Real-Space Green's Function Approach for Acceptor States: Anisotropic Effects and Orbital Magnetism

We present a real-space Green's functions formalism to investigate acceptor states in bulk semiconductors with inversion symmetry. Using a 4x4 Luttinger-Kohn Hamiltonian, our model goes beyond the conventional spherical approximation by incorporating anisotropic effective masses, offering a more accurate description of valence band mixing between heavy and light holes. This refinement is critical for systems where non-spherical symmetry significantly influences electronic behavior, as is the case in acceptor-based qubits in materials like silicon.

Our results emphasize the importance of anisotropic mass effects in shaping the interactions between hole states and nearby impurities. Additionally, we calculate the orbital magnetism generated by spin-correlated, dissipationless circulating currents around spin defects. The spatial structure of the acceptor's orbital magnetic moment plays a key role in its coupling to nearby rapidly oscillating fields, such as those generated by nuclear spins. This has direct implications for the spin dynamics and coherent control of acceptor-bound hole states, offering new strategies for enhancing the performance of qubits based on these localized defects.

The formalism easily extends to explore more complex impurity arrangements and their interactions with local environmental factors—such as impurity clustering, strain, and external fields—which significantly affect the magnetic and electronic properties of acceptor states.