THESIS
2017

xvi, 136 pages : illustrations ; 30 cm

**Abstract**
Superconductivity has been one of the central topics in condensed matter physics since its discovery.
The superconducting phase of a superconductor, characterized by its zero resistance and perfect
diamagnetism, is due to the formation of Cooper pairs. Conventional Cooper pairs are spin-singlet.
In this thesis, we study the novel properties of the superconducting phases of two-dimensional transition
metal dichalcogenides and of Nb doped topological insulator Bi

_{2}Se

_{3}, where unconventional
Cooper pairs can be found. Thus Majorana zero modes can be realized in such superconductors
which have potential applications in quantum computations.

In Chapter 1, important aspects of superconductivity are discussed. The general phenomenological
theories such as London theory, Ginzburg-Landau t...[

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Superconductivity has been one of the central topics in condensed matter physics since its discovery.
The superconducting phase of a superconductor, characterized by its zero resistance and perfect
diamagnetism, is due to the formation of Cooper pairs. Conventional Cooper pairs are spin-singlet.
In this thesis, we study the novel properties of the superconducting phases of two-dimensional transition
metal dichalcogenides and of Nb doped topological insulator Bi

_{2}Se

_{3}, where unconventional
Cooper pairs can be found. Thus Majorana zero modes can be realized in such superconductors
which have potential applications in quantum computations.

In Chapter 1, important aspects of superconductivity are discussed. The general phenomenological
theories such as London theory, Ginzburg-Landau theory and group theory are formulated,
and the microscopic Bardeen-Cooper-Schrieffer theory is briefly introduced. At last topological
superconductivity in both gapped and nodal systems is discussed in terms of specific examples.

In Chapter 2, we present experimental evidence of so-called Ising superconductivity found in
gated molybdenum disulfide, and explain the experimental data of enhanced in-plane upper critical
fields.

In Chapter 3, following Chapter 2, we give a systematic analysis and calculation on the in-plane
upper critical fields of monolayer transition metal dichalcogenides, including the low-temperature
effect and impurity effect. Due to the crystal structures, transition metal dichalcogenides have intrinsic
spin-orbit couplings called Ising spin-orbit couplings which only couple to the electron spin
component along out-of-plane direction. In the superconducting phase, Ising spin-orbit couplings
will induce spin-triplet Cooper pairs formed by equal-spin electrons with in-plane polarization,
which are robust against in-plane magnetic fields, and hence in-plane upper critical fields of monolayer
transition metal dichalcogenides are enhanced.

In Chapter 4, we firstly propose an alternative method to detect Ising superconductivity, namely
to detect spin-triplet Cooper pairs through spin-resolved tunneling experiments. Then we show that
spin-triplet Cooper pairs can be induced into half-metal wires on top of monolayer transition metal
dichalcogenides and Majorana fermions can hence be realized at the ends of the wires.

In Chapter 5, the superconducting phases niobium doped topological insulator bismuth selenides
are studied through a microscopic model Hamiltonian. Two types of superconducting
phases, the nematic phases breaking in-plane three-fold rotation symmetry and chiral phases breaking
time-reversal symmetry, can be found. The finite magnetic moments of Nb ions can polarize
Cooper pairs and thus enlarge the phase space of chiral phases. Importantly, the chiral phase is
found to be the topological Weyl superconducting phase supporting Majorana arc states on the
surfaces of this system.

Chapter 6 is the conclusion chapter and my publication list is also included.

Appendices A, B and C contain the details of experiments, data fitings and theoretical derivations
in previous chapters.

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