Gate-induced<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>-factor control and dimensional transition for donors in multivalley semiconductors

Rahman, Rajib; Park, Seung H.; Boykin, Timothy B.; Klimeck, Gerhard; Rogge, Sven; Hollenberg, Lloyd C. L.

doi:10.1103/physrevb.80.155301

Cited by 49 publications

(54 citation statements)

References 34 publications

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“…This effect was partially anticipated by earlier ab initio treatments in Ref. 22, but we improve those predictions with quantitative matching of experiments, and extend them to all donors with a more clear understanding of the underlining physics.…”

Section: Introductionsupporting

confidence: 66%

“…The relative importance of these two kinds of orbital coupling can be preliminarily assessed by comparing the energy differences between the respective unperturbed states to be coupled: the inter-band energy difference involved in the single-valley mechanism is two orders of magnitude larger than the E T 2 − E A1 splitting 43 , which is relevant for valley repopulation. It is thus predicted that the g-factor shifts will be much larger when the valley repopulation effect plays a role, and this has been indeed verified by ab initio calculations in Ge:P 22 . Thus, we limit ourselves to the calculation of the more important spin-orbit Stark shifts induced by valley repopulation, especially since approach relies on a single band approximation which is unable to account for the single valley g-factor shifts.…”

Section: B Spin-orbit Stark Shiftsmentioning

confidence: 63%

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Quantum gates with donors in germanium

Pica

Lovett

2016

Phys. Rev. B

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The possibility of quantum computing with spins in germanium nanoscale transistors has recently attracted interest since it promises highly tuneable qubits that have encouraging coherence times. We here present the first complete theory of the orbital states of Ge donor electrons, and use it to show that Ge could have significant advantages over silicon in the implementation of a donor-based quantum processor architecture. We show that the stronger spin-orbit interaction and the larger electron donor wave functions for Ge donors allow for greater tuning of the single qubit energy than for those in Si crystals, thus enabling a large speedup of selective (local) quantum gates. Further, exchange coupling between neighboring donor qubits is shown to be much larger in Ge than in Si, and we show that this greatly relaxes the precision in donor placement needed for robust two-qubit gates. To do this we compare two statistical distributions for Ge:P and Si:P pair couplings, corresponding to realistic donor implantation misplacement, and find that the spin couplings in Ge:P have a 33% chance of being within an order of magnitude of the largest coupling, compared with only 10% for the Si:P donors. This allows fast, parallel and robust architectures for quantum computing with donors in Ge.

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Section: Introductionsupporting

confidence: 66%

Section: B Spin-orbit Stark Shiftsmentioning

confidence: 63%

Quantum gates with donors in germanium

Pica

Lovett

2016

Phys. Rev. B

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“…19), as well as the electronic g factor (g e (E)) (ref. 20), has been calculated within the tight-binding formalism (see Methods). We found that the Stark shift of the g factor is at least an order of magnitude weaker for the 2-P cluster than for 1-P (see Supplementary Note 2).…”

Section: Discussionmentioning

confidence: 99%

Spin readout and addressability of phosphorus-donor clusters in silicon

et al. 2013

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The spin states of an electron bound to a single phosphorus donor in silicon show remarkably long coherence and relaxation times, which makes them promising building blocks for the realization of a solid-state quantum computer. Here we demonstrate, by high-fidelity (93%) electrical spin readout, that a long relaxation time T 1 of about 2 s, at B ¼ 1.2 T and TE100 mK, is also characteristic of electronic spin states associated with a cluster of few phosphorus donors, suggesting their suitability as hosts for spin qubits. Owing to the difference in the hyperfine coupling, electronic spin transitions of such clusters can be sufficiently distinct from those of a single phosphorus donor. Our atomistic tight-binding calculations reveal that when neighbouring qubits are hosted by a single phosphorus atom and a cluster of two phosphorus donors, the difference in their electron spin resonance frequencies allows qubit rotations with error rates E10 À 4 . These results provide a new approach to achieving individual qubit addressability.

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“…18 The atomistic configuration interaction method used here goes beyond these approximations to include the Stark effect, large wavefunction overlap and electron-electron exchange and correlations. In this work, we use a large-scale atomistic tight-binding method that describes the crystal as a linear combination of atomic orbitals, and captures the full-energy spectrum of a donor in silicon, including the conduction band valley degrees of freedom, the valley-orbit interaction, 24 the Stark shift of the donor orbitals, 18 and real and momentum space images of the donor obtained by scanning tunnelling microscope experiments. 25 Using the atomistic wavefunctions, we compute the two-electron states of donor and donor clusters in the presence of an electric field from an FCI technique.…”

Section: Methodsmentioning

confidence: 99%

Highly tunable exchange in donor qubits in silicon

et al. 2016

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In this article we have investigated the electrical control of the exchange coupling (J) between donor-bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We found that the asymmetric 2P-1P system provides a highly tunable exchange curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange coupling can be achieved using a modest range of electric field (3 MV/m) for~15-nm qubit separation. Compared with the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the gate density by a factor of~2. By combining large-scale atomistic tight-binding method with a full configuration interaction technique, we captured the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P-1P and 2P-1P qubits.npj Quantum Information (2016) 2, 16008; doi:10.1038/npjqi.2016.8; published online 12 April 2016 INTRODUCTION Donor qubits in silicon are promising candidates for spin-based quantum computation as they have exceptionally long T 1 (refs 1-3) and T 2 times 4-6 and offer both electron and nuclear spins for encoding quantum information 5-8 utilising commonly used silicon device technology. With recent demonstration of single qubits in silicon with both electronic and nuclear spins of donors, 5,7 the next biggest challenge is to demonstrate two-qubit gates based on the exchange interaction. Ideally, the exchange coupling J in a two-qubit gate needs to be tuned electrically by several orders of magnitude between an 'Off' and an 'On' state within a small and realisable bias range. To achieve this, the popular Kane architecture uses a J-gate between two phosphorus donors to tune the J-coupling. Recently A-gates that tune the hyperfine interaction for individual qubits have been demonstrated. 9 However, in the long run such a J-and A-gate architecture leads to a high gate density, requiring ultra-small gate widths to minimise electrical cross-talk between gates, and precise donor positioning relative to gates. Moreover, the tunability of the exchange coupling is limited both by the electric field range the J-gate can produce and by the field ionisation of the electrons to the surface. Previous calculations have also shown that the J-coupling oscillates as a function of donor separation due to crystal momentum states, 10 and is therefore sensitive to atomic-scale placement errors. All these issues lead to severe constraints in the implementation of a two-qubit gate in donors.In this work, we introduce an alternative design for an exchange gate in a two-qubit donor system, which allows flexibility in device fabrication and in tuning the exchange coupling. In principle, this new design can (1) eliminate the need for additional J-gates between the donors, (2) function with a range of donor separations, (3) provide an~5 orders of magnitude J-tunability within a modest E-field range of~3 MV/m and lowered 'Off' state exchange and (4) mitigate th...

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Gate-inducedg-factor control and dimensional transition for donors in multivalley semiconductors

Cited by 49 publications

References 34 publications

Quantum gates with donors in germanium

Quantum gates with donors in germanium

Spin readout and addressability of phosphorus-donor clusters in silicon

Highly tunable exchange in donor qubits in silicon

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