Collective amplitude mode fluctuations in a flat band superconductor formed at a semimetal surface

We study the fluctuations of the amplitude (i.e., the Higgs-Anderson) mode in a superconducting system of coupled Dirac particles proposed as a model for possible surface or interface superconductivity in rhombohedral graphite. This system also serves as a generic model of a topological semimetal with an interaction-driven transition on its surface. We show that the absence of Fermi energy and vanishing of the excitation gap of the collective amplitude mode in the model leads to a large fluctuation contribution to thermodynamic quantities, such as the heat capacity. As a consequence, the mean-field theory becomes inaccurate, indicating that the interactions lead to a strongly correlated state. We also present a microscopic derivation of the Ginzburg-Landau theory corresponding to this model.