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Valley interference and spin exchange at the atomic scale in silicon. Nat Commun 2020; 11:6124. [PMID: 33257680 PMCID: PMC7705737 DOI: 10.1038/s41467-020-19835-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 10/29/2020] [Indexed: 11/23/2022] Open
Abstract
Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon. Coupled donor wavefunctions in silicon are spatially resolved to evidence valley interference processes. An atomic-scale understanding of the interplay between interference, envelope anisotropy and crystal symmetries unveils a placement strategy compatible with existing technology where the exchange is insensitive to interference.
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Dwyer KJ, Dreyer M, Butera RE. STM-Induced Desorption and Lithographic Patterning of Cl–Si(100)-(2 × 1). J Phys Chem A 2019; 123:10793-10803. [DOI: 10.1021/acs.jpca.9b07127] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- K. J. Dwyer
- Department of Physics, University of Maryland, College Park, Maryland 20740, United States
| | - Michael Dreyer
- Department of Physics, University of Maryland, College Park, Maryland 20740, United States
| | - R. E. Butera
- Laboratory for Physical Sciences, 8050 Greenmead Drive, College Park, Maryland 20740, United States
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Abadillo-Uriel JC, Koiller B, Calderón MJ. Two-dimensional semiconductors pave the way towards dopant-based quantum computing. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:2668-2673. [PMID: 30416918 PMCID: PMC6204835 DOI: 10.3762/bjnano.9.249] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Accepted: 09/26/2018] [Indexed: 05/26/2023]
Abstract
Since the proposal in 1998 to build a quantum computer using dopants in silicon as qubits, much progress has been made in the nanofabrication of semiconductors and the control of charge and spins in single dopants. However, an important problem remains unsolved, namely the control over exchange interactions and tunneling between two donors, which presents a peculiar oscillatory behavior as the dopants relative positions vary at the scale of the lattice parameter. Such behavior is due to the valley degeneracy in the conduction band of silicon, and does not occur when the conduction-band edge is at k = 0. We investigate the possibility of circumventing this problem by using two-dimensional (2D) materials as hosts. Dopants in 2D systems are more tightly bound and potentially easier to position and manipulate. Moreover, many of them present the conduction band minimum at k = 0, thus no exchange or tunnel coupling oscillations. Considering the properties of currently available 2D semiconductor materials, we access the feasibility of such a proposal in terms of quantum manipulability of isolated dopants (for single qubit operations) and dopant pairs (for two-qubit operations). Our results indicate that a wide variety of 2D materials may perform at least as well as, and possibly better, than the currently studied bulk host materials for donor qubits.
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Affiliation(s)
- José Carlos Abadillo-Uriel
- Materials Science Factory, Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Belita Koiller
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil
| | - María José Calderón
- Materials Science Factory, Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
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Hile SJ, Fricke L, House MG, Peretz E, Chen CY, Wang Y, Broome M, Gorman SK, Keizer JG, Rahman R, Simmons MY. Addressable electron spin resonance using donors and donor molecules in silicon. SCIENCE ADVANCES 2018; 4:eaaq1459. [PMID: 30027114 PMCID: PMC6044739 DOI: 10.1126/sciadv.aaq1459] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2017] [Accepted: 06/01/2018] [Indexed: 05/27/2023]
Abstract
Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.
