Image-potential-induced spin-orbit interaction in one-dimensional electron systems

2017

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We consider a gated one-dimensional (1D) quantum wire disturbed in a contactless manner by an alternating electric field produced by a tip of a scanning probe microscope. In this schematic 1D electrons are driven not by a pulling electric field but rather by a non-stationary spin-orbit interaction (SOI) created by the tip. We show that a charge current appears in the wire in the presence of the Rashba SOI produced by the gate net charge and image charges of 1D electrons induced on the gate (iSOI). The iSOI contributes to the charge susceptibility by breaking the spin-charge separation between the charge-and spin collective excitations, generated by the probe. The velocity of the excitations is strongly renormalized by SOI, which opens a way to fine-tune the charge and spin response of 1D electrons by changing the gate potential. One of the modes softens upon increasing the gate potential to enhance the current response as well as the power dissipated in the system.Introduction.-Today we are witnessing the burst of interest in the ballistic electron transport in quantum wires [1][2][3][4][5]. For the last three decades the quantum wires formed by electrostatic gating of a high-mobility two-dimensional (2D) electron gas have been the favorite playground to study quantum many-body effects in one-dimensional (1D) electron systems [6], where a strongly correlated state known as the Tomonaga-Luttinger liquid emerges as a result of the electron-electron (e-e) interaction [7]. The dynamic transport experiments are the most subtle and precise methods to extract the many-body physics [8].Currently of most interest are the group III-V semiconductor nanowires as they represent basic building blocks for the topological quantum computing [9] and spintronics [10]. In particular, InAs and InSb nanowires are promising systems for the creation of helical states and as a host for Majorana fermions [11][12][13]. The fundamental reason behind these properties is the strong Rashba spin-orbit interaction (RSOI) in these materials [14].Recently we have found that RSOI is created by the electric field of the image charges that electrons induce on a nearby gate [15]. A sufficiently strong image-potential-induced spinorbit interaction (iSOI) leads to highly non-trivial effects such as the collective mode softening and subsequent loss of stability of the elementary excitations, which appear because of a positive feedback between the density of electrons and the iSOI magnitude.By producing a spin-dependent contribution to the e-e interaction Hamiltonian of 1D electron systems, the iSOI breaks the spin-charge separation (SCS), the hallmark of the Tomonaga-Luttinger liquid [7]. As a result, the spin and charge degrees of freedom are intertwined in the collective excitations, which both convey an electric charge and thus both contribute to the system electric response, in contrast to a common case of a purely plasmon-related ballistic conductivity. In addition, the iSOI renormalizes the velocities of the collective excitations. An attractive f...

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Dynamic Transport in a Quantum Wire Driven by Spin–Orbit Interaction

2017

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“…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.…”

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Dynamics of One‐Dimensional Electrons With Broken Spin–Charge Separation

Sablikov

2017

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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 Spin–Orbit Mechanism of Electron Pairing in Quantum Wires

Sablikov

2018

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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.