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Zeeman-like coupling to valley degree of freedom in Si-based spin qubits

Year: 2026
Type: article
Abstract: Increasing the valley splitting in Si-based heterostructures is critical for improving the performance of semiconductor qubits. This paper establishes that the two low-energy conduction band valleys are not independent parabolic bands. Instead, they originate from the point of the Brillouin zone, where they are interconnected by a degeneracy protected by the nonsymmorphic symmetry of the diamond lattice. This semi-Dirac-node degeneracy gives rise to the Δ 1 and Δ 2 ′ bands, which constitute the valley degrees of freedom. By explicitly computing the two-component Bloch functions X 1 ± , using the wave vector group at the point, we determine the transformation properties of the object ( X 1 + , X 1 − ) . We demonstrate that these properties are fundamentally different from those of a spinor. Consequently, we introduce the term “valleyor” to emphasize this fundamental distinction. The transformation properties of valleyors induce corresponding transformations of the Pauli matrices τ 1 , τ 2 and τ 3 in the valley space. Determining these transformations allows us to classify possible external perturbations that couple to each valley Pauli matrix, thereby identifying candidates for valley-magnetic fields, B ⃗ . These fields are defined by a Zeeman-like coupling B ⃗ · τ ⃗ to the valley degree of freedom. In this way, we identify scenarios where an applied magnetic field B ⃗ can leverage other background fields, such as strain, to generate a valley-magnetic field B ⃗ . This analysis suggests that beyond the well-known mechanism of potential scattering from Ge impurities, there exist additional channels—mediated by combinations of magnetic and strain-induced vector potentials—to control the valley degree of freedom.
DOI: 10.1103/64lc-9d5w
Language: English
Open Access status: hybrid
OpenAlex ID: W7117558609
FWCI:
Cites: 30
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Related to: 10