Abstract
The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Unfortunately, the orbital (valley) degeneracy of the conduction band of bulk Si makes it difficult to isolate individual two-level spin-1/2 states, limiting their development. This degeneracy is lifted within Si quantum wells clad between Ge-Si alloy barrier layers, but the magnitude of the valley splittings achieved so far is small—of the order of 1 meV or less—degrading the fidelity of information stored within such a qubit. Here we combine an atomistic pseudopotential theory with a genetic search algorithm to optimize the structure of layered-Ge/Si-clad Si quantum wells to improve this splitting. We identify an optimal sequence of multiple Ge/Si barrier layers that more effectively isolates the electron ground state of a Si quantum well and increases the valley splitting by an order of magnitude, to ∼9 meV.
Highlights
The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits
Si enjoys a number of advantages over III–V semiconductors in this respect, including long spin coherence lifetime[5,6], as well as advanced fabrication know-how, its major drawback is the orbital degeneracy of its lowest conduction band (Fig. 1a) located close to the X point in the Brillouin zone
This is no longer a two-level system determined solely by its spin, leading to considerable leakage and decoherence driven by the energetic proximity among the degenerate orbitals[6,7]. Whereas this six-fold valley degeneracy in the Oh-symmetric bulk Si can be partially removed by application of tensile biaxial strain[8], isolating the two lowest | þ zS and | À zS components from the rest (Fig. 1b), the creation of a sufficiently large energy splitting within this Z-valley subspace (hereby called valley splitting (VS), see Fig. 1c) has proven to be a challenge for the experimental realization of spin-only qubits in Si6
Summary
The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Whereas this six-fold valley degeneracy in the Oh-symmetric bulk Si can be partially removed by application of tensile biaxial strain[8], isolating the two lowest | þ zS and | À zS components from the rest (Fig. 1b), the creation of a sufficiently large energy splitting within this Z-valley subspace (hereby called valley splitting (VS), see Fig. 1c) has proven to be a challenge for the experimental realization of spin-only qubits in Si6 This is clearly indicated by the very limited range of VS (of the order of 1 meV or less) attainable for Si quantum wells surrounded by Ge–Si alloy barriers in experiment[9,10,11,12,13,14,15] and theory[16,17,18,19,20,21,22,23], which seriously hinders the further development of Si-based quantum computation. The enhanced VS is robust under reasonable inter-layer mixing between different species, and is interestingly ‘protected’ even if some larger mixing occurs
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