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We investigate the 1/3 monolayer $\alpha$-Pb/Si(111) surface by scanningtunneling spectroscopy (STS) and fully relativistic first-principlescalculations. We study both the high-temperature $\sqrt{3}\times\sqrt{3}$ andlow-temperature $3\times 3$ reconstructions and show that, in both phases, thespin-orbit interaction leads to an energy splitting as large as $25\%$ of thevalence-band bandwidth. Relativistic effects, electronic correlations andPb-substrate interaction cooperate to stabilize a correlated low-temperatureparamagnetic phase with well-developed lower and upper Hubbard bands coexistingwith $3\times3$ periodicity. By comparing the Fourier transform of STSconductance maps at the Fermi level with calculated quasiparticle interferencefrom non-magnetic impurities, we demonstrate the occurrence of two largehexagonal Fermi sheets with in-plane spin polarizations and oppositehelicities.

Chiral spin texture in the charge-density-wave phase of the correlated metallic Pb/Si(111) monolayer