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

Abstract

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...

Pair spin–orbit interaction in low-dimensional electron systems

“…e form of the PSOI Hamiltonian in a speci c low-dimensional structure is determined by the con guration of the Coulomb elds therein. In a 1D quantum wire the only source of the PSOI is the Coulomb eld of e-e interaction directed normally to the wire, which appears if the system is not symmetric in the radial direction [4][5][6][7]. Such asymmetry can be created, for example, by a proximate metallic gate.…”

“…It is clear that the behavior of the many-electron system depends on both e ects, the relative role of which is yet to be determined. In this section we focus on the PSOI-driven instability of the strongly correlated 1D electron liquids and on the PSOI signatures in electron transport in quantum wires [5,6]. e instability of the many-electron system is due to a qualitatively new property of PSOI, as compared to the single-electron Rashba SOI.…”

“…In the presence of the single-particle Rashba SOI, the SCS is respected in strictly 1D systems. However, the PSOI violates the SCS in 1D single-mode quantum wires, which leads to the formation of new collective excitations with intertwined spin and charge degrees of freedom [4][5][6]. e spin-charge composition of the collective mode is quantitatively characterized by a spincharge separation parameter ξ that is de ned via the relative weight of the electron densities with spin up n ↑ and down n ↓ in each mode, and can be directly expressed via the mode phase velocity…”

Spin-orbit-driven electron pairing in two dimensions

“…Recently, we have shown that in low-dimensional systems the SOI produced by the Coulomb interaction of electrons with the image charges induced on a nearby metallic gate leads to nontrivial effects in materials with large Rashba SOI constants [4][5][6]. The main effect is that because of this interaction, the electronelectron (e-e) interaction Hamiltonian acquires a spin-dependent component that is attractive for a particular spin orientation locked to momentum.…”

The Spin–Orbit Mechanism of Electron Pairing in Quantum Wires

“…In Refs. [3][4][5] these effects have been studied for the spin-orbit interaction caused by the potential of image charges (iSOI) that electrons induce on a metallic gate placed nearby. The main result is the fact that the spin-dependent component of the e-e interaction Hamiltonian produced by the iSOI is attractive for a particular spin orientation locked to momentum.…”