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Register a new userLuttinger liquid behavior in weakly disordered quantum wires
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We have measured the temperature dependence of the conductance in long V-groove quantum wires (QWRs) fabricated in GaAs/AlGaAs heterostructures. Our data is consistent with recent theories developed within the framework of the Luttinger liquid model, in the limit of weakly disordered wires. We show that for the relatively small amount of disorder in our QWRs, the value of the interaction parameter g is g=0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Trying to fit such data with perturbation-theory models leads inevitably to wrong (lower) values of g.
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An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a Luttinger liquid (LL) characterized by a power-law vanishing of the density of states at the Fermi level. Experiments on one-dimensional semiconductor wires and fractional quantum Hall conductors have been interpreted using this picture, but questions remain about the connection between theory and experiment. Recently, single-walled carbon nanotubes (SWNTs) have emerged as a new type of 1D conductor that may exhibit LL behavior. Here we present measurements of the conductance of individual ropes of such SWNTs as a function of temperature and voltage. Power law behavior as a function of temperature or bias voltage is observed: G~ T^a and dI/dV ~ V^a. Both the power-law functional forms and the inferred exponents are in good agreement with theoretical predictions for tunneling into a LL.
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a spinful model with an onsite Hubbard interaction.
We report strong electron-electron interactions in quantum wires etched from an InAs quantum well, a material known 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 spin-orbit interactions 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 and strong spin-orbit interactions.
We study the non-linear conductance $mathcal{G}simpartial^2I/partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductances functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $mathcal{G}sim0.006,E_mathrm{Th}^{-1}$ (and $langlemathcal{G}rangle=0$), where $E_mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $mathcal{G}_asim0.001,(gE_mathrm{Th})^{-1}$, where $ggg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_varphill L$, where $L_varphi$ is the phase coherence length, we get $mathcal{G}sim(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$, and $mathcal{G}_asim(L_varphi/L)^{11/2}(gE_mathrm{Th})^{-1}llmathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_Tll L_varphill L$ where $L_T=sqrt{D/T}$, we obtain $mathcal{G}sim(L_T/L)(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $mathcal{G}_asim(L_T/L)^2(L_varphi/L)^{7/2}(gE_mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.
The unexpected 0.7 plateau of conductance quantisation is usually observed for ballistic one-dimensional devices. In this work we study a quasi-ballistic quantum wire, for which the disorder induced backscattering reduces the conductance quantisation steps. We find that the transmission probability resonances coexist with the anomalous plateau. The studies of these resonances as a function of the in-plane magnetic field and electron density point to the presence of spin polarisation at low carrier concentrations and constitute a method for the determination of the effective g-factor suitable for disordered quantum wires.
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