Spin-dependent magnetotransport through a ring due to spin-orbit interaction

Abstract

Electron transport through a one-dimensional ring connected with two external leads, in the presence of spin-orbit interaction (SOI) of strength α and a perpendicular magnetic field is studied. Applying Griffith's boundary conditions we derive analytic expressions for the reflection and transmission coefficients of the corresponding one-electron scattering problem. We generalize earlier conductance results by Nitta et al. [Appl. Phys. Lett. 75, 695 (1999)] and investigate the influence of α, temperature, and a weak magnetic field on the conductance. Varying α and temperature changes the position of the minima and maxima of the magnetic-field dependent conductance, and it may even convert a maximum into a minimum and vice versa. 71.70.Ej, 03.65.Vf, Recently, much attention has been paid to the manipulation of the spin degrees of freedom of conduction charges in low-dimensional semiconductor structures. An important feature of the electron transport in multiply connected systems is that the conductance shows signatures of quantum interference that depend on the electromagnetic potentials:Aharonov-Bohm and Aharonov-Casher effect [1,2,3,4,5,6,7,8,9,10]. A comprehensive review of results for metallic rings is given in Ref. [11]. Many devices have been proposed to utilize additional topological phases acquired by the electrons travelling through quantum circuits [1,12,13,14,15]. Nitta et. al. proposed a spin-interference device [1] allowing considerable modulation of the electric current. This device is a one-dimensional ring connected with two external leads, made of a semiconductor structure in which the Rashba spin-orbit interaction (SOI) [16] is the dominant spin-splitting mechanism. The key idea was that, even in the absence of an external magnetic field, the difference in the Aharonov-Casher phase [3,6] acquired between carriers, travelling clockwise and counterclockwise, would produce interference effects in the spin-sensitive electron transport. By tuning the strength α of the SOI the phase difference could be changed, hence the conductance could be modulated.Nitta et. al. [1] found that the conductance G is given approximatively by

On the Quantum Transport through an Asymmetric Aharonov-Bohm Ring with Rashba Spin-Orbit Interaction

“…For an InGaAs based AB ring with the radius R = 250 nm, m * = 0.023m e (where m e is the free electron mass) and a Rashba SOI coupling constant α R = 2 × 10 −11 eV m [7,15], this corresponds to a dimensionless constant like ξ ∼ = 3.0142. In this case, the above condition yields w C 0.166 µm, which can be verified experimentally.…”

“…For a weak magnetic field, the Zeeeman term can be neglected and, in the limit of a very narrow ring, the 1D dimensionless Hamiltonian reads [15,28]:…”

“…where n ∈ Z is the orbital quantum number, σ is the spin index (σ = 1(↑) for the spin-up and σ = 2(↓) for the spin-down), Φ AB is the AB phase acquired by the charged particle in the quantum ring [15]:…”

“…2, the one--electron problem for the asymmetric AB ring in presence of the Rashba SOI is given, according to Ref. [15]. At the end of this section, the transmission amplitude is analytically derived using the transfer matrix formalism [25] and the conductance is obtained, in the Landauer formalism [27].…”

“…The spin-dependent properties of quantum rings with the Rashba coupling were studied in many papers [12][13][14][15][16][17], symmetric rings being utilized in most cases. On the other hand, recently there has been a growing interest for asymmetric configurations, in which the asymmetry has a great influence on the electron transport [18][19][20][21][22][23][24].…”