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Affiliation(s)
- Samuel J. Hile
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Lukas Fricke
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Matthew G. House
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Eldad Peretz
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Chin Yi Chen
- Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907, USA
| | - Yu Wang
- Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907, USA
| | - Matthew Broome
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Samuel K. Gorman
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Joris G. Keizer
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Rajib Rahman
- Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907, USA
| | - Michelle Y. Simmons
- Centre for Quantum Computation and Communication Technology (CQCT), School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
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Broome MA, Gorman SK, House MG, Hile SJ, Keizer JG, Keith D, Hill CD, Watson TF, Baker WJ, Hollenberg LCL, Simmons MY. Two-electron spin correlations in precision placed donors in silicon. Nat Commun 2018. [PMID: 29515115 PMCID: PMC5841377 DOI: 10.1038/s41467-018-02982-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16 ± 1 nm. By utilising an asymmetric system with two phosphorus donors at one qubit site and one on the other (2P−1P), we demonstrate that the exchange interaction can be turned on and off via electrical control of two in-plane phosphorus doped detuning gates. We determine the tunnel coupling between the 2P−1P system to be 200 MHz and provide a roadmap for the observation of two-electron coherent exchange oscillations. Donor impurities in silicon are promising candidates as qubits but in order to create a large-scale quantum computer inter-qubit coupling must be introduced by precise positioning of the donors. Here the authors demonstrate the fabrication, manipulation and readout of a two qubit phosphorous donor device.
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Affiliation(s)
- M A Broome
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - S K Gorman
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - M G House
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - S J Hile
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - J G Keizer
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - D Keith
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - C D Hill
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, VIC, 3010, Australia
| | - T F Watson
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - W J Baker
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia
| | - L C L Hollenberg
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, VIC, 3010, Australia
| | - M Y Simmons
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW, 2052, Australia.
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Pacheco JL, Singh M, Perry DL, Wendt JR, Ten Eyck G, Manginell RP, Pluym T, Luhman DR, Lilly MP, Carroll MS, Bielejec E. Ion implantation for deterministic single atom devices. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2017; 88:123301. [PMID: 29289172 DOI: 10.1063/1.5001520] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We demonstrate a capability of deterministic doping at the single atom level using a combination of direct write focused ion beam and solid-state ion detectors. The focused ion beam system can position a single ion to within 35 nm of a targeted location and the detection system is sensitive to single low energy heavy ions. This platform can be used to deterministically fabricate single atom devices in materials where the nanostructure and ion detectors can be integrated, including donor-based qubits in Si and color centers in diamond.
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Affiliation(s)
- J L Pacheco
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - M Singh
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - D L Perry
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - J R Wendt
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - G Ten Eyck
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - R P Manginell
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - T Pluym
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - D R Luhman
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - M P Lilly
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - M S Carroll
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - E Bielejec
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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Abadillo-Uriel JC, Calderón MJ. Interface effects on acceptor qubits in silicon and germanium. NANOTECHNOLOGY 2016; 27:024003. [PMID: 26618443 DOI: 10.1088/0957-4484/27/2/024003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dopant-based quantum computing implementations often require the dopants to be situated close to an interface to facilitate qubit manipulation with local gates. Interfaces not only modify the energies of the bound states but also affect their symmetry. Making use of the successful effective mass theory we study the energy spectra of acceptors in Si or Ge taking into account the quantum confinement, the dielectric mismatch and the central cell effects. The presence of an interface puts constraints to the allowed symmetries and leads to the splitting of the ground state in two Kramers doublets (Mol et al 2015 Appl. Phys. Lett. 106 203110). Inversion symmetry breaking also implies parity mixing which affects the allowed optical transitions. Consequences for acceptor qubits are discussed.
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Affiliation(s)
- J C Abadillo-Uriel
- Instituto de Ciencia de Materiales de Madrid, ICMM-CSIC, Cantoblanco, E-28049 Madrid, Spain
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Gullans MJ, Taylor JM. Optical Control of Donor Spin Qubits in Silicon. PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS 2015; 92:195411. [PMID: 28127227 PMCID: PMC5259753 DOI: 10.1103/physrevb.92.195411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon Λ-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective Λ-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons.
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Affiliation(s)
- M J Gullans
- Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA; Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - J M Taylor
- Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA; Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
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Schofield SR, Rogge S. Single dopants in semiconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:150301. [PMID: 25782475 DOI: 10.1088/0953-8984/27/15/150301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Affiliation(s)
- Steven R Schofield
- London Centre for Nanotechnology, and Department of Physics and Astronomy, University College London, London, WC1H 0AH, UK. Centre for Quantum Computation and Communication Technology, School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
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