Hidden crossover phenomena in strongly Pauli-limited multiband superconductors: Application to CeCu₂Si₂

Motivated by recent experiments on heavy fermion materials CeCu₂Si₂ and UBe₁₃, we develop a framework to capture generic properties of multiband superconductors with strong Pauli paramagnetic effect (PPE). In contrast to the single band case, the upper critical field H_c2 can remain a second-order transition even for strong PPE cases. The expected first-order transition is hidden inside H_c2 and becomes a crossover due to the interplay of multibandness. The present theory based on full self-consistent solutions of the microscopic Eilenberger theory explains several mysterious anomalies associated with the crossover and the "empty" vortex core state which is observed by recent STM experiment on CeCu₂Si₂.