Quantum correlations of a two-dimensional electron gas with Rashba spin-orbit coupling

We study the correlations of a two-dimensional electron gas with Rashba spin-orbit coupling (SOC). We obtain the two-particle density matrix and use it to derive the exchange hole. We find a nontrivial correlation for electrons with opposite spin projections that does not occur without Rashba SOC. The two-particle density matrix allows us to further study the quantum correlations of the system. We use it to obtain the concurrence and the entanglement of formation in order to quantify the entanglement of the electron spins. Additionally, we calculate the quantum discord and compare it with the entanglement and classical correlations.

Figure 1

Pair correlation function $R_{s{s}^{\prime }}$ versus the relative distance of electrons for a 2DEG with (solid line) and without (dashed line) Rashba SOC. In (a) the spins of electrons are parallel, while in (b) the spins are antiparallel.

Figure 2

Hamiltonian eigenbasis pair correlation function $R_{\gamma {\gamma }^{\prime }}$ versus the relative distance of electrons for all combinations of $\gamma$ and ${\gamma }^{\prime }$ and also, for comparison, spin pair correlation function $R_{\uparrow \uparrow }$ for a 2DEG with (solid line) and without (dashed line) Rashba SOC.

Figure 3

Quantum mutual information $I$ (solid line), concurrence $C$ (dotted-dashed line), and entanglement of formation (EoF; dashed line) versus the relative distance between electrons for a 2DEG with Rashba SOC.

Figure 4

Entanglement of formation versus the relative distance between electrons for a 2DEG with (solid line) and without (dashed line) Rashba SOC. The Rashba SOC seems to reduce the entanglement of the spins of the electrons.

Figure 5

Quantum discord $Q$ (solid line), concurrence $C$ (dashed line), and classical correlation $C_{\mathrm{cl}}$ (dot-dashed line) versus the relative distance between electrons for a 2DEG with Rashba SOC.