Abstract
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 field induced SOC can dominate spin relaxation of donor-bound electrons. Eliminating this lifetime-limiting effect by careful alignment of an external vector magnetic field 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 confined spins.
Highlights
Individual spins confined to solids are attracting considerable interest due to their potential as quantum bits in future quantum information processors.1,2 In particular, electron spins bound to phosphorus donors have demonstrated exceptionally long spin life (T1) and coherence (T2) times, both of order seconds in isotopically purified 28Si.3 Recent demonstrations of highfidelity4 spin readout,5 manipulation,6 and controllable exchange,7,8 promise the realisation of scalable donor-based quantum computing.2,9One reason for the extremely long spin lifetimes of electrons in silicon is their inherently weak spin–orbit coupling (SOC), which has been found to dominate spin relaxation in inversion asymmetric polar semiconductors, such as GaAs.10–12 In the absence of surfaces and interfaces,13,14 SOC for electrons in silicon is usually considered negligible15 due to its small atomic number and large band gap
We show that careful design of the local electromagnetic environment in nanoelectronic devices allows us to eliminate these lifetime-limiting effects—an important factor in designing future qubit architectures—and allow us to demonstrate the bulklimit of donor spin lifetimes within a nanoelectronic device for the first time
To explain the observed spin-relaxation anisotropy, we turn to the full effective mass Hamiltonian for donor electron spins in an electric field, expanded up to fourth order in perturbation theory29
Summary
Individual spins confined to solids are attracting considerable interest due to their potential as quantum bits (qubits) in future quantum information processors. In particular, electron spins bound to phosphorus donors have demonstrated exceptionally long spin life (T1) and coherence (T2) times, both of order seconds in isotopically purified 28Si. Recent demonstrations of highfidelity spin readout, manipulation, and controllable exchange, promise the realisation of scalable donor-based quantum computing.. For donor-bound electrons SOC enters spinlattice relaxation only as a weak time-dependent perturbation of spin–valley states via deformation potential phonons.. For donor-bound electrons SOC enters spinlattice relaxation only as a weak time-dependent perturbation of spin–valley states via deformation potential phonons.16–18 This has resulted in extended spin lifetimes, exceeding those in GaAs by more than an order of magnitude.. We report the presence of such electric field induced magnetoelectric coupling for the first time, using measurements of electron spin-relaxation rates of an individual. Demonstrating its impact on spin relaxation in the controlled electromagnetic environment of an atomically engineered nanoelectronic device, we solve a long-standing mystery as per why spin lifetimes in silicon devices (~sec) have been found substantially shorter, compared to those in bulk (~min).. Demonstrating its impact on spin relaxation in the controlled electromagnetic environment of an atomically engineered nanoelectronic device, we solve a long-standing mystery as per why spin lifetimes in silicon devices (~sec) have been found substantially shorter, compared to those in bulk (~min). we show that careful design of the local electromagnetic environment in nanoelectronic devices allows us to eliminate these lifetime-limiting effects—an important factor in designing future qubit architectures—and allow us to demonstrate the bulklimit of donor spin lifetimes within a nanoelectronic device for the first time
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