A silicon metal-oxide-semiconductor electron spin-orbit qubit

ARTICLE DOI: 10.1038/s41467-018-04200-0 OPEN A silicon metal-oxide-semiconductor electron spinorbit qubit 1234567890():,; Ryan M. Jock 1, N. Tobias Jacobson2, Patrick Harvey-Collard1,3, Andrew M. Mounce1, Vanita Srinivasa2, Dan R. Ward1, John Anderson1, Ron Manginell1, Joel R. Wendt1, Martin Rudolph1, Tammy Pluym1, John King Gamble2, Andrew D. Baczewski2, Wayne M. Witzel2 & Malcolm S. Carroll1 The silicon metal-oxide-semiconductor (MOS) material system is a technologically important implementation of spin-based quantum information processing. However, the MOS interface is imperfect leading to concerns about 1/f trap noise and variability in the electron g-factor due to spin–orbit (SO) effects. Here we advantageously use interface–SO coupling for a critical control axis in a double-quantum-dot singlet–triplet qubit. The magnetic fieldorientation dependence of the g-factors is consistent with Rashba and Dresselhaus interface–SO contributions. The resulting all-electrical, two-axis control is also used to probe ? the MOS interface noise. The measured inhomogeneous dephasing time, T2m , of 1.6 μs is 28 consistent with 99.95% Si enrichment. Furthermore, when tuned to be sensitive to exchange fluctuations, a quasi-static charge noise detuning variance of 2 μeV is observed, competitive with low-noise reports in other semiconductor qubits. This work, therefore, demonstrates that the MOS interface inherently provides properties for two-axis qubit control, while not increasing noise relative to other material choices. 1 Sandia National Laboratories, Albuquerque, NM 87185, USA. 2 Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, USA. 3 Département de Physique et Institut Quantique, Université de Sherbrooke, 2500 boul. de l’Université, Sherbrooke, QC J1K 2R1, Canada. Correspondence and requests for materials should be addressed to R.M.J. (email: ) or to M.S.C. (email: ) NATURE COMMUNICATIONS | (2018)9:1768 | DOI: 10.1038/s41467-018-04200-0 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-04200-0 S pin qubits in silicon metal-oxide-semiconductor (MOS) structures offer a promising path towards implementing quantum information processing. The MOS system combined with enriched 28Si provides a magnetic vacuum1 and promises to leverage the extensive complementary metal-oxidesemiconductor (CMOS) fabrication platform. Recently, several critical demonstrations have shown long spin coherence times2, two-qubit couplings of single spins in a multi-quantum dot layout3, large tunable valley-splitting2,4,5, and importantly similar valley splittings in different process flows and multiple devices4,5. Yet, there are persistent concerns about the intrinsically imperfect Si/SiO2 interface produces persistent concerns about charge noise from the disordered interface. Two potentially key performance challenges identified are extra detrimental charge noise and variable g-factors6,7. Charge traps and two-level fluctuators near the interface are believed to be potential sources of noise in MOS devices8–10. To attempt to suppress the challenges of disorder and trap noise Si quantum dot (QD) spin qubits have also been developed in heteroepitaxial Si/SiGe11–16. The imperfect crystal–dielectric interface is shifted further away. This is the predominant choice despite reports of difficulties with small or variable valleysplitting13–15,17. Nevertheless qubits have successfully been demonstrated and charge noise has been studied in Si/SiGe qubits12,16,18,19, but only indirect measures of charge noise in MOS qubits have been reported3,20,21. Direct characterization of charge noise at the MOS interface is needed for comparison. a Variability in g-factors recently observed in silicon QDs is also feared to introduce potentially challenging complications for many qubit device architectures7. In bulk Si, the spin–orbit (SO) interaction leads to only weakly perturbed electron g-factors that are close to g = 2. However, the inversion asymmetry of the crystal at an interface leads to a SO interaction22–25, as shown in Fig. 1. When a magnetic field is applied with a component parallel to the interface, electron cyclotron motion establishes a non-zero net momentum component along the interface (Fig. 1a). The coupling of the electron momentum perpendicular to the effective electric field at the interface produces the SO interaction. The vertical electric potential at the interface leads to a Rashba SO contribution due to structural inversion asymmetry (SIA). A second interaction, the Dresselhaus contribution, is attributed to microscopic interface inversion asymmetry (IIA)26, due to the largely unknown and possibly position dependent inter-atomic electric fields at the Si/SiO2 boundary. Recent work has attributed the variability in electron g-factor at silicon interfaces to SO coupling and interface disorder2,6,27–30. However, while the effects of vertical electric field and in-plane magnetic field direction have been observed, the full dependence on magnetic field strength and orientation has not, to date, been characterized in the MOS material system. We further note that this interface effect is not theoretically unique to Si MOS or SiGe/Si interfaces22,23,31 and variability in g-factor has also been observed in GaAs/AlGaAs QDs32,33, as well as holes in silicon QDs34. Because of its strength and angular dependence, which is similar to bulk SO effects, it is possible that the contribution of the interface b n+ poly-Si c n+ poly-Si Beff,D SiO2 J ↓↑ Beff,R Si [100] d ↑↓ SO T Energy 28 B S [010] T J ↑↓ S SO (2,0) (1,1) ↓ Detuning ′ p′  p ↑ EZ = gLBB ↑ EZ = gRBB ↓ Charge sensor current (a.u) Δ V′ V ↓ f Δ e 0 500 1000 1500 2000 2500 3000 Manipulation time (ns) Fig. 1 MOS spin–orbit-driven singlet–triplet qubit. a Cartoon representation of the interface spin–orbit interaction. For an electron confined to a QD, an inplane magnetic field will cause a finite momentum at the interface which, in the presence of broken inversion symmetry, leads to a spin–orbit interaction. The position of the QDs presented in this work, relative to the gates, differs from what is portrayed here (see Supplementary Fig. 2). b Schematic example of the effective spin–orbit field due to the Dresselhaus (red) and Rashba (orange) interactions for in-plane electron momentum. c Schematic energy diagram of the DQD near the (2, 0) → (1, 1) charge transition, showing the energy of the singlet and triplet states as a function of QD–QD detuning, ϵ. Near the interdot transition (ϵ = 0), the exchange energy, J, dominates the electronic interaction and drives rotations about the Z-axis (red arrow in inset). Deep into the (1, 1) charge sector (ϵ > 0), J is small and the electronic states rotate about the X-axis due to a difference in Zeeman energy between each QD (blue arrow in inset). d Details of the interface at the inter-atomic bon (...truncated)