Probing the Spatial Variation of the Inter-Valley Tunnel Coupling in a Silicon Triple Quantum Dot

TL;DR

This study uses microwave spectroscopy to investigate how valley splitting and inter-valley tunnel couplings vary spatially in silicon triple quantum dots, revealing significant inhomogeneities affecting qubit fidelity.

Contribution

It provides the first detailed measurement of spatial variations in valley splitting and inter-valley tunnel couplings in silicon quantum dots, highlighting the impact of local disorder.

Findings

Large spatial variations in inter-valley to intra-valley tunnel coupling ratios.

Inter-valley tunnel coupling scales linearly with intra-valley coupling.

Local inhomogeneities significantly influence valley interactions.

Abstract

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted in silicon quantum wells due to strain and electronic confinement, but the "valley splitting" of the two lowest lying valleys is known to be sensitive to atomic-scale disorder. Large valley splittings are desirable to have a well-defined spin qubit. In addition, an understanding of the inter-valley tunnel coupling that couples different valleys in adjacent quantum dots is extremely important, as the resulting gaps in the energy level diagram may affect the fidelity of charge and spin transfer protocols in silicon quantum dot arrays. Here we use microwave spectroscopy to probe spatial variations in the valley splitting, and the intra- and inter-valley tunnel couplings ($t_{ij}$ and $t'_{ij}$) that couple dots $i$ and $j$ in a triple quantum dot (TQD). We uncover large spatial variations in the ratio of inter-valley to intra-valley tunnel couplings $t_{12}'/t_{12}=0.90$ and $t_{23}'/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that $t'_{ij}$ scales linearly with $t_{ij}$, as expected from theory. The results indicate strong interactions between different valley states on neighboring dots, which we attribute to local inhomogeneities in the silicon quantum well.