We study the effect of external electric fields on superconductor-semiconductor coupling by measuring the electron transport in InSb semiconductor nanowires coupled to an epitaxially grown Al superconductor. We find that the gate voltage induced electric fields can greatly modify the coupling strength, which has consequences for the proximity induced superconducting gap, effective g-factor, and spin-orbit coupling, which all play a key role in understanding Majorana physics. We further show that level repulsion due to spin-orbit coupling in a finite size system can lead to seemingly stable zero bias conductance peaks, which mimic the behavior of Majorana zero modes. Our results improve the understanding of realistic Majorana nanowire systems. gate induced electric fields. Due to the change in coupling, the renormalization of material parameters is altered, as evidenced by a change in the effective g-factor of the hybrid system. Furthermore, the electric field is shown to affect the spin-orbit interaction, revealed by a change in the level repulsion between Andreev states. Our experimental findings are corroborated by numerical simulations.
Experimental set-upWe have performed tunneling spectroscopy experiments on four InSb-Al hybrid nanowire devices, labeled A-D, all showing consistent behavior. The nanowire growth procedure is described in [20]. A scanning electron micrograph (SEM) of device A is shown in figure 1(a). Figure 1(b) shows a schematic of this device and the measurement set-up. For clarity, the wrap-around tunnel gate, tunnel gate dielectric and contacts have been removed on one side. A normal-superconductor (NS) junction is formed between the part of the nanowire covered by a thin shell of aluminum (10 nm thick, indicated in green, S), and the Cr /Au contact (yellow, N). The transmission of the junction is controlled by applying a voltage V Tunnel to the tunnel gate (red), galvanically isolated from the nanowire by 35 nm of sputtered SiN x dielectric. The electric field is induced by a global back gate voltage V BG , except in the case of device B, where this role is played by the side gate voltage V SG . Further details on device fabrication and design are included in appendices A and B. To obtain information about the density of states (DOS) in the proximitized nanowire, we measure the differential conductance dI/dV Bias as a function of applied bias voltage V Bias . In the following, we will label this quantity as dI/dV for brevity. A magnetic field is applied along the nanowire direction (x-axis in figures 1(b), (c)). All measurements are performed in a dilution refrigerator with a base temperature of 20 mK.
Theoretical modelThe device geometry used in the simulation is shown in figure 1(c). We consider a nanowire oriented along the x-direction, with a hexagonal cross-section in the yz-plane. The hybrid superconductor-nanowire system is described by the Bogoliubov-de Gennes (BdG) Hamiltonian