Zero-field-splitting in triplet-state nanotubes

Chirality Dependence of Triplet Excitons in (6,5) and (7,5) Single-Wall Carbon Nanotubes Revealed by Optically Detected Magnetic Resonance

The excitonic structure of single-wall carbon nanotubes (SWCNTs) is chirality dependent and consists of multiple singlet and triplet excitons (TEs) of which only one singlet exciton (SE) is optically bright. In particular, the dark TEs have a large impact on the integration of SWCNTs in optoelectronic devices, where excitons are created electrically, such as in infrared light-emitting diodes, thereby strongly limiting their quantum efficiency. Here, we report the characterization of TEs in chirality-purified samples of (6,5) and (7,5) SWCNTs, either randomly oriented in a frozen solution or with in-plane preferential orientation in a film, by means of optically detected magnetic resonance (ODMR) spectroscopy. In both chiral structures, the nanotubes are shown to sustain three types of TEs. One TE exhibits axial symmetry with zero-field splitting (ZFS) parameters depending on SWCNT diameter, in good agreement with the tighter confinement expected in narrower-diameter nanotubes. The ZFS of this TE also depends on nanotube environment, pointing to slightly weaker confinement for surfactant-coated than for polymer-wrapped SWCNTs. A second TE type, with much smaller ZFS, does not show the same systematic trends with diameter and environment and has a less well-defined axial symmetry. This most likely corresponds to TEs trapped at defect sites at low temperature, as exemplified by comparing SWCNT samples from different origins and after different treatments. A third triplet has unresolved ZFS, implying it originates from weakly interacting spin pairs. Aside from the diameter dependence, ODMR thus provides insights in both the symmetry, confinement, and nature of TEs on semiconducting SWCNTs.

Anomalous Zero-Field Splitting for Hole Spin Qubits in Si and Ge Quantum Dots

An anomalous energy splitting of spin triplet states at zero magnetic field has recently been measured in germanium quantum dots. This zero-field splitting could crucially alter the coupling between tunnel-coupled quantum dots, the basic building blocks of state-of-the-art spin-based quantum processors, with profound implications for semiconducting quantum computers. We develop an analytical model linking the zero-field splitting to the Rashba spin-orbit interaction that is cubic in momentum. Such interactions naturally emerge in hole nanostructures, where they can also be tuned by external electric fields, and we find them to be particularly large in silicon and germanium, resulting in a significant zero-field splitting in the μeV range. We confirm our analytical theory by numerical simulations of different quantum dots, also including other possible sources of zero-field splitting. Our findings are applicable to a broad range of current architectures encoding spin qubits and provide a deeper understanding of these materials, paving the way toward the next generation of semiconducting quantum processors.