We propose a spin-interference device which works even without any ferromagnetic electrodes and any external magnetic field. The interference can be expected in the Aharonov-Bohm ͑AB͒ ring with a uniform spin-orbit interaction, which causes the phase difference between the spin wave functions traveling in the clockwise and anticlockwise direction. The gate electrode, which covers the whole area of the AB ring, can control the spin-orbit interaction, and therefore, the interference. A large conductance modulation effect can be expected due to the spin interference.

We describe in detail the procedure for obtaining the correct one-dimensional Hamiltonian of electrons moving on a ring in the presence of Rashba spin-orbit interaction. The subtlety of this seemingly trivial problem has not been fully appreciated so far and it has led to some ambiguities in the existing literature. Our work illustrates the origin of these ambiguities and solves them. DOI: 10.1103/PhysRevB.66.033107 PACS number͑s͒: 71.70.Ej, 72.25.Ϫb, 73.23.Ϫb The effect of Rashba spin-orbit ͑SO͒ interaction 1 on electrons moving in a mesoscopic ring has been studied in several contexts, such as magnetoconductance oscillations, 2,3 Peierls transition, 4,5 and persistent current. 6,7 Essentially all these theoretical studies have employed one-dimensional ͑1D͒ model Hamiltonians. Since different Hamiltonians have been used by different authors some ambiguity currently exists with regard to the correct form of the 1D Hamiltonian. For instance, Aronov and Lyanda-Geller, who studied the effect of Rashba SO interaction on the Aharonov-Bohm conductance oscillations, 2 used a non-Hermitean operator as Hamiltonian. 8 Zhou, Li, and Xue 9 noticed this fact and derived a different ͑Hermitean͒ Hamiltonian operator. However, in their Hamiltonian the Rashba SO term originates from an electric field pointing in the radial direction and not in the direction perpendicular to the plane of the ring. This is physically not correct. Subsequently others 3,5,7,10 have employed a now commonly used 1D Hamiltonian for electrons on a ring, without explicitly discussing its derivation.The purpose of this short paper is to identify the origin of the existing ambiguity and to discuss in detail the procedure to obtain the correct 1D Hamiltonian operator for electrons moving on a ring in the presence of Rashba SO interaction. We will show that the subtlety of this seemingly trivial problem has not been fully appreciated so far.The ''conventional'' way to obtain the Hamiltonian for a 1D ring from the Hamiltonian in two dimensions consists of two steps. First the Hamiltonian operator is transformed into cylindrical coordinates r and . Then r is set to a constant and all terms proportional to derivatives with respect to r are discarded ͑i.e., set to 0͒. This procedure works correctly in simple cases, such as free electrons or electrons in the presence of a ͑uniform or textured 11 ͒ magnetic field. However, it does not work in the presence of Rashba SO interaction, as we will illustrate below.The ͑2D͒ Hamiltonian for a ͑single͒ electron in the presence of Rashba spin-orbit interaction and a magnetic field is given bywhere A is the vector potential, ␣ is the SO constant, E and B are pointing in the ẑ direction ͑perpendicular to the plane͒. In cylindrical coordinates, with xϭr cos and yϭr sin , this operator readswith ⌽ is the magnetic flux through the ring, ⌽ 0 ϭh/e, and ˆx ,y,z are the usual Pauli spin matrices. Notice also that we have redefined ␣ (␣→បE z ␣). If we now set r to a constant value (rϭa) and neglect the derivative terms, we obtain...

