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arXiv:1809.08320 · Physical Review Applied

Spin-Blockade Spectroscopy of Si / Si - Ge Quantum Dots

A.M. Jones, E.J. Pritchett, Edward H. Chen, T.E. Keating, R.W. Andrews, J.Z. Blumoff, L.A. De Lorenzo, K. Eng, S.D. Ha, Andrey A. Kiselev, S.M. Meenehan, S.T. Merkel, J.A. Wright, L.F. Edge, R.S. Ross, M.T. Rakher, M.G. Borselli, A. Hunter

Published Jul 15, 2019• 29 citations
arXivHTMLPDF

Abstract

Singlet-triplet spin states of a quantum dot support promising semiconductor-based qubits, yet often suffer from poor state preparation and measurement, due to low-lying excited states. Engineering a large energy splitting is impeded by the inability to accurately measure both large and small energy splittings with the device biased to nominal operation. The authors present a measurement and fitting approach that accurately extracts both large and small splittings in this regime. They also find evidence that both orbital and valley degrees of freedom may set this energy separation, significantly affecting which paths to pursue in device design.

DOI
10.1103/physrevapplied.12.014026

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Singlet-triplet spin states of a quantum dot support promising semiconductor-based qubits, yet often suffer from poor state preparation and measurement, due to low-lying excited states. Engineering a large energy splitting is impeded by the inability to accurately measure both large and small energy splittings with the device biased to nominal operation. The authors present a measurement and fitting approach that accurately extracts both large and small splittings in this regime. They also find evidence that both orbital and valley degrees of freedom may set this energy separation, significantly affecting which paths to pursue in device design.
The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter space. We demonstrate a form of spectroscopy that is capable of mapping the energy level structure of a double quantum dot as a function of level detuning, interdot tunnel coupling, and magnetic field. In the one electron regime, we directly observe the transition from the atom like energy levels of isolated quantum dots to molecular like bonding and anti bonding states with increasing interdot tunnel coupling. We also resolve the Zeeman splitting of ground and excited valley states in a magnetic field. In the two electron regime, we gain access to the detuning dependent singlet triplet splitting. Our work may be extended to a broader class of systems, such as strong spin-orbit materials or proximitized quantum dots, allowing the direct extraction of various energy gaps.
One obstacle that has slowed the development of electrically gated metal-oxide-semiconductor (MOS) singlet-triplet qubits is the frequent lack of observed spin blockade, even in samples with large singlet-triplet energy splittings. We present theoretical and experimental evidence that this problem in MOS double quantum dots can be caused by stray positive charges in the oxide, inducing accidental localized levels near the device's active region that lead to the lifting of the spin blockade. We also present evidence that these effects can be mitigated by device design modifications, such as overlapping gates.
The presence of low-lying valley states in Si may hinder the development of large-scale spin-based quantum processors. Rapid prototyping of novel Si/SiGe heterostructures and gate stacks will be central to identifying pathways that increase the valley splitting. We compare the performance of pulsed-gate spectroscopy (PGS) and detuning axis spectroscopy (DAPS) at temperatures up to 700 mK. We find that DAPS outperforms PGS, with DAPS resolving valley splittings as small as ~86 μμμeV, while the energy resolution of PGS is only ~210~μμμeV. Our work demonstrates that DAPS can be used to efficiently extract valley splittings at elevated temperatures in high throughput cryostats.
While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the ggg-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.
The ground state of two-electron quantum dots in single-valley materials like GaAs is always a spin singlet regardless of what the potential and interactions are. This statement cannot be generalized to the multivalley materials like nnn-doped Si. Here we calculate numerically the spectrum of a two-electron Si quantum dot and show that the dot with the lateral size of several nm can have the spin triplet ground state which is impossible in the single-valley materials. Predicted singlet-triplet level crossing in two-electron Si quantum dots can potentially establish the platform for quantum simulation of magnetic many body systems based on quantum dots. We suggest several examples of such systems that open a way to controlled quantum simulations within the condensed matter setting.
Single electron spins can be used to encode and process information in semiconductor quantum devices. Progress has been hindered by materials challenges, such as the small energy splitting between low-lying valley states and hyperfine coupling to nuclear spins. Here we use density functional theory to optimize the valley splitting and spin dephasing time in realistic Si/SiGe heterostructures. Reductions in the Si quantum well width generally increase the valley splitting. However, in narrow quantum wells, a larger fraction of the electronic wavefunction resides in the SiGe buffer layers, which increases the hyperfine coupling with spinful 73^{73}73Ge. Our work shows that Si/SiGe heterostructures with 3~--~4~nm wide quantum wells and 73^{73}73Ge and 29^{29}29Si concentrations of 50 ppm should support average valley splittings EvE_{v}Ev​~>>>~500~μμμeV and spin dephasing times T2∗T_2^*T2∗​ exceeding 15~μμμs assuming an effective quantum dot area of 700 nm2^22. In addition, sharper Si/SiGe interfaces in general result in larger valley splittings and longer spin dephasing times.