Atomic engineering of donor-based spin qubits results in long lifetimes and high-fidelity two-qubit readout.
The energy spectrum of spin-orbit coupled states of individual sub-surface boron acceptor dopants in silicon have been investigated using scanning tunneling spectroscopy (STS) at cryogenic temperatures. The spatially resolved tunnel spectra show two resonances which we ascribe to the heavyand light-hole Kramers doublets. This type of broken degeneracy has recently been argued to be advantageous for the lifetime of acceptor-based qubits [Phys. Rev. B 88 064308 (2013)]. The depth dependent energy splitting between the heavy-and light-hole Kramers doublets is consistent with tight binding calculations, and is in excess of 1 meV for all acceptors within the experimentally accessible depth range (< 2 nm from the surface). These results will aid the development of tunable acceptor-based qubits in silicon with long coherence times and the possibility for electrical manipulation. Meanwhile, rapid progress in scanning tunnelling microscopy (STM) based lithography has paved the way towards atomically precise placement of dopant atoms [3]. While phosphorous donors in silicon remains among the most compelling candidates for dopant-based quantum computing to date, other impurity systems have recently drawn considerable attention. In particular, boron acceptors could provide a pathway towards electrically addressable spin-qubits via spin-orbit coupling [4] analogues to electrically driven spin manipulation in gate defined electron [5,6] and hole [7] quantum dots in III-V materials. Compared with other spin-orbit qubits, acceptors in silicon have several advantages: gates are not required for hole confinement and each qubit experiences the same confinement potential; furthermore the holespin decoherence, due to the nuclear spin bath, can be effectively eliminated by isotope purification of the silicon host.Unlike the ground state of donor-bound electrons in silicon, the acceptor-bound hole ground state is four-fold degenerate, reflecting the heavy-hole/light-hole degeneracy of the silicon valence band. Recent theoretical work has suggested the regime of long lifetimes for acceptors with a four-fold degenerate ground state is only accessible for small magnetic fields [4]. Interestingly, this work also suggests that symmetry breaking due to strain or electric fields could yield longer-lived qubits based on acceptor-bound holes at higher magnetic fields. The symmetry breaking perturbation of biaxial strain [4] renders the lowest two (qubit) levels within a Kramers degenerate pair, such that they do not directly couple to electric fields. Quantum confinement could provide a similar form of protection. In this Letter we demonstrate that the symmetry-reduction of a potential boundary renders the lowest two levels Kramers degenerate and heavy-hole like. Recent transport spectroscopy studies of an individual acceptor embedded in nano-scale transistors have shown that for acceptors ∼10 nm away from an interface the bulk-like four-fold degeneracy is maintained [8]. Here we demonstrate that the presence of a nearby interface (<2 nm) lift...
An atomistic method of calculating the spin-lattice relaxation times (T1) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of T1 with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as B 5 in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wavefunctions in nanostructures, T1 times can be varied by orders of magnitude.PACS numbers: 71.55. Cn, 03.67.Lx, 85.35.Gv, 71.70.Ej Due to the extremely long spin coherence times, in some cases exceeding seconds [1,2], and the existing industrial fabrication infrastructure, silicon is well-suited to be an outstanding platform for semiconductor quantum computer technology [3][4][5][6][7][8]. Qubits hosted by donors in silicon [3] have some added advantages as they are readily available few-electron systems with a rich electronic structure and can form identical qubits [9]. In the last few years, several key experimental milestones have been achieved in dopant based quantum computing, including the demonstration of electron [10] and nuclear [11] spin qubits, single spin read-out and initialization [12,13], and the observation of spin blockade and exchange towards two qubit coupling [14,15]. Recent advances in Scanning Tunneling Microscope (STM) lithography has enabled placement of single donors with atomic scale precision [16], with the result that various functional units such as quantum wires [17], single electron transistors (SET) [13,18], and quantum dots [19] can all be realized in-plane with densely packed donor islands. The STM approach provides the fabrication precision needed to develop test-bed quantum chips for the demonstration of quantum algorithms in a solid-state quantum computer.One of the two most important timescales for a spin qubit is the spin-lattice relaxation time (T 1 ). Recent experiments have measured T 1 times in a single donor and in a few-donor cluster indicating shorter T 1 times in the latter [12,13]. Previous theoretical works exist in the literature qualitatively describing two different spin relaxation mechanisms in a bulk donor system [20,21]. However, a comprehensive quantitative theory which combines all the different mechanisms under a unified framework and accounts for the local inhomogeneous environment of the donors in a realistic nanostructure is still lacking. Moreover, there is no theoretical work yet to explain the measured T 1 times in densely packed donor clusters. In this letter, we present a comprehensive approach to compute the T 1 times in single donors and...
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 (T 1) 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.
Controlling electron tunneling is of fundamental importance in the design and operation of semiconductor nanostructures such as field effect transistors (FETs) and quantum computing device architectures. The exponential sensitivity of tunneling with distance requires precise fabrication techniques to engineer the desired device dimensions to achieve the appropriate tunneling resistances/tunnel rates. This is particularly important for high fidelity spin readout and qubit exchange in quantum computing architectures. Here, it is shown by combining precision fabrication techniques with accurate atomistic modeling, predictive device design criteria are achieved at atomic length scales. Such a tool is useful when devices become more complex or have arbitrary shapes/geometries. In particular, in this study, atomic precision patterning of monolayer degenerately phosphorus-doped silicon tunnel junctions patterned by scanning tunnelling microscopy lithography and tight-binding nonequilibrium Green's function (TB-NEGF) modeling is combined to describe the dependence of tunnel junction resistance R T on junction length. An agreement with experiment to within a factor of 2 over 4 orders of magnitude in R T is found, and this model allows to accurately determine the barrier height V 0 = 57.5 ± 1 meV and lateral seam s xy = 0.39 ± 0.01 nm in these nanoscale junctions. This study confirms the use of the TB-NEGF formalism to accurately model highly doped atomically precise tunnel junctions in silicon. Further applications of this model will enable improved device performance at the nanoscale.
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