We systematically investigate how the interplay between the Rashba spin-orbit interaction and Zeeman coupling affects the electron transport and the spin dynamics in InGaAs-based 2D electron gases. From the quantitative analysis of the magnetoconductance, measured in the presence of an in-plane magnetic field, we conclude that this interplay results in a spin-induced breaking of time reversal symmetry and in an enhancement of the spin relaxation time. Both effects are due to a partial alignment of the electron spin along the applied magnetic field, and are found to be in excellent agreement with recent theoretical predictions. Achieving control of the orbital motion of electrons by acting on their spin is a key concept in modern spintronics and is at the basis of many proposals in the field of quantum information. 1 Two physical mechanisms are used to influence the dynamics of the electron spin in normal conductors: spinorbit interaction (SOI) and Zeeman coupling. In the presence of elastic scattering, these two mechanisms affect the spin in different ways. SOI is responsible for the randomization of the spin direction whereas the Zeeman coupling tends to align the spin along the applied magnetic field. Depending on the relative strength of these interactions, this interplay of SOI and Zeeman coupling is responsible for the occurrence of a variety of physical phenomena. 2,3 Quantum wells (QW's) that define two-dimensional electron gases (2DEG's) are particularly suitable for the experimental investigation of the competition between SOI and Zeeman coupling, since they give control over many of the relevant physical parameters. Specifically, in these systems the SOI strength can be controlled by an appropriate QW design 4 and by applying a voltage to a gate electrode. 5,6 The electron mobility is usually density dependent, so that the elastic scattering time can also be tuned by acting on the gate. Finally, Zeeman coupling to the spin can be achieved with minimal coupling to the orbital motion of the electrons by applying a magnetic field parallel to the conduction plane.In this Communication we study the competition of SOI and Zeeman coupling via magnetoconductance measurements in InGaAs-based 2DEG's with different Rashba SOI strength. From the detailed quantitative analysis of the weak antilocalization as a function of an applied in-plane magnetic field ͑B ʈ ͒, we find that the partial alignment of the spin along B ʈ results in a spin-induced time reversal symmetry (TRS) breaking, and in an increase of the spin relaxation time. The increase in spin relaxation time is found to be quadratic with B ʈ , and strongly dependent on the SOI strength and the elastic scattering time. For both the spin-induced TRS breaking and the increase in spin relaxation time we find excellent quantitative agreement with recent theory. We also show that the quantitative analysis permits us to determine the in-plane g factor of the electrons.The three InAlAs/ InGaAs/ InAlAs quantum wells used in our work are very similar to those descri...

We have experimentally studied the spin-induced time reversal symmetry (TRS) breaking as a function of the relative strength of the Zeeman energy (E(Z)) and the Rashba spin-orbit interaction energy (E(SOI)), in InGaAs-based 2D electron gases. We find that the TRS breaking, and hence the associated dephasing time tau(phi)(B), saturates when E(Z) becomes comparable to E(SOI). Moreover, we show that the spin-induced TRS breaking mechanism is a universal function of the ratio E(Z)/E(SOI), within the experimental accuracy.

We discuss a statistical analysis of Aharonov-Bohm conductance oscillations measured in a two-dimensional ring, in the presence of Rashba spin-orbit interaction. Measurements performed at different values of gate voltage are used to calculate the ensemble-averaged modulus of the Fourier spectrum and, at each frequency, the standard deviation associated to the average. This allows us to prove the statistical significance of a splitting that we observe in the h/e peak of the averaged spectrum. Our work illustrates in detail the role of sample specific effects on the frequency spectrum of Aharonov-Bohm conductance oscillations and it demonstrates how fine structures of a different physical origin can be discriminated from sample specific features. The investigation of Aharonov-Bohm ͑AB͒ conductance oscillations in mesoscopic devices permits to study different aspects of phase-coherent transport of electrons. One of the aspects that has recently attracted considerable attention is the effect of the electron spin.1 It has been theoretically predicted that in the presence of spin-orbit interaction ͑SOI͒, the electron spin modifies the properties of AB conductance oscillations in an observable way. 2,3Experimental attempts have been reported in which features observed in either the envelope function of the AB oscillations or their Fourier spectrum were attributed to the presence of Rashba SOI. 4,5 In a few cases 5 these claims were based on the interpretation of single magnetoconductance measurements. The interpretation of such experiments is difficult, however, due to the sample specific nature of the h/e oscillations. In particular, a certain scatterer configuration in the ring might cause features that are similar to those due to SOI. In the analysis of past experiments this possibility has not been considered thoroughly.In this paper we show experimentally how sample specific effects in the Fourier spectrum ͑FS͒ of the AB oscillations can be quantifiably suppressed in a controlled way. In particular, we perform a statistical analysis of the ensemble averaged FS. At each frequency, the mean Fourier amplitude and standard deviation are calculated. We find features in the averaged FS that are significantly larger than the standard deviation. These features can therefore be discriminated from remnant sample specific effects and their origin attributed to a different physical phenomenon.The AB oscillations used in our analysis have been measured in a two-dimensional ring fabricated using an InGaAsbased heterostructure ͑Fig. 2, bottom inset͒, in which Rashba SOI is particularly strong 6 ͑Fig. 2, top inset͒; ␣Ϸ0.8 ϫ10 Ϫ11 eVm. The mean radius and width, respectively, 350 nm and 180 nm, are smaller than the mean-free path (Ӎ1 m) and transport is quasiballistic.7 A gate electrode covering the ring permits to change the Fermi energy as well as the strength of the SOI ͑the maximum expected gate induced change is 20%-30%͒. 6 The magnetoconductance of the ring "G(B)… was measured at different values of the gate voltage V g rang...