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We demonstrate that the size of the electric-field-induced Rashba spin splitting in an 80 nm wide modulation-doped InGaSb quantum well can depend strongly on the spatial variation of the electric field. In a slightly asymmetric quantum well it can be an order of magnitude stronger than for the average uniform electric field. For even smaller asymmetry spin subbands can have wave functions and/or expectation values of the spin direction that are completely changed as the in-plane wave vector varies. The Dresselhaus effect can give an anticrossing at which the spin rapidly flips.

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