Engineering Topological Nodal Line Semimetals in Rashba Spin-Orbit Coupled Atomic Chains

In this paper, we study an atomic chain in the presence of modulated charge potential and modulated Rashba spin-orbit coupling (RSOC) of equal periods. We show that for commensurate periodicities, λ = 4 n with integer n, the three-dimensional synthetic space obtained by sliding the two phases of the charge potential and RSOC features a topological nodal-line semimetal protected by an anti-unitary particle-hole symmetry. The location and shape of the nodal lines strongly depend on the relative amplitude between the charge potential and RSOC.