This thesis investigates superconductivity in a system with flat electronic bands. Systems like this potentially host superconductivity with high TC. To fully classify the superconducting state, the coherence length and the London penetration depth are calculated by extracting information on the length scales from the breakdown of the superconducting order parameter when introducing a finite momentum.

A class of systems attracting significant recent interest are graphene-based system that host flat band due to specific structural configurations. The model investigated in this thesis is a conceptually simple model of a flat band hybridized with graphene that can be realized in two-dimensional adatom heterostructures.

The finine momentum pairing method is applied to both this decorated graphene model and a one-band Hubbard model with a local attractive interaction to calculate the superconducting length scales.

The whole manuscript can be found in this repository.