Class of topological phase transitions of Rashba spin-orbit coupled fermions on a square lattice

Abstract

Searching for the first topological superfluid (TSF) remains a primary goal of modern science. Here we study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling (SOC) in a normal Zeeman field. By imposing self-consistence equations at half filling, we find there are 3 phases: Band insulator ( BI ), Superfluid (SF) and Topological superfluid (TSF) with a Chern number C = 2. The C = 2 TSF happens in small Zeeman fields and weak interactions which is in the experimentally most easily accessible regime. The transition from the BI to the SF is a first order one due to the multi-minima structure of the ground state energy landscape. There is a new class of topological phase transition from the SF to the C = 2 TSF at the low critical field hc1, then another one from the C = 2 TSF to the BI at the upper critical field hc2. We derive effective actions to describe the two new classes of topological phase transitions, then use them to study the Majorana edge modes and the zero modes inside the vortex core of the C = 2 TSF near both hc1 and hc2, especially explore their spatial and spin structures. We find the edge modes decay into the bulk with oscillating behaviors and determine both the decay and oscillating lengths. We compute the bulk spectra and map out the Berry Curvature distribution in momentum space near both hc1 and hc2. We also elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. Experimental implications in both 2d non-centrosymmetric materials under a periodic substrate and cold atoms in an optical lattice are given.I.

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

“…Therefore, our proposal could provide an easier way of achieving higher Chern number superfluids via constructing non-trivial topology through orbital mixing. It frees up the usually challeng- ing requirements of previous works, such as multilayer structures [53,56], spin-orbit coupling, or other artificial gauge fields [54,55,57]. This mechanism would shed light on new possibilities for edge-mode engineering through fabrication of orbital-hybridized higher Chern number phases in both electronic solids and atomic gases.…”

“…It confirms that the tSF state satisfies the bulk-edge correspondence. We now discuss the sharp distinction between our scheme for realizing higher Chern number superfluids and that proposed in previous studies [53][54][55][56][57][58][59]. The conventional approach relies on higher partial wave pairing to achieve higher Chern number superfluidity.…”

Superfluid transition temperature and fluctuation theory of spin-orbit and Rabi coupled fermions with tunable interactions

“…Thus, while the holy grail of a full optical simulation of QCD remains years in the future, there do exist notable analogies between quark matter and cold atomic systems (e.g., non-Abelian fields, evolution between strongly and weakly coupled limits) within near-term experimental reach [32][33][34][35]. Investigations of spin-orbit coupled ultracold gases have also included optical lattices [36][37][38][39][40][41][42][43][44][45], thus enlarging the number of possible physical systems that can be accessible experimentally.…”

Topological semimetal and superfluid of s-wave interacting fermionic atoms in an orbital optical lattice

“…bers are preferable in achieving more efficient edge channel transport. Therefore, our scheme would shed light on the new possibilities for edge-mode engineering through the fabrication of topological phases in both electronic solid state and atomic gas matter [46][47][48][49][50].…”