![]() The resulting band structure is highly anisotropic. In (b) and (d) the x − z degeneracy is lifted and only the x − y degeneracy remains. Away from the singular Γ point, the hole bands are all doubly degenerate. ![]() The lowest or “split-off” band is completely detached from the others. In (a) and (c) cubic symmetry also makes the X and Z points equivalent and enforces a degeneracy between the top two hole bands at the Γ point. Here we focus on the ( x) and ( z) axes because of their relevance for quantum dot formation, and we note that and are equivalent. ![]() (c) and (d) Blown-up band structures corresponding to (a) and (b). To the left of each plot we show the corresponding real and reciprocal space crystal structures (lower and upper diagrams, respectively), with lattice constants ( a and c) and symmetry points ( Γ, X, Z, and L), as indicated. Our results provide a theoretical foundation for recent experimental advances in Ge hole-spin qubits.Įlectronic band structures for (a) relaxed vs (b) uniaxially strained Ge, obtained using DFT. ![]() The microscopic mechanism of this spin-orbit coupling is discussed, along with its implications for quantum gates based on electric-dipole spin resonance, stressing the importance of coupling terms that arise from the underlying cubic crystal field. The strong spin-orbit coupling in Ge quantum wells may be harnessed to implement electric-dipole spin resonance, leading to gate times of several nanoseconds for single-qubit rotations. Compared to electrons in quantum dots, hole qubits do not suffer from the presence of nearby quantum levels (e.g., valley states) that can compete with spins as qubits. We theoretically investigate the properties of holes in a Si x Ge 1 − x / Ge / Si x Ge 1 − x quantum well in a perpendicular magnetic field that make them advantageous as qubits, including a large ( > 100 meV) intrinsic splitting between the light and heavy hole bands, a very light ( ∼ 0.05 m 0) in-plane effective mass, consistent with higher mobilities and tunnel rates, and larger dot sizes that could ameliorate constraints on device fabrication.
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