Spin-dependent transport caused by the local magnetic moments inserted in the Aharonov–Bohm rings

Abstract

We analyse the conductance of an Aharonov-Bohm (AB) ring with a quantum point contact (QPC) that is inserted in one of its arms and which contains a single electron. The conductance of the device is calculated as a function of the one-dimensional (1D) carrier concentration and the value of the magnetic field perpendicular to the plane of the AB ring. The exchange interaction between the electron localized inside QPC and freely propagating electrons is shown to modify the conductance pattern at small carrier concentration significantly, giving rise to the effects related to the formation of the '0.7 feature' in the quantum conductance staircase.

Spin transport in an Aharonov-Bohm ring with exchange interaction

“…This approximation is legitimate as long as the Fermi energy and the leads cross-section area are small enough and the condition that only lowest subband of the dimensional quantization is occupied holds: mL 2 E F /π 2 2 < 1. 25 . The ring contains spontaneously spin polarized electron gas with uncompensated spin J ≥ 1/2.…”

“…Here V dir characterizes the Coulomb interaction between the moving and localized electrons plus the effect of the applied bias voltage; V ex corresponds to the exchange interaction; V ± = V dir ± V ex ; the spin operators σ e and σ S correspond to the propagating and localized electrons, respectively. Hamiltonian (1) can be easily diagonalized by the canonical transformation, 25 and we obtain:…”

“…Using the formalism of Ref. 25 , we can write the expression for the ballistic conductance of the AB ring with exchange interaction (at finite temperature):…”

“…To find the transmittion amplitudes (using other scattering amplitudes), we will address the scattering matrix approach discussed in works. 25,28 The amplitudes of the transmitted and reflected waves can be found from the conditions of the conservation of the flux at the contacts connecting the AB ring and the leads. As we account for the exchange interaction inside the ring, we should consider separately the cases when the spins of the propagating and localized electrons are aligned parallel or anti-parallel.…”

“…It was shown that the insert of a quantum point contact (QPC) in one of the ring's arms, changes the conductance pattern of the AB ring significantly due to the exchange interaction between the electron localized inside the QPC and a propagating electron. It manifests itself in the formation of "0.7 feature" on the quantum conductance staircase of the whole ring structure 25 .…”