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arXiv:2307.07877 · Communications Physics

Resonant fractional conductance through a 1D Wigner chain

Rose Davies, Igor V. Lerner, I. V. Yurkevich

Published Feb 28, 2024• 3 citations
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Abstract

Abstract In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.

DOI
10.1038/s42005-024-01545-5

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•Nov 20, 2001•0 citations
Abstract In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.
We study one-dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time-reversal symmetry holds, they may lead to two-terminal fractional quantized conductance and fractional shot noise. The condition on the commensurability of the Fermi momenta of the different channels and the strength of the interactions resulting in such remarkable phenomena are explored using Abelian bosonization. Finite temperature and length effects are accounted for by a generalization of the Luther-Emery refermionization at specific values of the interaction strength, in the strongly interacting regime. We discuss the connection of our model to recent experiments in a confined two-dimensional electron gas, featuring possible fractional conductance plateaus, including situations with a zero magnetic field, when time-reversal symmetry is conserved. One of the most dominant observed fractions, with two-terminal conductance equal to 2/5(e^{2}/h), is found in several scenarios of our model. Finally, we discuss how at very small energy scales the conductance returns to an integer value and the role of disorder.
We show that the conductance of a 1D channel with one point-like impurity critically depends on the asymptotic behavior of the e - e interaction at low momenta k (about the inverse length of the channel). The conductance reemerges (contrary to the case of a point-like repulsive potential) if the potential satisfies the condition V ( k = 0) = 0. For example, this happens if the bare e - e interaction is screened by the charges in the bulk. The relation of this phenomenon to the long-range order present in the Luttinger model is discussed. We consider spinless electrons but generalization is straightforward.
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single δ barrier in a finite one-dimensional wire connected to contacts.Our results exhibit features known from correlated many-body models.In particular, the conductance decays with the wire length as ∝ L -2α , where the power α is universal.We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the δ barrier in a one-dimensional ring, where it is known that I ∝ L -1-α .
Transport between two Fermi liquid reservoirs through a one channel wire of length LLL is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ ( vc{v}_{c}vc​ is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).
Based on a recent proposal [O.P. Sushkov, Phys. Rev. B 64, 155319 (2001)], we relate the quantum conductance through a sample in which electrons are strongly correlated to the persistent current of a large ring, composed of the sample and a noninteracting lead. A scaling law in the lead length allows to extrapolate to a well-defined value of the conductance, depending only on intrinsic properties of the sample and the nature of the contacts between the sample and the lead. For strongly disordered samples, the conductance is found to be enhanced by the interaction.
We discuss the conductance of quantum wires (QW) 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 {\it bulk} contact the leading order corrections to the conductance for two different boundary conditions, which reproduce in the absence of {\it bulk} contact, respectively, the standard 2T source-drain (SD) conductance GSD(2)=e2/hG_{\rm SD}^{(2)}=e^2/hGSD(2)​=e2/h and GSD(2)=ge2/hG_{\rm SD}^{(2)}=ge^2/hGSD(2)​=ge2/h, where ggg is the TLL charge interaction parameter. We find that under these two boundary conditions for the {\it end} contacts the 3T SD conductance GSD(3)G_{\rm SD}^{(3)}GSD(3)​ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the ohmic limit. Non-trivial scaling exponents are predicted as a result of electron fractionalization.