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Electron exchange energy of neutral donors inside a quantum well
摘要： We calculated the exchange energy of a pair of donor-bound electrons placed in the middle of an in?nite quantum well (QW). In order to obtain this energy for any interdonor distance and for any QW thickness, we have ?rst adapted to a QW the method developed by Gor’kov and Pitaevskii [L. P. Gor’kov and L. P. Pitaevskii, Dokl. Akad. Nauk SSSR 151, 822 (1963)] for a three-dimensional (3D) distribution of donors, and calculated the asymptotic form of the exchange energy. Second we have calculated the exchange energy of a “helium atom” in a QW; and third, inspired by the interpolation procedure proposed by Ponomarev et al. [I.V. Ponomarev et al., Phys. Rev. B 60, 5485 (1999)], we have obtained an interpolated expression for any interdonor distance. The obtained exchange energy is written in units of effective hartree, and the distance between the donors, as well as the width of the QW, are expressed in units of effective Bohr radius. We calculated the exchange energy for some commonly studied semiconductor materials, and discussed also the relationship between the exchange energy and the spin relaxation time for a donor concentration close to the insulator-metal transition.
关键词： insulator-metal transition,exchange energy,donor-bound electrons,spin relaxation time,quantum well
更新于2025-09-10 09:29:36
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Spin–orbit coupling in silicon for electrons bound to donors
摘要： Spin–orbit coupling (SOC) is fundamental to a wide range of phenomena in condensed matter, spanning from a renormalisation of the free-electron g-factor, to the formation of topological insulators, and Majorana Fermions. SOC has also profound implications in spin-based quantum information, where it is known to limit spin lifetimes (T1) in the inversion asymmetric semiconductors such as GaAs. However, for electrons in silicon—and in particular those bound to phosphorus donor qubits—SOC is usually regarded weak, allowing for spin lifetimes of minutes in the bulk. Surprisingly, however, in a nanoelectronic device donor spin lifetimes have only reached values of seconds. Here, we reconcile this difference by demonstrating that electric ?eld induced SOC can dominate spin relaxation of donor-bound electrons. Eliminating this lifetime-limiting effect by careful alignment of an external vector magnetic ?eld in an atomically engineered device, allows us to reach the bulk-limit of spin-relaxation times. Given the unexpected strength of SOC in the technologically relevant silicon platform, we anticipate that our results will stimulate future theoretical and experimental investigation of phenomena that rely on strong magnetoelectric coupling of atomically con?ned spins.
关键词： silicon,spin relaxation,Spin–orbit coupling,donor-bound electrons,quantum information
更新于2025-09-04 15:30:14