Abstract
We study a three-terminal spin-valley topological insulator/superconductor/insulator (TI/S/TI) device to realize perfect Cooper-pair splitting in real space. The key point is to construct a single topologically-protected interface state in each TI electrode that is valley helical and spin polarized. It is shown that only the crossed Andreev reflection of electrons is allowed when the opposite topological interface states are engineered in the two TI electrodes, but the normal reflection, local Andreev reflection, as well as the electron cotunneling are entirely prohibited. The quantized and noiseless crossed Andreev reflection is protected by the bulk topological invariants of the TI electrodes and persists in a very long junction $(L>{\ensuremath{\xi}}_{s})$ as well as in moderate disorders.
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