Electrons in a non-centrosymmetric crystal experience effective Zeeman fields in momentum space, known as spin-orbit coupling(SOC) fields. Unlike usual Zeeman fields, these SOC fields pin the spins of electrons with opposite momentum to opposite directions. In this thesis, we present theoretical studies on two types of SOC fields, the Rashba SOC and the Ising SOC, with particular emphasis on their roles in creating novel superconducting states and Berry phase effects.

In Chapter 2, we discuss the origin of a zero bias peak(ZBP) and a conductance plateau recently found in a topological insulator(TI)/superconductor junction. By considering realistic experimental conditions, our theoretical calculations reveal that the ZBCP/conductance plateau originates from weak/strong supercond...[ Read more ]

Electrons in a non-centrosymmetric crystal experience effective Zeeman fields in momentum space, known as spin-orbit coupling(SOC) fields. Unlike usual Zeeman fields, these SOC fields pin the spins of electrons with opposite momentum to opposite directions. In this thesis, we present theoretical studies on two types of SOC fields, the Rashba SOC and the Ising SOC, with particular emphasis on their roles in creating novel superconducting states and Berry phase effects.

In Chapter 2, we discuss the origin of a zero bias peak(ZBP) and a conductance plateau recently found in a topological insulator(TI)/superconductor junction. By considering realistic experimental conditions, our theoretical calculations reveal that the ZBCP/conductance plateau originates from weak/strong superconducting proximity effects in the bulk/surface states of the TI. Our study provides solid evidence for a sizable pairing gap induced in the surface states, establishing the primary condition for realizing Majorana fermions.

In Chapter 3-4, we study the special property of Cooper pairs in the recently discovered Ising superconductors in superconducting transition-metal dichalcogenides(TMDs). We point out that the Ising SOC in TMDs generates equal-spin Cooper pairs in the superconducting states, with their spins pointing to in-plane directions. Importantly, placing a half-metal wire with in-plane spin-polarizations on top of an Ising superconductor results an effective Kitaev chain supporting Majorana end states. Direct ways to probe equal-spin Cooper pairs in half-metal lead/Ising superconductor junctions are also discussed.

Chapter 5-6 are devoted to our recent finding of a new type of valley Hall effect in TMDs with Rashba SOCs, called spin valley Hall effects. Different from conventional valley Hall effects due to inversion breaking in orbital degrees of freedom, the spin valley Hall effect originates from combined effects of Rashba and Ising SOCs that break inversion symmetry in spin degrees of freedom. Detection scheme for spin valley Hall effects using Kerr effects are proposed.