Quantum geometry quantifies the change in amplitude (quantum metric) and phase (Berry curvature) of quantum states that evolve in parameter space. The consequences of the geometry of the normal Bloch state for superconductivity have been widely investigated, including the possibility of superconductivity in flat bands [1]. However, the geometry of emergent Bogoliubov quasiparticles has received little attention [2,3,4]. We thus explore the geometry of the eigenstates of the Bogoliubov-de Gennes Hamiltonian, and its interplay with the normal state geometry. Under specific assumptions on the Hamiltonian, we show that the Quantum Geometric Tensor (QGT) separates into normal and quasiparticle contributions. We further derive analytically the QGT for spin-singlet and spin-triplet cases, and provide examples to illustrate those cases.

[1] P. Törmä, S. Peotta and B.A. Bernevig, Superconductivity, superfluidity and quantum geometry in twisted multilayer systems Nat. Rev. Phys. 4 528 (2022).

[2] D. Porlles W. Chen, Quantum geometry of singlet superconductors, Phys. Rev. B 08, 094508 (2023).

[3] A. Daido et al., Quantum Geometry Encoded to Pair Potentials, Phys. Rev. B 110, 094505 (2024).

[4] F. Simon, Normal-State Quantum Geometry, Nonlocality, and Superconductivity, Phys. Rev. B, 112, 104504 (2025).