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Non-Abelian geometric phases and conductance of spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>holes
Angular momentum $J=$$\frac{3}{2}$ holes in semiconductor heterostructures are shown to accumulate non-Abelian geometric phases as a consequence of their motion. We provide a general framework for analyzing such a system and compute conductance oscillations for a simple ring geometry. We also analyze a figure-eight geometry that captures intrinsically non-Abelian interference …