Electron spin resonance and spin–valley physics in a silicon double quantum dot

Abstract Silicon quantum dots are a leading approach for solid-state quantum bits. However, developing this technology is complicated by the multi-valley nature of silicon. Here we observe transport of individual electrons in a silicon CMOS-based double quantum dot under electron spin resonance. An anticrossing of the driven dot energy levels is observed when the Zeeman and valley splittings coincide. A detected anticrossing splitting of 60 MHz is interpreted as a direct measure of spin and valley mixing, facilitated by spin–orbit interaction in the presence of non-ideal interfaces. A lower bound of spin dephasing time of 63 ns is extracted. We also describe a possible experimental evidence of an unconventional spin–valley blockade, despite the assumption of non-ideal interfaces. This understanding of silicon spin–valley physics should enable better control and read-out techniques for the spin qubits in an all CMOS silicon approach. Introduction It has long been speculated that qubits based on individual electron spins in Si quantum dots (QDs) have considerable potential for quantum information processing. Attractive features are the extremely long coherence time of spins in Si bulk materials and the possibility to approach zero hyperfine interaction to nuclear spins in isotopically purified structures. Furthermore, the extensive collection of Complementary Metal-Oxide-Semiconductor (CMOS)-based techniques, accumulated over decades, is expected to be very important for fabricating many qubits. Electric and magnetic fields along with charge detection enable qubit gates and read-out. A long coherence time was recently confirmed for the singlet and triplet states in a Si/SiGe double quantum dot (DQD) qubit1. Electron spin resonance (ESR) is a direct means to drive rotations of a spin qubit. For electron spins bound in Si, an ensemble of spins in various structured materials2, single electrons in a single defect3 and in a single donor4 have been explored with ESR, using various detection schemes. Physical implementations of ESR on individual bound electronic spins have proven to be successful in GaAs-based QD transport experiments5,6, where the essential role of the spin (Pauli) blockade and the nuclear spin bath in that systems were established. However, spin detection via electronic transport in gate-defined Si QDs has remained challenging. Here we report the detection of microwave-driven ESR transport of individual electrons in a silicon metal-oxide-semiconductor (MOS)-based DQD. The lifting of the blockade via ESR is detectable only in a narrow region where Zeeman split spin states of different valley content anticross where the Zeeman splitting EZ equals the valley splitting of EV≃86.2 μeV. We show that the anticrossing is due to spin–orbit coupling (SOC) in the heterostructure, in the presence of interface roughness, that mixes spin and valley states (similar mixing mechanism was first established in the electron spin relaxation in a small single Si QD7). The gap at anticrossing of Δfanticross≃60 MHz is a measure of this spin–valley mixing and also provides a means to access higher valley states via ESR. Analysis of the ESR spectrum provides a lower-bound estimation of an inhomogeneous decoherence time, , which is much longer than that in GaAs8; it also compares well with the direct measurement of for a Si qubit encoded by singlet–triplet states1. The nature of the experimental blockade regime, and its dependence on the applied magnetic field and interdot energy detuning are discussed. Since the observed blockade region includes detunings larger than the valley splitting, we can conclude that a spin–valley blockade takes place, related to the impossibility for an inelastic (via phonons) electron tunnelling to happen. This blockade survives even in the presence of a non-ideal interface. The observations made in this paper encourage further development of Si MOS-based spin qubits and further suggest that the additional valley degree of freedom1,7,9,10,11,12 is critical to understanding silicon qubits. Results DQD device The cross-sectional view of the Si MOS QD device is shown in Fig. 1a. A scanning electron microscope image of the essential part of a similar device is shown in Fig. 1b. A DQD is defined by six confinement gates, which are labelled as ‘T’, ‘L’, ‘PL’, ‘M’, ‘PR’ and ‘R’. A coplanar strip (CPS) loop (see Methods for device details), situated about 1.5 μm away, is used to deliver an oscillating (AC) magnetic field Bac, perpendicular to the DQD interface. The oscillation frequency fac is scanned to resonance with the electron spin precession oscillations in an in-plane external magnetic field B, Fig. 1b. The DQD is characterized by the DC transport current. Figure 1c shows a typical charge stability diagram of the device with source–drain bias voltage of Vsd=−1 mV, in which the transport current is recorded while the plunger gates Vpl and Vpr are scanned13. The device does not contain a charge-sensing channel and the identified electron numbers are the approximate ones. The estimated electron occupation numbers in the left and right dots are labelled by (NL, NR). At lower electron numbers (more negative voltage at the plunger gates ‘PL’, ‘PR’) the tunnelling from (out of) source (drain) is suppressed, so higher biasing triangles will be examined on electronic transport. Electron transitions into and out of the left (right) dot are labelled by white dashed (blue dash-dotted) lines in Fig. 1c. The honeycomb structure and the biasing triangles here show the characteristic features of a well-defined DQD13. Figure 1: Silicon MOS DQD. (a) The cross-sectional view of the device. (b) The scanning electron microscope image of a similar device (scale bar, 1 μm). DQD (blue circles) is defined at the Si/SiO2 interface by the confinement gates (labelled as ‘T’, ‘L’, ‘PL’, ‘M’, ‘PR’ and ‘R’). Microwave applied to CPS loop generates an AC magnetic field at the QD. (c) Stability diagram at few-electron region (log scale), with additional labels for estimated electron numbers and guidelines for transitions between different electron configurations. Full size image Spin blockade Spin blockade of the electronic transport is the well-known method for sensing and manipulation of confined electron spins in semiconductor heterostructures1,5,8,14. For a DQD confining two electrons, the standard statement is that an electron cannot flip spin under tunnelling, and so a transition from a (1,1) charge configuration to a (2,0) configuration is only possible between the corresponding singlet or triplet spin states: S(1,1)→S(2,0), T(1,1)→T(2,0), respecting the Pauli exclusion principle (see Fig. 2a,b insets). In a typically biased DQD (with detuning much larger than tunnelling, ε>>tc), the delocalized states S(1,1), T(1,1) are only slightly shifted by an exchange energy , while the localized states S(2,0), T(2,0) are split by large ΔST>>J (given a higher orbital (...truncated)