Discrete energy levels of Caroli-de Gennes-Martricon states in quantum limit due to small Fermi energy in FeTe_0.55Se_0.45

Caroli-de Gennes-Martricon (CdGM) states were predicted as low energy excitations within vortex cores in type-II superconductors. In the quantum limit, namely T/T_c<<Δ/E_F, the energy levels of these states were predicted to be discrete with the basic levels at E_μ = ± μΔ²/E_F (μ = 1/2, 3/2, 5/2, …). However, due to the small ratio of Δ/E_F in most type-II superconductors, it is very difficult to observe the discrete CdGM states, but rather a symmetric peak appears at zero-bias at the vortex center. Here we report a clear observation of these discrete energy levels of CdGM states in FeTe_0.55Se_0.45. The rather stable energies of these states versus space clearly validates our conclusion. Analysis based on the energies of these CdGM states indicates that the Fermi energy in the system is very small.