Abstract
We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling at low electron density (namely the Fermi energy EF is lower than the energy ER of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy () decreases, due to two reasons. First, the density of states at increases as . Second, the particle–hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum (or ) channel with Chern number C = 4 (or ), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be ±1 and Majorana zero modes exist in the vortex cores.
Highlights
We study the superconducting instability and the resulting superconducting states in a twodimensional repulsive Fermi gas with Rashba spin-orbit coupling at low electron density
Novel systems with spin-orbit coupling (SOC) playing a significant role are found recently, such as topological insulators[1, 2], two-dimensional (2D) Rashba gases at interfaces of oxides[3, 4], Weyl semimetals[5] and SOC-induced Mott insulators[6] and other states in 5d series[7]; while in ultracold quantum gases, atoms are neutral, synthetic SOC can be generated by atom-light interaction
While in the low-density limit, Ekλ the Fermi energy is much smaller than Coulomb interaction and SOC energy, and Wigner crystalline phases are found[13], we focus o√n the weak-coupling limit uNtot 1 ( Ntot ∼ 1/ F as discussed below), where u is the short-range repulsion and Ntot is the total density of states (DOS) at Fermi energy
Summary
The superconductivity in repulsive systems was first studied by Kohn and Luttinger[33]. Due to the extremely low transition temperature, to observe such superconductivity is a formidable task. Assuming the bandwidth A is of order ∼ eV , and uNtot
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