to the usually two-dimensional Fermi surface residing at a finite chemical potential. Because of this, the critical temperature is exponentially suppressed compared to the microscopic energy scales. On the other hand, pairing electrons around a dispersionless (flat) energy band leads to very strong superconductivity, with a mean-field critical temperature linearly proportional to the microscopic coupling constant. The prize to be paid is that flat bands can generally be generated only on surfaces and interfaces, where high-temperature superconductivity would show up. The flat-band character and the low dimensionality also mean that despite the high critical temperature such a superconducting state would be subject to strong fluctuations. Here we discuss the topological and non-topological flat bands discussed in different systems, and show that graphite is a good candidate for showing high-temperature flat-band interface superconductivity.