Detection of a Large Valley-Orbit Splitting in Silicon with Two-Donor Spectroscopy

Roche, B.; Dupont-Ferrier, Eva; Voisin, B.; Cobián, Manuel; Jehl, X.; Wacquez, R.; Vinet, M.; Niquet, Yann-Michel; Sanquer, M.

doi:10.1103/physrevlett.108.206812

Cited by 56 publications

(80 citation statements)

References 22 publications

(27 reference statements)

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“…We have observed electronic valley quantum interference for a single donor atom whose depth and electric field have been independently empirically determined, capabilities not available in singleelectron transport spectroscopy of donors in nanoscale transistors 2,11,15 . We have identified that a donor 2.85 ± 0.45 nm from an interface and in a low field E z = 0.3±1.9 MV/m has an electronic valley population deviating by only ∼ 5% compared with a donor in bulk silicon.…”

Section: 30mentioning

confidence: 99%

“…However, addressable control and coupling within qubit arrays requires local gates and control interfaces, whose atomic-scale potentials strongly influence electronic valley degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16] . While these unconventional orbital degrees of freedom play no role in conventional silicon microelectronics, they invariably arise in quantized states in indirect gap materials, and are pervasive in quantum electronics.…”

Section: Fabrication Of Devicesmentioning

confidence: 99%

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Spatially resolving valley quantum interference of a donor in silicon

Salfi¹,

Mol²,

Rahman³

et al. 2014

Nature Mater

105

187

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Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunctions, preventing direct experimental access to valley population, donor position, and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunneling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley perturbation-induced enhancement of spin relaxation will be negligible for depths > 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest to emerging schemes proposing to encode information directly in valley polarization. Fabrication of devices1,2 , spin readout 1 , and quantum control of spins 3,4 in silicon has been accomplished at the single-donor level. However, addressable control and coupling within qubit arrays requires local gates and control interfaces, whose atomic-scale potentials strongly influence electronic valley degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16] . While these unconventional orbital degrees of freedom play no role in conventional silicon microelectronics, they invariably arise in quantized states in indirect gap materials, and are pervasive in quantum electronics. In silicon, valley physics determines qubit relaxation rates 13,17,18 and are predicted to strongly influence two qubit gates Here, individual states of subsurface donors were measured using cryogenic scanning tunneling spectroscopy. Quantum mechanical valley interference patterns were observed in real space, associated with linear quantum superpositions of wavevectors in the six conduction band valleys of silicon. Enabled by high-accuracy empirical determination of donor depth and electric field, we perform a parameter-free comparison with atomistic theory establishing that the z-valley population is ∼ 38 ± 2% for a 2.85 ± 0.45 nm deep donor, perturbed by only ∼ 5% compared with ∼ 33.3% for a donor in bulk silicon. Consequently, donors more than 3 nm deep should not experience a significant valley-repopulation induced increase in spin-lattice relaxation. Moreover, the nearly bulklike valley interference observed will render two-qubit excha...

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Section: 30mentioning

confidence: 99%

Section: Fabrication Of Devicesmentioning

confidence: 99%

Spatially resolving valley quantum interference of a donor in silicon

Salfi¹,

Mol²,

Rahman³

et al. 2014

Nature Mater

105

187

View full text Add to dashboard Cite

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“…6,20 On a donor site, on the other hand, the valley ground state jAi 21 and excited states are gapped by excitation energies larger than 10 meV. 22 This gap is of the same order as the donor orbital excitation energy, which is larger than 30 meV. 23 While it is reported that an electric field perpendicular to the SOI interface can induce a transition of the electronic wave function from donor-like to QD-like, such an effect is only caused by an electric field larger than the Coulomb field, 20,24,25 which is not the case in this experiment.…”

mentioning

confidence: 99%

Resonant tunneling spectroscopy of valley eigenstates on a donor-quantum dot coupled system

Kobayashi

Heijden

House

et al. 2016

Applied Physics Letters

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We report electronic transport measurements through a silicon hybrid double quantum dot consisting of a donor and a quantum dot. Transport spectra show resonant tunneling peaks involving different valley states, which illustrate the valley splitting in a quantum dot on a Si/SiO2 interface. The detailed gate bias dependence of double dot transport allows a first direct observation of the valley splitting in the quantum dot, which is controllable between 160-240 eV with an electric field dependence 1.2  0.2 meV/(MV/m). A large valley splitting is an essential requirement to implement a physical electron spin qubit in a silicon quantum dot.Electrons confined in silicon nanostructures satisfy some crucial requirements for the physical implementation of quantum computation such as their long spin coherence time and excellent controllability [1][2][3][4]. To isolate two electronic states used as qubit bases from other states, the degeneracy of the silicon conduction band minima (valleys) must be lifted. Recent investigations have revealed that a large spin-valley hybridization relaxes electron spin qubit states rapidly [5,6], increasing the importance of controlling the valley splitting [5,[7][8][9][10][11]. While electric field controllability of the valley splitting in a quantum dot (QD) has been evaluated by measuring spin relaxation [5], the direct measurement by transport spectroscopy in a QD has not been reported.In this paper, we report transport measurements through a silicon hybrid double QD (DQD) consisting of a phosphorus donor and an electrostatically defined QD [12]. The donor ground level is electrically tuned through resonance with the QD valley ground and excited states, which results in two separated resonant tunneling peaks. From the gate voltage dependence of the separation between these peaks, we evaluate the electric field dependence of the valley splitting in the QD. The obtained electric field dependence of 1.2 meV/(MV/m) is one order of magnitude larger than a previous report on a thermal Si/SiO2 interface [5], being comparable with that on a Si/SiO2 interface defined by oxygen implantations [7]. Such a large electric field dependence provides an effective experimental means to tune the valley splitting in situ.

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“…Experimental systems encompass coupled semiconductor 3 , graphene 4 and carbon nanotube 5 quantum dots and quantum dots built from atom pairs 6 . For single molecules, electron transport through an organic double quantum dot (DQD) molecule has not been studied to the same extend despite the fact that the energy scales of its electronic states are generally larger than in its counterparts, therefore relaxing the requirements for millikelvin temperatures for operation.…”

Section: Introductionmentioning

confidence: 99%

Spin excitations in an all-organic double quantum dot molecule

2016

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We realize a strongly coupled double quantum dot in a single all-organic molecule by introducing a non-conjugated bridge in between two identical conjugated moieties. Spin-1/2 Kondo and Kondo enhanced low-energy excitations for respectively the odd and even electron occupation are observed in off-resonant transport. The ground state in the even occupation can be the singlet or the triplet state varying between samples. This observation suggests that both anti-ferromagnetic and ferromagnetic interactions between spins are of the same order of magnitude.

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Detection of a Large Valley-Orbit Splitting in Silicon with Two-Donor Spectroscopy

Cited by 56 publications

References 22 publications

Spatially resolving valley quantum interference of a donor in silicon

Spatially resolving valley quantum interference of a donor in silicon

Resonant tunneling spectroscopy of valley eigenstates on a donor-quantum dot coupled system

Spin excitations in an all-organic double quantum dot molecule

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