Band Topology of Bismuth Quantum Films

The topological soliton in Peierls semimetal Sb

Sb is a three-dimensional Peierls insulator. The Peierls instability gives rise to doubling of the translational period along the [111] direction and alternating van der Waals and covalent bonding between (111) atomic planes. At the (111) surface of Sb, the Peierls condition is violated, which in theory can give rise to properties differing from the bulk. The atomic and electronic structure of the (111) surface of Sb have been simulated by density functional theory calculations. We have considered the two possible (111) surfaces, containing van der Waals dangling bonds or containing covalent dangling bonds. In the models, the surfaces are infinite and the structure is defect free. Structural optimization of the model containing covalent dangling bonds results in strong deformation, which is well described by a topological soliton within the Su-Schrieffer-Heeger model centered about 25 Å below the surface. The electronic states associated with the soliton see an increase in the density of states (DOS) at the Fermi level by around an order of magnitude at the soliton center. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements reveal two distinct surface regions, indicating that there are different surface regions cleaving van der Waals and covalent bonds. The DFT is in good agreement with the STM/STS experiments.

A closer look at how symmetry constraints and the spin-orbit coupling shape the electronic structure of Bi(111)

Fully relativistic density-functional-theory calculations of Bi(111) thin films are analyzed to revisit their two metallic surface-states branches. We first contrast these metallic branches with surface states arising at gaps in the valence band opened by the spin-orbit coupling (SOC). We find that the two metallic branches alongΓM‾do not overlap with the bulk band at the zone boundary,M. We show that the spin texture observed in such states cannot be traced to the lifting of Kramers' degeneracy. Instead, we track them to themj=±1/2-mj=±3/2SOC splitting, the potential anisotropy for in-plane and out-of-plane states, and the coupling between the opposite surfaces of a slab occurring nearM, which is driven by a spatial redistribution of the four metallic states composing the two metallic branches. Each of these branches appears to be non-degenerate at the tested surface, yet each is degenerate with another state of opposite spin at the other surface. Nevertheless, the four metallic states bear some contribution on both surfaces of the film because of their spatial redistribution nearM. The overlapping among these states nearM, afforded by their spatial redistribution on both surfaces, causes a hybridization that perpetuates the splitting between the two branches, makes the film's electronic structure thickness dependent nearM, extinguishes the magnetic moment of the metallic states avoiding the magnetic-moment discontinuity atM, and denies the need or expectancy of the metallic branches becoming degenerate atM. We propose that theoppositespin polarization observed for the two metallic branches occurs because the surface atoms retain their covalent bonds and thus cannot afford magnetic polarization. We show that the Rashba-splitting of the metallic states for inversion-asymmetric films does not have a fixed magnitude but can be tuned by changing the perturbation breaking inversion symmetry.

Emergent and Tunable Topological Surface States in Complementary Sb/Bi2Te3 and Bi2Te3/Sb Thin-Film Heterostructures

Epitaxial thin-film heterostructures offer a versatile platform for realizing topological surface states (TSSs) that may be emergent and/or tunable by tailoring the atomic layering in the heterostructures. Here, as an experimental demonstration, Sb and Bi₂Te₃ thin films with closely matched in-plane lattice constants are chosen to form two complementary heterostructures: Sb overlayers on Bi₂Te₃ (Sb/Bi₂Te₃) and Bi₂Te₃ overlayers on Sb (Bi₂Te₃/Sb), with the overlayer thickness as a tuning parameter. In the bulk form, Sb (a semimetal) and Bi₂Te₃ (an insulator) both host TSSs with the same topological order but substantially different decay lengths and dispersions, whereas ultrathin Sb and Bi₂Te₃ films by themselves are fully gapped trivial insulators. Angle-resolved photoemission band mappings, aided by theoretical calculations, confirm the formation of emergent TSSs in both heterostructures. The energy position of the topological Dirac point varies as a function of overlayer thickness, but the variation is non-monotonic, indicating nontrivial effects in the formation of topological heterostructure systems. The results illustrate the rich physics of engineered composite topological systems that may be exploited for nanoscale spintronics applications.

Evidence of magnetism-induced topological protection in the axion insulator candidate EuSn2P2

We unravel the interplay of topological properties and the layered (anti)ferromagnetic ordering in EuSn₂P₂, using spin and chemical selective electron and X-ray spectroscopies supported by first-principle calculations. We reveal the presence of in-plane long-range ferromagnetic order triggering topological invariants and resulting in the multiple protection of topological Dirac states. We provide clear evidence that layer-dependent spin-momentum locking coexists with ferromagnetism in this material, a cohabitation that promotes EuSn₂P₂ as a prime candidate axion insulator for topological antiferromagnetic spintronics applications.

Surface Modification and Subsequent Fermi Density Enhancement of Bi(111)

Defects introduced to the surface of Bi(111) break the translational symmetry and modify the surface states locally. We present a theoretical and experimental study of the 2D defects on the surface of Bi(111) and the states that they induce. Bi crystals cleaved in ultrahigh vacuum (UHV) at low temperature (110 K) and the resulting ion-etched surface are investigated by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) as well as spectroscopy (STS) techniques in combination with density functional theory (DFT) calculations. STS measurements of cleaved Bi(111) reveal that a commonly observed bilayer step edge has a lower density of states (DOS) around the Fermi level as compared to the atomic-flat terrace. Following ion bombardment, the Bi(111) surface reveals anomalous behavior at both 110 and 300 K: Surface periodicity is observed by LEED, and a significant increase in the number of bilayer step edges and energetically unfavorable monolayer steps is observed by STM. It is suggested that the newly exposed monolayer steps and the type A bilayer step edges result in an increase to the surface Fermi density as evidenced by UPS measurements and the Kohn-Sham DOS. These states appear to be thermodynamically stable under UHV conditions.