Extended Data Fig. 8: Shifting the MBS wavefunction - comparison to analytical result.
From: Observation of edge and bulk states in a three-site Kitaev chain
At a three-site Kitaev chain sweet spot, with ϕΔ = 0, detuning either of the outer QDs shifts the MBS wave-function to the middle QD. In Methods, we derive that this reflects in the zero-bias conductance of each site and depends only on the coupling parameters t1/t2 (= Δ1/Δ2) (see Eqs. (16)). To do this analysis experimentally, first the chemical-potential energies μL, μR of QDL and QDR are measured as a function of a.VQDL and b.VQDR, by measuring each QD spectrum with the unused QDs in Coulomb blockade. With all parameters tuned to the sweet spot values, we detune VQDL around charge degeneracy and measure c. GLL and d. GMM, as shown in Fig. 3a. Additionally, we detune VQDR and measure e. GRR and f. GMM. As visualised in g. and h., these experiments result in the shifting of the MBS wave-function from the outer QD to the inner QD. In (c,d), the conductances measured at VL,VM = 0 depend only on μL and t1. Similarly for (e,f) they scale according to μR and t2. i. We extract GLL and GMM along VL,VM = 0 from (c) and (d) and convert VQDL to μL using (a). Fitting the analytical formulas shown in (g), with an additional scaling factor, an estimate for t1 of 17.6 μeV is obtained. This can be compared to the width of the excitation gap at μL = 0, which theory predicts to be 2t1. j. shows the line-trace, with the dashed lines indicating the expected location of the excited states based on the extraction in (i). k. We repeat this procedure for GRR and GMM along VR,VM = 0 from (e) and (f), converting VQDL to μR using (b). Now fitting the formulates shown in (h), we can estimate t2 of 23.7 μeV. l. This again agrees with the excitation gap at μR = 0.
