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 Bi₂Se₃, 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...[ Read more ]

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 Bi₂Se₃, 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.