Electronic States, Spin-Orbit Coupling and Magnetism in Germanium 60° Dislocations

Abstract

Defects in semiconductors have recently attracted renewed interest owing to their potential in novel quantum applications. Here we investigate the electronic and magnetic properties induced by 60° dislocations in Ge. Using large-scale DFT calculations, we determine the band structure for both the shuffle and glide sets in their lowest-energy configurations. We also perform charged-defect calculations to aid in the interpretation of complex photoluminescence spectra observed in epitaxial Ge layers. The band structure for the shuffle set reveals defect-induced dispersive bands localized within the band gap near the Γ point, whereas for the glide set, we observe strong overlap with the conduction band. Defect-induced band splitting evident away from Γ reveals Rashba-Dresselhaus spin-orbit coupling, an effect previously reported only for screw dislocations. Remarkably, we find evidence that specific dislocation arrangements can stabilize antiferromagnetic ordering with sizable local magnetic moments and considerable exchange splitting between opposite spin states. These results uncover rich physics in Ge dislocations through the combination of spin-orbit coupling and magnetic ordering, potentially enabling novel defect-based functionalities in Ge devices.

Figures (6)

• Figure 1: a) S3 shuffle and b) glide core reconstructions of the 60° dislocation with a planar view normal to the dislocation line. Core atoms are highlighted in orange.
• Figure 2: Band structure and partial density of states (PDOS) of the defective supercell, projected onto the dislocation-core atoms. The band structures are plotted along the $-Z$ -- $\Gamma$ -- $Z$ path, $Z$ being a high symmetry point in the reciprocal space of the supercell, with relative coordinates $\pm Z = (0,0,\pm0.5)$. Panels (a) and (b) show the unfolded band structures projected onto the shuffle S3 dislocation core atoms and glide dislocation core atoms, respectively. The color scale represents the combined weight of the band unfolding and the projection onto the dislocation core atoms, obtained through the normalized local density of states. The gray shaded region indicates the bulk Ge bandgap, with the valence-band maximum set to 0 eV. In panel (b), the inset shows a magnified view of the region delimited by the black box, where the energy splitting of the glide dislocation bands has been enhanced by a factor of three to improve visibility.
• Figure 3: a) Charge density (yellow surfaces) localization on the shuffle S3 core; b), c) and d) Spin-resolved band structure of the mixed dislocation dipole. Black solid lines denote bulk states, while dotted lines correspond to the shuffle S3 states. The color scale represents the normalized expectation values of the spin projections $S_x$ (panel b), $S_y$ (panel c), and $S_z$ (panel d)
• Figure 4: Bandstructure of the nonmagnetic 60° shuffle S3 dislocation dipole. The green and purple solid lines denote two pairs of degenerate bands associated with the dislocation cores.
• Figure 5: Spin resolved band structures of the antiferromagnetic 60° shuffle S3 dislocation dipole. Dislocation bands are shown as circles while the bulk states are represented by the black curves. Color code represents the expectation values of the spin projections for the $S_x$ spin projections (panel a), $S_y$ spin projection (panel b) and $S_z$ spin projection (panel c), with z parallel to the dislocation line. The corresponding (directional) spin densities are shown below. Blue (red) color indicates the negative (positive) isovalues in the isosurface plots.