We show that the spin-orbit interaction (SOI) arising due to the in-plane electric field of the Coulomb repulsion between electrons in a two-dimensional quantum well produces an attractive component in the pair interaction Hamiltonian that depends on the spins and momenta of electrons. If the Rashba SOI constant of the material is high enough the attractive component overcomes the Coulomb repulsion and the centrifugal barrier, which leads to the formation of the two-electron bound states. There are two distinct types of two-electron bound states. The relative bound states are formed by the electrons orbiting around their common barycenter. They have the triplet spin structure and are independent of the center-of-mass momentum. In contrast, the convective bound states are formed because of the center-of-mass motion, which couples the electrons with opposite spins. The binding energy in the meV range is attainable for realistic conditions.

The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their behavior, which characterize the electron ordering and the deformation of Wigner crystal by boundaries. The distribution function has a $\delta$-like singularity at the Fermi momentum $k_F$. The Fourier spectrum of the density has a step-like form at the wavevector $2k_F$, with the harmonics being absent or vanishing above this threshold. These features are found by calculations using exact diagonalization method. They are shown to be caused by Wigner ordering of electrons, affected by the boundaries. However the common Luttinger liquid model with open boundaries fails to capture these features, because it overestimates the deformation of the Wigner crystal. An improvement of the Luttinger liquid model is proposed which allows one to describe the above features correctly. It is based on the corrected form of the density operator conserving the particle number.Comment: 11 pages, 11 figures. Typos corrected and figures improve

We study the spin-orbit interaction effects in a one-dimensional electron system that result from the image charges in a nearby metallic gate. The nontrivial property of the image-potential-induced spin-orbit interaction (iSOI) is that it directly depends on the electron density because of which a positive feedback arises between the electron density and the iSOI magnitude. As a result, the system becomes unstable against the density fluctuations under certain conditions. In addition, the iSOI contributes to the electron-electron interaction giving rise to strong changes in electron correlations and collective excitation spectra. We trace the evolution of the spectrum of the collective excitations and their spin-charge structures with the change in the iSOI parameter. One out of two collective modes softens as the iSOI amplitude grows to become unstable at its critical value. Interestingly, this mode evolves from a pure spin excitation to a pure charge one. At the critical point its velocity turns to zero together with the charge stiffness.

A two‐body problem for electrons in a one‐dimensional system is solved here to show that two‐electron bound states can arise as a result of the image‐potential‐induced spin–orbit interaction (iSOI). The iSOI contributes an attractive component to the electron–electron interaction Hamiltonian that competes with the Coulomb repulsion and overcomes it under certain conditions. It is found that there exist two distinct types of two‐electron bound states, depending on the type of the motion that forms the iSOI: the relative motion or the motion of the electron pair as a whole. The binding energy lies in the meV range for realistic material parameters and is tunable by the gate potential.

No abstract

In low-dimensional structures with strong Rashba spin-orbit interaction (SOI), the Coulomb fields between moving electrons produce a SOI component of the pair interaction that competes with the potential Coulomb repulsion. If the Rashba SOI constant of the material is sufficiently high, the total electron-electron interaction becomes attractive, which leads to the formation of the two-electron bound states. We show that because of the dielectric screening in a thin film the binding energy is significantly higher as compared to the case of the bulk screening.

Spin-charge separation is known to be broken in many physically interesting one-dimensional (1D) and quasi-1D systems with spin-orbit interaction because of which spin and charge degrees of freedom are mixed in collective excitations. Mixed spin-charge modes carry an electric charge and therefore can be investigated by electrical means. We explore this possibility by studying the dynamic conductance of a 1D electron system with imagepotential-induced spin-orbit interaction. The real part of the admittance reveals an oscillatory behavior versus frequency that reflects the collective excitation resonances for both modes at their respective transit frequencies. By analyzing the frequency dependence of the conductance the mode velocities can be found and their spin-charge structure can be determined quantitatively.Spin-orbit interaction (SOI) causes a range of non-trivial effects in low-dimensional electron systems, especially if combined with electron-electron (e-e) interaction.[1] Below we investigate one yet little studied aspect of SOI in one-dimensional (1D) and quasi-1D systems. Owing to the e-e interaction 1D electrons form a strongly correlated state known as the TomonagaLuttinger liquid, the hallmark of which is a spin-charge separation (SCS).[2] The SCS was studied in detail in systems without SOI. In the presence of SOI the SCS is still respected in strictly 1D systems. However, the SCS is violated in realistic quasi-1D structures with transverse quantization sub-bands since the spin is no longer a good quantum number there, resulting in new collective excitations modes, in which spin and charge degrees of freedom are mixed. [3] Even more interesting effects accompanied by the SCS violation appear in 1D electron systems with the spin-dependent e-e interaction. This happens when a 1D electron system is placed close to a metallic gate. The electric field of the image charges that electrons induce on the gate gives rise to the imagepotential-induced spin-orbit interaction (iSOI), which produces a spin-dependent contribution to the e-e interaction Hamiltonian. The iSOI not only breaks the SCS, but also leads the system to the instability for sufficiently strong interaction. [4] The SCS can also be violated in 1D edge states of two-dimensional topological insulators. These states are known to have a helical structure with the spin locked to the electron momentum. In the simplest commonly studied case of the S z symmetry when the spin orientation depends only on the momentum direction but not on its magnitude, the SCS is respected.[5] However, the S z symmetry is not an inherent property of the topological insulator. Generally, the S z symmetry is violated by the SOI.[6-9] The single-particle states are then modeled as the Kramers pair of 1D states with the spin orientation depending on the momentum magnitude rather then on its direction alone. [10,11] The packet composed of such states does not possess a definite spin and, which is particularly interesting, the e-e interaction becomes effectively spin-dependen...

The density operator in the Luttinger model consists of two components, one of which describes long-wave fluctuations and the other is related to the rapid oscillations of the charge-density-wave (CDW) type, caused by short-range electron correlations. It is commonly believed that the conductance is determined by the long-wave component. The CDW component is considered only when an impurity is present. We investigate the contribution of this component to the dynamic density response of a Luttinger liquid free from impurities. We show that the conventional form of the CDW density operator does not conserve the number of particles in the system. We propose the corrected CDW density operator devoid of this shortcoming and calculate the dissipative conductance in the case when the one-dimensional conductor is locally disturbed by a conducting probe. The contribution of the CDW component to conductance is found to dominate over that of the long-wave component in the low-frequency regime.