Charge transport of a spin-orbit-coupled Luttinger liquid

Abstract

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., 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.

Helical Liquids in Semiconductors

“…Second, while the 2PB process from both a local impurity and quenched disorder result in similar power-law resistance, they differ in the crossover value of the interaction parameter below which the channel becomes insulating, namely K < 1/4 and K < 3/8, respectively. This difference, arising from the different scaling dimensions of the corresponding operators, has been pointed out in the context of nonhelical channels (Giamarchi 2003, Hsu, Stano, Sato, Matsuo, Tarucha & Loss 2019. Generally speaking, the additional time integral in the disorder-averaged effective action [see (98a)] makes the backscattering due to quenched disorder more RG relevant than the one due to a single impurity.…”

“…First, for a clean hTLL that is free from backscattering and adiabatically connected to Fermi-liquid leads, it was found that the dc conductance of the helical channel does not depend on K (Hsu et al 2018a), resembling the ballistic conductance in a nonhelical channel (Maslov & Stone 1995, Ponomarenko 1995, Safi & Schulz 1995. Second, while in the presence of backscattering sources the conductance through a helical channel in general depends on the interaction strength, knowledge of the backscattering mechanism and resistance sources is required to extract K. This complication makes the extraction of the experimental K value highly nontrivial, as pointed out by (Väyrynen et al 2016, Hsu et al 2017, Hsu, Stano, Sato, Matsuo, Tarucha & Loss 2019.…”

“…First, for an ensemble of magnetic impurities along the channel, the resistance grows with the length L, in contrast to the single-impurity case where the conductance correction does not scale with L. Second, instead of assuming a random potential [see ( 30) and ( 32)], one might start with a single weak impurity and then sum up the contributions from many alike impurities by assuming that they are independent (Väyrynen et al 2016). However, the second approach does not capture the localization feature and leads to different RG flow equations, thus missing the renormalization of bulk quantities u and K as in nonhelical systems (Giamarchi 2003, Hsu, Stano, Sato, Matsuo, Tarucha & Loss 2019. Nonetheless, the approach employed by (Väyrynen et al 2016) allows one to obtain the refined form of the resistance near the crossover eV ≈ k B T , which was not captured by (36) due to the limitation of the RG approach.…”

Effects of a single impurity in a Luttinger liquid with spin-orbit coupling

“…Spin-orbit coupling (SOC) in these systems plays an important role on the realization of spintronic devices [28,29]. Thus, an interplay of (large) SOC and (large) e-e interactions in the TLL regime is an interesting question and has gained both theoretical and experimental attention in recent years [30][31][32]. Impurity effects in conventional TLLs with decoupled channels were studied in the original works [12,13], and can be summarized by phase portrait at T = 0, presented in Fig.…”

“…The modification of the phase portrait in the presence of SCC has not yet been considered, although there are several studies which partially addressed this question in different aspects [34,35]. Particularly, impurity effects on transport properties in the case of the SCC caused by SOC were recently studied [31,32]. As our main motivation of this work we consider modification of the phase portrait in the presence of SOC.…”