The quantum anomalous Hall insulator (QAHI) is predicted to become a p + ip type topological superconductor (TSC) once proximity coupled to an ordinary s-wave superconductor (SC). Extended chiral Majorana edge modes (CMEM) and Majorana bound states (MBS) are further thought to emerge at the edges of two-dimensional (2D) and at the ends of one-dimensional (1D) p + ip type TSCs, respectively. Potential use of MBS in the fabrication of topological quantum computers drives the current research interest in the search for these peculiar quasiparticles. Albeit promising, QAHI-SC hybrid devices are less studied platforms in this regard. My efforts documented in this thesis have been devoted to characterizing various transport properties of such device structures in 2D and quasi-1D regimes.

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The quantum anomalous Hall insulator (QAHI) is predicted to become a p + ip type topological superconductor (TSC) once proximity coupled to an ordinary s-wave superconductor (SC). Extended chiral Majorana edge modes (CMEM) and Majorana bound states (MBS) are further thought to emerge at the edges of two-dimensional (2D) and at the ends of one-dimensional (1D) p + ip type TSCs, respectively. Potential use of MBS in the fabrication of topological quantum computers drives the current research interest in the search for these peculiar quasiparticles. Albeit promising, QAHI-SC hybrid devices are less studied platforms in this regard. My efforts documented in this thesis have been devoted to characterizing various transport properties of such device structures in 2D and quasi-1D regimes.

Half-quantized conductance plateaus in the magnetoconductance curves of QAHI-SC devices were predicted to be the signature of CMEM. To investigate this effect, we first studied the longitudinal magnetotransport across a QAHI-Nb section on the 2D QAHI film. Although it is now accepted that the observation of the plateaus alone cannot make a strong case for chiral Majorana modes, we have observed such plateaus in the magnetoconductance curves of two devices and have shown their disappearance due to sample edge modification.

We have further studied the transport of current through narrow QAHI nanoribbons in the quasi-1D limit. The edge states of QAHI are predicted to hybridize when their separation is around 100 nm. We were able to successfully channel current through the nanoribbons of widths down to ~75 nm. The quantum anomalous Hall (QAH) effect appears to be preserved in such narrow devices although increased dissipation is observed presumably due to finite interaction of the edge modes.

When superconductivity is induced in the quasi-1D QAHI channel with finite hybridization between its edge states, MBS are expected to form at each end of the channel. We performed Andreev reflection spectroscopy at the interface of QAHI/QAHI-SC junction to detect the conductance signatures of MBS. In four devices, we observed multiple in-gap differential conductance peaks as a function of bias voltage as well as an elevated background conductance. Theoretical simulations suggest that the Fermi level of the device is shifted to the bulk bands and the single channel regime can be reached by applying perpendicular magnetic fields. Once there is only one channel in the nanoribbon, a single zero-bias conductance peak should emerge due to the MBS. Our observations are in good agreement with the theoretical prediction.