Extended Data Fig. 8: Numerical analysis of E_gap and E_det.

Numerical calculations supporting the results presented in Fig. 4. Through the procedure detailed in Methods, Majorana sweet spots are obtained and analysed for fields between 0 mT and 300 mT. a, Field evolution of G_RR line-traces at each sweet spot, showing the excitations above the ZBPs gradually increasing in energy and then saturating at ± 30 μeV. b, Field evolution of G_RR line-traces when QDR detuned by 3Δ_ind, showing the excited states increase linearly in energy. From calculations in (a) and (b), E_gap and \({E}_{\det }\) are obtained, given by the energy between the lowest even-parity state and second-lowest odd-parity state. c, Extraction of E_gap (solid) and the Majorana polarization (dashed), for different values of the tunneling parameter t. In each case t_so = 0.4t. Larger tunnel coupling results in larger hybridization between ABSs, in turn lowering the MP at a specific magnetic field. d, Extraction of \({E}_{\det }\) for various values of detuning μ_R. In each case the slope at low fields corresponds to 2E_z (dashed grey line). The larger the detuning of μ_R, the longer this holds. The dashed black line shows the energy of the ABS E_ABS. At large detuning \({E}_{\det }\) will increase linearly with 2E_z, until becoming of comparable E_ABS becomes the lowest energy scale.