Transition-metal dopants in tetrahedrally bonded semiconductors: symmetry and exchange interactions from tight-binding models

It has become increasingly apparent that the future of electronic devices can and will rely on the functionality provided by single or few dopant atoms. The most scalable physical system for quantum technologies, i.e. sensing, communication and computation, are spins in crystal lattices. Diamond is an excellent host crystal offering long room temperature spin coherence times and there has been exceptional experimental work done with the nitrogen vacancy center in diamond demonstrating many forms of spin control. Transition metal dopants have additional advantages, large spin-orbit interaction and internal core levels, that are not present in the nitrogen vacancy center. This work explores the implications of the internal degrees of freedom associated with the core d levels using a tight-binding model and the Koster-Slater technique. The core d levels split into two separate symmetry states in tetrahedral bonding environments and result in two levels with different wavefunction spatial extents. For 4d semiconductors, e.g. GaAs, this is reproduced in the tight-binding model by adding a set of d orbitals on the location of the transition metal impurity and modifying the hopping parameters from impurity to its nearest neighbors. This model does not work in the case of 3d semiconductors, e.g. diamond, where there is no physical reason to drastically alter the hopping from 3d dopant to host and the difference in wavefunction extent is not as pronounced. In the case of iron dopants in gallium arsenide the split symmetry levels in the band gap are responsible for a decrease in tunneling current when measured with a scanning tunneling microscope due to interference between two elastic tunneling paths and comparison between wavefunction measurements and tight-binding calculations provides information regarding material parameters. In the case of transition metal dopants in diamond there is less distinction between the symmetry split d levels. When considering pairs of transition metal dopants an important quantity is the exchange interaction between the two, which is a measure of how fast a gate can be operated between the pair and how well entanglement can be created. The exchange interaction between pairs of transition metal dopants has been calculated in diamond for several directions in the (110) plane, and for select transition metal dopants in gallium arsenide. In tetrahedral semiconductors transition metal dopants provide an internal degree of freedom due to the symmetry split d levels and this included functionality makes them special candidates for single spin based quantum technologies as well as physical systems to learn about fundamental physics.