Geometric Properties of Unconventional Superconductivity

In recent years, the influence of the geometry of Bloch bands on physical quantities, i.e., quantum geometric effects, has attracted much attention in condensed matter physics. The quantum geometric tensor, which characterizes quantum geometry, is composed of the quantum metric and the Berry curvature, and recently many studies have revealed various phenomena related to the quantum metric. In particular, the quantum metric makes superconductivity possible even in perfectly flat bands, where the effective mass of the electrons diverges to infinity. The effects of quantum geometry on superconductivity have been investigated intensively for s-wave superconductors. However, quantum geometric effects on unconventional superconductivity remain largely elusive. In this study, we discuss the role of quantum geometry in unconventional superconductors. In particular, we study the temperature dependence, magnetic field dependence, and current dependence of the geometric term in the superfluid weight, which takes a finite value only through quantum geometry, and compare the behavior of the geometric contribution with that of the conventional Fermi liquid contribution.