THESIS
2022
1 online resource (xvi, 92 pages) : illustrations (some color)
Abstract
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...[
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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
Li
2Pd
3B and Li
2Pt
3B 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 Li
2Pd
3B, originating from the nontrivial band topology are found.
Importantly, it has been shown experimentally that Li
2Pd
3B and Li
2Pt
3B are fully gapped
and gapless superconductors, respectively. By analyzing the possible pairing symmetries,
we suggest that Li
2Pd
3B is a conventional s-wave superconductor or DIII class topological
superconductor with Majorana surface states. Li
2Pt
3B, 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.
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