In this thesis we study three examples, where novel superconducting properties all arise from normal state electronic wave functions.

In Chapter 2, we study chiral Majorana edge modes (CMEMs) in a quantum anomalous hall/superconductor hybrid system. CMEM is predicted to induce an unique half quantized plateau as its transport signature[1, 5, 6]. This was recently found in the experiments[2]. However, it was argued that without Majorana, disorder could also induce such signature[3, 7]. Here we propose to use local tunneling spectroscopy to directly probe the edge state of the hybrid system. We use Recursive Green’s Function to show that for topological phase with Chern number N = ±1/ ± 2 which hosts 1/2 CMEMs would have a plateau or dip in differential conductance measurements, respectiv...[ Read more ]

In this thesis we study three examples, where novel superconducting properties all arise from normal state electronic wave functions.

In Chapter 2, we study chiral Majorana edge modes (CMEMs) in a quantum anomalous hall/superconductor hybrid system. CMEM is predicted to induce an unique half quantized plateau as its transport signature[1, 5, 6]. This was recently found in the experiments[2]. However, it was argued that without Majorana, disorder could also induce such signature[3, 7]. Here we propose to use local tunneling spectroscopy to directly probe the edge state of the hybrid system. We use Recursive Green’s Function to show that for topological phase with Chern number N = ±1/ ± 2 which hosts 1/2 CMEMs would have a plateau or dip in differential conductance measurements, respectively. We also compare the feature between the model simulation with recent experimental findings.

In Chapter 3, we consider superconductivity in multifold fermion metals. Taking Li₂Pd₃B and Li₂Pt₃B as examples, we find a large number of unconventional degenerate points, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in Li₂Pd₃B, originating from the nontrivial band topology are found. Importantly, it has been shown experimentally that Li₂Pd₃B and Li₂Pt₃B are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest that Li₂Pd₃B is a conventional s-wave superconductor or DIII class topological superconductor with Majorana surface states. Li₂Pt₃B, being gapless, is likely to be a nodal topological superconductor with dispersionless surface Majorana modes. We further identify several other noncentrosymmetric superconductors, which serve as platforms for investigating the interplay between superconductivity and topologically nontrivial Fermi surfaces.

In Chapter 4, we study fractal superconductivity in a 2D Ando model with Bardeen-Cooper-Schrieffer (BCS) superconductivity. Multifractal metal/insulator regions in the normal state are first identified by studying the two-eigen correlation function. With added superconductivity, it is found that fractality in normal state gives rise to fractal superconductivity between homogeneous and granular case. With an enhanced mean pairing amplitude and multifractal statistics, it is shown that fractal superconductivity can be recognized by a convolutional neural network.