Shaping electron wave functions in a carbon nanotube with a parallel magnetic field Supplementary Material

In Figure 2c of the main text, the conductance resonances lowermost in bias voltage Vbias abruptly change both curvature and amplitude in the magnetic field range 4 T . B‖ . 8 T (i.e., when reaching Vbias = 0). This behaviour can be explained by reminding us of the measurement technique. The conductance traces in Figures 2b and 2c are recorded at constant gate voltage V ∗ gate = 0.675 V. As an example, the conductance trace dI/dVbias(B‖ = 0, Vbias) from Figure 2b and Figure 2c is equivalent to the conductance trace dI/dVbias(Vgate = 0.675 V, Vbias) from the measurement of Figure 2a. Applying a magnetic field shifts the gate voltage position of the charge degeneracy point visible in Figure 2a, where single electron tunneling is possible at zero bias. When increasing the magnetic field parallel to the carbon nanotube axis above B‖ ' 4 T, this degeneracy point crosses the gate voltage value V ∗ gate chosen in Figures 2b and 2c. Consequently, for the magnetic field range 4 T . B‖ . 8 T the constant gate voltage traces of Figure 2c at low bias do not cut through the N = 0 band gap region, but through the N = 1 charge occupation Coulomb blockade region instead. At the edge of the 0 ≤ N ≤ 1 single electron tunneling region, visible in Figure 2c as the first line of finite differential conductance, the electrochemical potential of the quantum dot is for 4 T . B‖ . 8 T aligned with the Fermi edge of the source contact, not the drain contact as is the case outside this magnetic field range. Thus, a significantly stronger conductance signal is observed for this field range.