Two-band Luttinger liquid with spin-orbit coupling: Applications to monatomic chains on surfaces

Abstract

Recently, monatomic chains on surfaces have been synthesized that show evidence of Luttinger liquid physics. The experimental data point to a dispersion along the chain with four Fermi points. Here we investigate a general low-energy effective Hamiltonian for such a two-band model where SU(2) spin symmetry is broken but time-reversal symmetry persists, as is expected due to the surface geometry. Spin-orbit coupling gives rise to an energy scale ${\ensuremath{\varepsilon}}_{\text{SO}}$ much smaller than the Fermi energy ${\ensuremath{\varepsilon}}_{F}$ and to spin-nonconserving scattering processes. We derive the generic phase diagram at zero temperature as well as an effective phase diagram at temperatures ${\ensuremath{\varepsilon}}_{\text{SO}}<T\ensuremath{\ll}{\ensuremath{\varepsilon}}_{F}$. For the part of the phase diagram where a Luttinger liquid is found to be stable, the density of states and the spectral function are calculated and discussed in relation to the experimental data.