Electron Entanglement Detected by Quantum Spin Hall Systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell’s inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell’s inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.

Figure 1

Illustration of the proposed setup. A superconductor (the green bar labeled by $S$) is weakly coupled to two QSHs so that two spin entangled particles can be separately injected from a Cooper pair into the edges of QSHs. Two spin channels are sketched as blue solid lines for spin up and red dashed lines for spin down with their moving directions labeled by arrows. The middle areas of the QSHs are deformed so that two edges are close to each other. There are also gate voltages (yellow square) applied on these areas. $t_{1,2L}$ and $t_{1,2R}$ represent the same-edge transmission and cross-edge transmission in the left and right QSHs, respectively. Four terminals sketched as gray bars ($\pm L$, $\pm R$) are the receivers for spins of different polarization directions.

Figure 2

Plot of $B$ as functions of $t_{2L,R}/t_{1L,R}$. The solid lines are the contour of $B=2$.