Fig. 3. Theoretical modeling of the Zeeman splitting across the quantum phase transition (QPT).

a The sketches illustrate the level structures of a YSR state at finite magnetic field in different regimes across the QPT. The Zeeman effect lifts the spin degeneracy of the doublet state leading to two possible transitions in the screened spin regime (shaded blue). The YSR states are split by the Zeeman energy E_z = gμ_BB, where g is the g-factor and μ_B is the Bohr magneton. The crossover regime (shaded yellow) in the proximity of the QPT still allows for a second transition involving thermal excitation of the YSR state and two-electron tunneling processes. The free spin regime (shaded brown) allows only for one transition. b Calculation of the differential conductance spectra across the QPT based on a master equation including single electron and two electron processes. The experimental data in Fig. 2b is well reproduced.