The properties of Rashba wave function in the planar one-dimensional waveguide are studied, and the following results are obtained. Due to the Rashba effect, the plane waves of electron with the energy E divide into two kinds of waves with the wave vectors k 1 =k 0 +k δ and k 2 =k 0 −k δ , where k δ is proportional to the Rashba coefficient, and their spin orientations are +π/2 (spin up) and −π/2 (spin down) with respect to the circuit, respectively. If there is gate or ferromagnetic contact in the circuit, the Rashba wave function becomes standing wave form exp(±ik δ l)sin[k 0 (l−L)], where L is the position coordinate of the gate or contact. Unlike the electron without considering the spin, the phase of the Rashba plane or standing wave function depends on the direction angle θ of the circuit. The travel velocity of the Rashba waves with the wave vector k 1 or k 2 are the same ħk₀/m * . The boundary conditions of the Rashba wave functions at the intersection of circuits are given from the continuity of wave functions and the conservation of current density. Using the boundary conditions of Rashba wave functions we study the transmission and reflection probabilities of Rashba electron moving in several structures, and find the interference effects of the two Rashba waves with different wave vectors caused by ferromagnetic contact or the gate. Lastly we derive the general theory of multiple branches structure. The theory can be used to design various spin polarized devices.
Rashba wave function, one-dimensional waveguide, boundary conditionThe physics of ballistic electron structures is governed by the elastic mean-free path, which can approach 100 μm in modulated-doped GaAs/AlGaAs hetero-junctions cooled to low temperatures. After an elastic collision the electron energy is unchanged and the phase memory is preserved. However, after an inelastic collision both energy and momentum change in an essentially random fashion and the phase information is lost. At low temperature, the phase coherence time is larger than the inelastic collision time.Some of the first observations of quantum interference were made using thin metal films and silicon inversion layers [1,2]. From then most of the quantum interferences and ballistic transports are observed in two-dimensional systems. The physics of the quantum interference includes: the Aharonov-Bohm effect, quantum interference transistors, universal conductance fluctuations, ballistic electron transport and Landauer-Büttiker formula, quantized conductance in point contacts, multi-terminal devices, quantum dot resonant tunneling devices, etc. In these structures the electron movement is dominated by the quantum mechanics, not the classical mechanics. In recent twenty years, mesoscopic physics and spintronics become two most active areas in condensed matter physics. Xia [3] considered that if the width of the structure is narrow enough compared to its length so that the transverse confinement energy is much larger than the longitudinal moving energy, then the electron movemen...
