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

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 ∆E = 25 meV for Pb/Si(111) and 22 meV for Pb/Ge (111), but the inclusion of SOC reverses their relative stability as ∆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 ∼0.59 and ∼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.

Spin-resolved band structure of a densely packed Pb monolayer on Si(111)

“…4. The band map reveals again the S1-surface state, which crosses E F at k x ≈ 0.4Å −1 and forms additionally a small electron pocket around E F at k x ≈ 0.75Å −1 in full agreement with recent DFT calculations [12,13]. Compared to the DFT calculations, the chemical potential in our experiment is shifted by around 130 meV, thus, the S1 state crosses E F three times between the and the M points.…”

“…In the following, we will first discuss the surface bands and their spin character. These findings will be correlated with recent DFT calculations [12,13].…”

“…Albeit atomic details about the structure are intensively studied, less attention was paid to the electronic band structure. Moreover, the interpretation of former angle-resolved photoemission spectroscopy (ARPES) band structure measurements disagree with recent calculations [4,12,13].…”

“…The progression of the S2 state is taken from Ref. [13] and is in good agreement with the experiment. The Rashba splitting of S1 is k x = 0.04Å −1 .…”

“…Due to the threefold rotational symmetry of the ( √ 3× √ 3) reconstruction, the S1* feature is induced by the projection of the (reentered) S1 state of the equivalent K √ 3 M √ 3 directions [12,13]. Most remarkably, the intensity feature located at the K √ 3 point with a binding energy of 0.4 eV is not the minimum of a surface band that crosses E F , but belongs to the second spin-split surface band S2 that is fully occupied.…”