I discuss the simultaneous effects of Zeeman and spin-orbit fields during

the evolution from BCS to BEC superfluidity for ultra-cold fermions.I focus on spin-orbit couplings with equal Rashba and Dresselhaus strengths, and show that topological phase transitions of the Lifshitz class occur through the emergence of Majorana and/or Dirac fermions as Zeeman and

spin-orbit fields are varied. Topological quantum phase transitions in superfluids with non-s-wave order parameters have been conjectured theoretically for p-wave and d-wave systems for many years, but never observed experimentally due to the absence of tunable parameters. However, Zeeman or spin-orbit fields and interactions can be tuned in the context of ultra-cold atoms and allow for the visitation of several different phases. For systems with zero Zeeman field, the evolution from BCS to BEC superfluidity in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges. In contrast, for finite Zeeman fields, spin-orbit coupling induces a triplet component in the order parameter that produces nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally, a fully gapped phase exists, where a crossover from indirect to direct gap occurs. For spin-orbit couplings with equal Rashba and Dresselhaus strengths the nodal quasi-particles are Dirac fermions that live at and in the vicinity of rings of nodes.Transitions from and to nodal phases can occur via the emergence of zero-mode Majorana

fermions at phase boundaries, where rings of nodes of Dirac fermions annihilate. Lastly, I characterize different phases via spectroscopic and thermodynamic properties and conclude that Lifshitz is the “Lord of the Rings”.

       报告人简介：Prof. Carlos Sa de Melo received his Ph.D. at Stanford University

in the field of Condensed Matter Physics under the supervision of Prof. Sebastian Doniach. He was a post-doctoral fellow at the National Science Foundation Science and Technology Center for

Superconductivity in Illinois and worked under the supervision of Dr. Alexei Abrikosov (Nobel Laureate in Physics – 2003). He is currently a faculty member at the Georgia Institute of Technology, where he conducts research on topics involving ultra-cold atoms and molecules. He is best known for his works on the evolution from BCS to BEC superfluidity, low-dimensional superconductors in high magnetic fields, and the interplay of magnetism and superconductivity at the nanometer scale.