We study the effects of Rashba splitting on two-leg ladders with weakly screened Coulomb interactions. Past research has shown that in this class of systems the two backscattering channels with the largest amplitude favor ordering of canonically conjugated collective fields which effectively renders the system gapless. Here we show that the band-dependent Rashba spin-orbit interaction breaks this symmetry of scattering channels, leading to a new fixed point with yet unexplored instabilities. Exotic properties can be found, for instance, the mixing of the magnetism with the charge-density wave. We then investigate the physical consequences of this partial spectral gap opening. We find a striking difference in signatures of order observed in single-particle (spectral-function) and two-body (susceptibilities) experimental probes. We conclude this paper by comparing theoretical and experimental results obtained on the Au-Si(553) platform. In STM measurements, we identify the lowest-lying soliton excitation as a hallmark of the gapped sine-Gordon model in an apparently metallic system. This implies the presence of partial spectral gaps opening. Furthermore, by ARPES measurements we confirm the expected temperature dependence of the outer bands backfolding. These two findings constitute the experimental evidence of the many-body physics proposed here.

• Received 29 April 2021
• Revised 22 September 2021
• Accepted 11 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.205407