# PhD Defense: Esben Bork Hansen

Majorana Bound States in Semiconductor-Superconductor Hybrid Devices.

This thesis presents the results of theoretical studies of superconductor-semiconductor (SC-SM) hybrid nanowire systems with the focus on detecting Majorana bound states (MBSs) by methods using electron tunneling spectroscopy.

We model the SC-SM nanowire using three Hamiltonian models: the first is the 1D spinless $p$-wave SC, and the other two are a 1D SM nanowire with Rashba spin-orbit interaction, Zeeman field, and induced $s$-wave superconductivity, where the superconductivity is either modeled as a constant gap or an energy-dependent self-energy term. Electron tunneling spectroscopy will be simulated in the grounded nanowire setup using the scattering formalism and in the charged island setup using a master equation model.

We will present and discuss the results of five projects in this thesis. In the first project, we study a SC-normal-SC nanowire setup and simulate differential conductance measured at the end of the nanowire. We find that there exist 2 or 4 MBSs in the topological regime, depending on the phase difference between the two SCs. This phase dependence gives rise to distinctive $2\pi$ period features in the differential conductance, which are absent in the trivial phase and may be used to identify MBSs.

The second project is centered around modeling the experimental setup of a quantum dot coupled to the end of a SC-SM nanowire and understanding the observed differential conductance data. The experimental data is consistent with our model where the nanowire hosts MBSs and the levels in the quantum dot can be tuned in and out of resonance with the nanowire. We find that the observed energy splitting upon resonance with a dot level is due to the MBS wavefunction leaking into the quantum dot.

In the third project, we investigate the effect of the normal-conducting drain lead on the parent SC of the SC-SM nanowire. A below-gap density of states is induced into the parent SC at the normal-SC interface. Depending on the coherence length of the SC, this below-gap density of states may provide a leakage channel for the MBSs in the nanowire. This leakage may, depending on coherence length of the superconductor, result in a quenching of the energy oscillations and a suppression of the $2e^2/h$ quantized conductance usually associated with MBSs.

In the fourth project, we model quasiparticle poisoning in a charged SC-SM nanowire island and estimate the quasiparticle poisoning rate by comparing with experimental data.

In the final project, we find that the electron and hole components of the lowest-energy subgap state can be extracted from the ratio of consecutive conductance peaks measured at zero bias in a charged SC-SM nanowire island in the sequential tunneling regime. We study the correlation between this ratio and the energy splitting oscillations of the subgap state in case of MBSs and trivial Andreev bound states (ABSs). We find that certain kinds of trivial ABSs with MBS-like conductance features can be distinguished from true MBSs by comparing this ratio with energy splitting as function of magnetic field and chemical potential.

Although many indirect MBS signatures using electron spectroscopy do not provide unambiguous evidence of the presence of MBSs in SC-SM nanowire, they are still important in guiding the search for MBSs and developing a better understanding of quantum phenomena in SC-SM nanowires.