Probing the Variation of the Intervalley Tunnel Coupling in a Silicon Triple Quantum Dot

Abstract

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk band structure 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 intervalley 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 variations in the valley splitting, and the intra- and intervalley tunnel couplings (t_{ij} and t_{ij}^{′}) that couple dots i and j in a triple quantum dot. We uncover large variations in the ratio of intervalley to intravalley 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.