Spin defects and circulating currents in two-dimensional tight-binding models*

Single spins associated with point defects in solid-state materials are promising candidates for qubits and novel quantum spintronic devices for communication, sensing, and information processing [1] . To further understand the electronic interactions for qubit gates a microscopic theory of the spin-correlated currents associated with localized spins in semiconductors is needed. These spin-correlated currents are dissipationless and can be computed analytically for simple continuum models of quantum dots [2] as well as numerically for more complex geometries [3]. However similar results are not available for tight-binding descriptions of spin centers in semiconductors.

Here we extend on our previous work [4] and present a tight-binding theory of dissipationless circulating current induced by a spin defect in two-dimensional materials. An effective model for graphene which takes into account the spin-orbit interaction due to the influence of high-energy unoccupied d orbital is used to calculate circulating currents associated with the broken time-reversal symmetry caused by the local magnetic moment of local spin defects. The formalism can be extended to other two-dimensional lattice materials with stronger atomic spin-orbit coupling, such as the recently synthesized group IV two-dimensional germanene and silicene, thus opening up a possibility to be used at higher temperatures. In our previous work [4] we showed that the dissipationless circulating currents are significant and their anisotropic spatial structure can be detectable by current nanoscale magnetometry [5]. The spatial structure of the defect orbital magnetic moment affects its coupling to nearby rapidly oscillating fields from, e.g., nuclear spins, with implications for spin dynamics and coherent control of single spin states.

[1] Wolfowicz, G. et al., Nat. Rev. Mater. 6, 906 (2021)

[2] van Bree, J., Silov, A. Yu, Koenraad, P.M. and Flatté M.E., Phys. Rev. Lett. 112, 187201 (2014)

[3] van Bree, J., et al Phys. Rev. B 93, 035311 (2016)

[4] da Cruz, A.R. and Flatté, M.E., Phys. Rev. Lett. 131, 086301 (2023)

[5] Palm, M. L. , et al., Phys. Rev. Appl. 17, 054008 (2022)