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arXiv:1810.06259 · Physical review. B./Physical review. B

Strong electron-electron interactions of a Tomonaga-Luttinger liquid observed in InAs quantum wires

Yosuke Sato, Sadashige Matsuo, Chen-Hsuan Hsu, Peter Stano, Kento Ueda, Yuusuke Takeshige, Hiroshi Kamata, Joon Sue Lee, Borzoyeh Shojaei, Kaushini S. Wickramasinghe, Javad Shabani, C. J. Palmstrøm, 康弘 都倉, Daniel Loss, Seigo Tarucha

Published Apr 16, 2019• 24 citations
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Abstract

We report strong electron-electron interactions in quantum wires etched from an InAs quantum well, a material generally expected to have strong spin-orbit interactions. We find that the current through the wires as a function of the bias voltage and temperature follows the universal scaling behavior of a Tomonaga-Luttinger liquid. Using a universal scaling formula, we extract the interaction parameter and find strong electron-electron interactions, increasing as the wires become more depleted. We establish theoretically that the spin-orbit interaction cause only minor modifications of the interaction parameter in this regime, indicating that genuinely strong electron-electron interactions are indeed achieved in the device. Our results suggest that etched InAs wires provide a platform with both strong electron-electron interactions and the strong spin-orbit interaction.

DOI
10.1103/physrevb.99.155304

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We report strong electron-electron interactions in quantum wires etched from an InAs quantum well, a material generally expected to have strong spin-orbit interactions. We find that the current through the wires as a function of the bias voltage and temperature follows the universal scaling behavior of a Tomonaga-Luttinger liquid. Using a universal scaling formula, we extract the interaction parameter and find strong electron-electron interactions, increasing as the wires become more depleted. We establish theoretically that the spin-orbit interaction cause only minor modifications of the interaction parameter in this regime, indicating that genuinely strong electron-electron interactions are indeed achieved in the device. Our results suggest that etched InAs wires provide a platform with both strong electron-electron interactions and the strong spin-orbit interaction.
The charge transport of a Tomonaga-Luttinger liquid with tunnel barriers exhibits universal scaling: the current-voltage curves measured at various temperatures collapse into a single curve upon rescaling. The exponent characterizing this single curve can be used to extract the strength of electron-electron interaction. Motivated by a recent experiment on InAs nanowires (Sato et al., arXiv:1810.06259), we theoretically investigate the analogous behavior of a spin-orbit-coupled Tomonaga-Luttinger liquid. We find that the scaling exponent differs for different impurity strengths, being weak (disorder potential) or strong (tunnel barriers), and their positions, either in the bulk or near the edge of the wire. For each case we quantify the exponent of the universal scaling and its modification due to the spin-orbit coupling. Our findings serve as a guide in the determination of the interaction strength of quasi-one-dimensional spin-orbit-coupled quantum wires from transport measurements.
The charge transport of a (Tomonaga-)Luttinger liquid with tunnel barriers exhibits universal scaling: the current-voltage curves measured at various temperatures collapse into a single curve upon rescaling. The exponent characterizing this single curve can be used to extract the strength of electron-electron interaction. Motivated by a recent experiment on InAs nanowires [Y. Sato et al., Phys. Rev. B 99, 155304 (2019)], we theoretically investigate the analogous behavior of a spin-orbit-coupled Luttinger liquid. We find that the scaling exponent differs for different impurity strengths, being weak (disorder potential) or strong (tunnel barriers), and their positions, either in the bulk or near the edge of the wire. For each case we quantify the exponent of the universal scaling and its modification due to the spin-orbit coupling. Our findings serve as a guide in the determination of the interaction strength of quasi-one-dimensional spin-orbit-coupled quantum wires from transport measurements.
One-dimensional (1D) quantum wires provide a versatile platform for studying strong electron-electron interactions and collective excitations under confinement. Coulomb drag between 1D systems offers a powerful probe of Tomonaga-Luttinger liquid (TLL) physics, with theoretical predictions suggesting distinct power-law in temperature dependencies between the spin-full and the spin-polarized regimes. However, experimental verification has thus far remained limited. Here, we report measurements of reciprocal and nonreciprocal Coulomb drag between vertically coupled quasi-1D quantum wires in the spin-polarized regime. Clear signatures of spin splitting are observed in both the wires conductance and the drag signal. We observed a connection between electron-hole asymmetry and negative drag, and demonstrated different power-law behaviors in spin-full and spin-polarized regimes, yielding consistent TLL interaction parameters. These results validate the theoretical predictions for backscattering induced drag in the reciprocal regime and extend them to the nonreciprocal and the multiple subband regimes. Furthermore, the nonmonotonic density dependence of the reciprocal interaction parameter correlates with the subband occupation of the drag wire, revealing the complexity of the scattering mechanisms in multichannel systems.
We discuss the conductance of quantum wires in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization-group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of bulk contact the leading-order corrections to the conductance for two different boundary conditions, which reproduce in the absence of bulk contact, respectively, the standard 2T source-drain (SD) conductance GSD(2)=e2/h{G}_{\mathrm{SD}}^{(2)}{=e}^{2}/hGSD(2)​=e2/h and GSD(2)=ge2/h,{G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,GSD(2)​=ge2/h, where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance GSD(3){G}_{\mathrm{SD}}^{(3)}GSD(3)​ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.
The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters ${K}_{\ensuremath{\rho}}$ and ${v}_{\ensuremath{\sigma}}.$ In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density wave to localized in character as the density is lowered. Our results for ${K}_{\ensuremath{\rho}}$ are in good agreement with weak-coupling perturbative estimates ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}\ensuremath{\sim}{n}^{1/2}$ vanishes at small carrier density n, whereas we conjecture that ${K}_{\ensuremath{\rho}}\ensuremath{\rightarrow}1/2$ when $\stackrel{\ensuremath{\rightarrow}}{n}0,$ implying that ${K}_{\ensuremath{\rho}}$ should pass through a minimum at an intermediate density. Observation of this nonmonotonic dependence could be used to measure the effective interaction range in a realistic semiconductor quantum wire geometry. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing n. Strong correlation effects make it difficult to obtain fully consistent estimates of ${v}_{\ensuremath{\sigma}}$ from Hartree-Fock calculations. We conjecture that ${v}_{\ensuremath{\sigma}}{/v}_{\mathrm{F}}\ensuremath{\propto}{n/V}_{0},$ where V0{V}_{0}V0​ is the interaction strength, in the limit $\stackrel{\ensuremath{\rightarrow}}{n}0.$