Spin-orbit coupling effects on the stability of two competing structures in Pb/Si(111) and Pb/Ge(111)

TL;DR

This study uses first-principles DFT calculations to show that spin-orbit coupling can reverse the relative stability of two Pb/Si(111) and Pb/Ge(111) structures, highlighting SOC's role in surface state properties.

Contribution

It reveals how spin-orbit coupling influences the stability and electronic properties of Pb surface structures, a novel insight into surface state behavior.

Findings

SOC reverses the stability order of H3 and T4 structures

SOC induces larger Rashba spin splitting in H3

Energy barriers suggest coexistence of structures at low temperatures

Abstract

Using first-principles density-functional theory (DFT) calculations, we investigate the 4/3-monolayer structure of Pb on the Si(111) or Ge(111) surface within the two competing structural models termed the H$_3$ and T$_4$ structures. We find that the spin-orbit coupling (SOC) influences the relative stability of the two structures in both the Pb/Si(111) and Pb/Ge(111) systems: i.e., our DFT calculation without including the SOC predicts that the T$_4$ structure is energetically favored over the H$_3$ structure by ${\Delta}E$ = 25 meV for Pb/Si(111) and 22 meV for Pb/Ge(111), but the inclusion of SOC reverses their relative stability as ${\Delta}E$ = $-$12 and $-$7 meV, respectively. Our analysis shows that the SOC-induced switching of the ground state is attributed to a more asymmetric surface charge distribution in the H$_3$ structure, which gives rise to a relatively larger Rashba spin splitting of surface states as well as a relatively larger pseudo-gap opening compared to the T$_4$ structure. By the nudged elastic band calculation, we obtain a sizable energy barrier from the H$_3$ to the T$_4$ structure as ${\sim}$0.59 and ${\sim}$0.27 eV for Pb/Si(111) and Pb/Ge(111), respectively. It is thus likely that the two energetically competing structures can coexist at low temperatures.