Probing the magnitude of Rashba spin–orbit coupling in a double quantum dot system via finite-frequency shot noise

In the coupled quantum dot (QD) system, the electrical manipulation of spin degree of freedom of electron based on the spin–orbit coupling (SOC) is one of the important research fields for QD-based spintronic devices. Consequently, how to quantitatively extract the magnitude of the SOC of the coupled QD system is an important issue. Here, we study the finite-frequency shot noise of electron transport through a serially coupled double QD system with Rashba SOC. It is demonstrated that the existence of peaks and dips of the finite-frequency shot noise originates from the quantum coherence of the serially coupled double QD system, and the positions of the peaks and dips are determined by the differences between the energy eigenvalues of the coherent singly-occupied eigenstates that forming the off-diagonal elements of the reduced density matrix. In particular, when the degeneracy of the differences between the energy eigenvalues of the coherent singly-occupied eigenstates equals one, the finite-frequency shot noise shows a peak, whereas the degeneracy equals two, the finite-frequency shot noise shows a dip. Moreover, the spin polarization of the electrodes and the QD-electrode coupling strength have almost no influence on the positions of the peaks and dips, but have some influences on the width and values of peaks and dips. Therefore, the magnitude of the Rashba SOC and the spin-conservation hopping strength can be quantitatively determined by the positions of peaks and dips of the finite-frequency shot noise.