Zero Field Splitting of Heavy-Hole States in Quantum Dots

Abstract

Using inelastic cotunneling spectroscopy we observe a zero field splitting within the spin triplet manifold of Ge hut wire quantum dots. The states with spin ±1 in the confinement direction are energetically favored by up to 55 μeV compared to the spin 0 triplet state because of the strong spin–orbit coupling. The reported effect should be observable in a broad class of strongly confined hole quantum-dot systems and might need to be considered when operating hole spin qubits.

Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots

“…This signature of the exchange anisotropy is consistent with recent experimental observations in Ref. [45], supporting our theory of ZFS in Ge hut wires.…”

“…For example, we find that ZFS of a few neV can also be induced by short-range corrections of the Coulomb interaction arising from the p-type orbital wavefunctions of the valence band [34,59]. In addition, our theory relates the axis of the exchange anisotropy to the direction of the SOI, and corroborates the observed response of the QDs to small magnetic fields [45]. Importantly, because in long QDs comprising two holes the Coulomb repulsion of the two particles forms a double QD [60][61][62][63], our theory describes the exchange anisotropy also in tunnelcoupled QDs, the prototypical building blocks of current spin-based quantum processors [31,55,64], and thus our findings have profound implications in the growing research field of quantum computing with holes.…”

“…We presented a simple analytical model explaining the large anomalous triplet splitting at zero magnetic field, emerging in QDs occupied by two holes and shedding some light on recent experimental findings [45]. We related the ZFS to a cubic SOI that is externally tunable by electric fields and can be engineered by the design of the QD.…”

“…1(a), in a doubly occupied long QD, with l z a B , the Coulomb repulsion forces the two particles towards opposite ends of the dot [60][61][62], effectively resulting in two coupled dots. We also remark that because a B ∼ 12 nm (a B ∼ 3 nm) in Ge (Si), the condition l z a B of long QDs is typically respected in current experimental setups [13,45,70].…”

“…Recent experiments in Ge QDs with even hole occupation have also detected a large anomalous lifting of the threefold degeneracy of triplet states at zero magnetic field [45], yielding another striking difference between electrons and holes. A similar zero-field splitting (ZFS) has been reported in other quantum systems e.g., divacancies in silicon carbide [46], nitrogen-vacancies in diamond [47,48], and carbon nanotubes [49], where it * bence.hetenyi@unibas.ch is associated to the anisotropy of the two-particle exchange interaction.…”