Quantum energy storage in graphene SNS junctions

We investigate quantum energy storage in graphene superconductor-normal-superconductor (SNS) Josephson junctions from the perspective of Andreev bound-state(ABS) dynamics. Within the Dirac-Bogoliubov-de Gennes framework, we analyze the phase-dependent ABS spectrum and investigate how time-dependent superconducting phase ramps drive nonadiabatic Landau-Zener transitions across the avoided level crossing. The resulting excited-state population is characterized using the ergotropy formalism to quantify the maximum extractable work. Analytical expressions relating junction transparency, phase-ramp duration, excitation probability, and ergotropy are obtained, providing insight into the charging dynamics. We further discuss the scaling of the maximum extractable work with the spin and valley degeneracies of graphene and the number of transverse ballistic modes, and estimate representative charging times and output power using experimentally reported graphene-Al junction parameters. Our results provide a quantum thermodynamic interpretation of phase-controlled ABS dynamics and illustrate the potential of graphene SNS Josephson junctions as a platform for coherent energy storage studies.