[Paper Review] Mapping of valley-splitting by conveyor-mode spin-coherent electron shuttling

M. Volmer, Tom Struck+11 more|arXiv (Cornell University)|Dec 29, 2023

Quantum and electron transport phenomena43 references4 citations

TL;DR

This paper presents a high-resolution, time-efficient method for mapping local valley splitting in Si/SiGe heterostructures using conveyor-mode spin-coherent electron shuttling. By shuttling one electron of a spin-entangled pair to probe magnetic field-induced anticrossings between ground and excited valley states, the technique achieves sub-microelectronvolt energy resolution and nanometer lateral resolution, enabling dense 2D mapping of valley splitting across a 210 nm × 18 nm area with statistical fidelity matching established magnetospectroscopy.

ABSTRACT

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with high spatial and energy resolution are lacking. Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling, we introduce a method for two-dimensional mapping of the local valley splitting by detecting magnetic field dependent anticrossings of ground and excited valley states using entangled electron spin-pairs as a probe. The method has sub-μeV energy accuracy and a nanometer lateral resolution. The histogram of valley splittings spanning a large area of 210 nm by 18 nm matches well with statistics obtained by the established but time-consuming magnetospectroscopy method. For the specific heterostructure, we find a nearly Gaussian distribution of valley splittings and a correlation length similar to the quantum dot size. Our mapping method may become a valuable tool for engineering Si/SiGe heterostructures for scalable quantum computing.

Motivation & Objective

• To address the lack of fast, high-resolution methods for probing local valley splitting variations in Si/SiGe heterostructures, which hinder scalability of silicon spin qubits.
• To overcome the limitations of conventional magnetospectroscopy, which is time-consuming and covers limited areas, by enabling efficient, spatially resolved valley splitting mapping.
• To develop a scalable, statistically robust method to characterize the distribution and spatial correlation of valley splitting across a quantum chip.
• To enable engineering of Si/SiGe heterostructures with reduced valley splitting fluctuations for fault-tolerant quantum computing.

Proposed method

• Utilizes conveyor-mode spin-coherent electron shuttling to transport one electron of a spin-entangled pair to a distant quantum dot for local probing.
• Employs magnetic field-dependent anticrossing detection between ground and excited valley states as a probe for local valley splitting energy $E_{\mathrm{VS}}$.
• Applies voltage offsets to two long gates parallel to the shuttle path to displace the shuttle trajectory, enabling two-dimensional mapping over a 210 nm × 18 nm area.
• Achieves sub-microelectronvolt energy resolution and nanometer lateral resolution by leveraging coherent electron shuttling and precise electrostatic control.
• Uses triangulation based on cross-capacitance measurements and finite-element Poisson simulations to determine quantum dot positions with sub-10 nm accuracy.
• Combines experimental measurements with simulated electrostatic potential variations to map $E_{\mathrm{VS}}$ as a function of position and gate voltage differences.

Experimental results

Research questions

• RQ1 Can conveyor-mode electron shuttling enable high-resolution, spatially mapped measurements of local valley splitting in Si/SiGe heterostructures?
• RQ2 What is the spatial distribution and statistical behavior of valley splitting across a large area of a Si/SiGe quantum chip?
• RQ3 How does the resolution and accuracy of this new mapping method compare to conventional magnetospectroscopy?
• RQ4 What role do local electrostatic disorder and unintentional tunneling events play in the observed valley splitting variations?
• RQ5 Can the method resolve the correlation length of valley splitting fluctuations relative to quantum dot size?

Key findings

• The method achieves sub-microelectronvolt energy resolution and nanometer lateral resolution, enabling dense 2D mapping of valley splitting across a 210 nm × 18 nm area.
• Measured valley splitting values range from 4.6 μeV to 59.9 μeV, with a nearly Gaussian distribution across the mapped area.
• The spatial correlation length of valley splitting fluctuations is found to be comparable to the quantum dot size, indicating local material inhomogeneity at the atomic scale.
• Sudden jumps in valley splitting are attributed to unintentional tunneling events during conveyor-mode shuttling, which can be mitigated by vertical displacement of the shuttle channel.
• The statistical distribution of valley splitting from the new method matches well with results from conventional, time-consuming magnetospectroscopy, validating its accuracy.
• The technique enables efficient, high-statistics mapping of valley splitting, making it a promising tool for engineering scalable Si/SiGe quantum computing platforms.