Effect of short-range electron correlations in dynamic transport in a Luttinger liquid

Sablikov

2007

Phys. Rev. B

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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

Section: Interpretation Of the Resultsmentioning

confidence: 99%

“…where we retain only m = 0, ±1 harmonics, and halve the amplitude of the CDW component to obtain the correct transition to the non-interacting case 22 . The density operator of Eq.…”

Section: B Density Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deformed Wigner crystal in a one-dimensional quantum dot

Sablikov

2007

Phys. Rev. B

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“…e analysis of the ac-conductance is known to be a powerful tool for extracting and studying the e-e interaction e ects in 1D electronic systems. e real and imaginary parts of the ac-conductance [78][79][80] and especially the ballistic resonances of the admi ance [81,82] allow one to determine the interaction parameters in the Lu inger liquid, and even to extract the e ect of the short-range electron correlations [83]. In recent years, this technique has been strongly developed and successfully applied to the study of electron liquid in carbon nanotubes in the terahertz range [84][85][86].…”

Section: The Spin-charge Separation Breaking and Psoi Signatures In Tmentioning

confidence: 99%

Pair spin–orbit interaction in low-dimensional electron systems

Eur. Phys. J. Spec. Top.

Sablikov

2020

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The pair spin-orbit interaction (PSOI) is the spin-orbit component of the electron-electron interaction that originates from the Coulomb fields of the electrons. This relativistic component, which has been commonly assumed small in the low-energy approximation, appears large and very significant in materials with the strong SOI. The PSOI, being determined by the spins and momenta of electrons, has highly unusual properties among which of most interest is the mutual attraction of the electrons in certain spin configurations. We review the nature of the PSOI in solids and its manifestations in low-dimensional systems that have been studied to date. The specific results depend on the configuration of the Coulomb fields in a particular structure. The main actual structures are considered: one-dimensional quantum wires and two-dimensional layers, both suspended and placed in various dielectric media, as well as in the presence of a metallic gate. We discuss the possible types of the two-electron bound states, the conditions of their formation, their spectra together with the spin and orbital structure. In a many-particle system, the PSOI breaks the spin-charge separation as a result of which spin and charge degrees of freedom are mixed in the collective excitations.At sufficiently strong PSOI, one of the collective modes softens. This signals of the instability, which eventually leads to the reconstruction of the homogeneous state of the system. arXiv:1905.06340v2 [cond-mat.str-el] 8 Jul 2019 Pair spin-orbit interaction in solidsElectrons in solids form a fruitful ground to raise many ideas born in relativistic quantum theory and to give life to plenty of unexpected phenomena arising from the realization of electron states and band spectra that only recently appeared truly exotic. is became possible largely due to the discovery of new materials and technological advances in nanostructures.Just recall the discovery of graphene [14] and carbon nanotubes [15], topological insulators [16][17][18], Weyl and Dirac semi-metals [19], 2D transition metal dichalcogenides [20], and many more. e wide variety of non-trivial electronic states and spectra is due to the presence of the crystal. Electron motion in the crystal potential is generally speaking described by the relativistic Dirac equation [21], but in practice a quasi-relativistic approximation based on a small ratio /c of the electron velocity to the speed of light is su cient to describe the electronic spectrum of any material. Such an approximation is successful, in particular, in describing the behavior of electron spins, which has opened a whole new land of spin phenomena in solids [22].

“…Such schematic was discussed in Ref. [19] in the context of local disturbance of the charge subsystem [20]. We emphasize that the probe electric field, which grows even faster than the potential as the probe approaches the wire, also gives an essential contribution to RSOI thereby disturbing the spin subsystem, too [21].…”

mentioning

confidence: 99%

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

Physica Rapid Research Ltrs

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...