Coulomb Drag Shot Noise in Coupled Luttinger Liquids

Abstract

Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized e.g. in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales. PACS: 71.10.Pm, 73.40.Gk Shot noise in mesoscopic systems has started to attract much interest [1] because it provides information not contained in the current-voltage characteristics alone, and can for instance reveal the fractional charge of quasiparticles in exotic electronic phases such as the fractional quantum Hall (FQH) liquid. Shot noise in FQH bars can be described by the chiral Luttinger liquid (LL) theory [2], and the predicted fractional charge e * smaller than the electron charge e has been seen experimentally for filling factors ν = 1/3 [3] and ν = 2/5 [4]. While in Hall bars right and left moving currents are spatially separated, we address here current noise in non-chiral Luttinger liquids [5], where right and left movers interact in the same channel. Experimental realizations of this generic model for interacting electrons in 1D are for instance provided by single-wall nanotubes (SWNTs) [6,7] or semiconductor quantum wires [8]. For clarity, we focus on SWNTs, with very similar effects expected for other non-chiral 1D interacting metals, and restrict ourselves to the case of spinless electrons [9]. According to available experiments [7], the standard LL interaction parameter in SWNTs is g ≈ 0.2, indicating the presence of strong Coulomb interactions [10].The two-terminal shot noise of a nanotube with an impurity is due to backscattered quasiparticles constructed out of the zero-modes and plasmons of the bosonized LL theory [11] carrying a fractional charge e * = ge. Naively, one might expect that what happens at the impurity should be observable in the shot noise, namely that the two-terminal shot noise in the weak impurity limit can be written as e * times the backscattered current [1]. On the other hand, as noted previously for the average current [12][13][14], the coupling to Fermi liquid reservoirs needs to be incorporated explicitly in the model. We demonstrate that d.c. shot noise does not probe the fractional charge but coincides with the noise in a noninteracting wire. To experimentally access the expected quasiparticle charge then requires more complicated four-terminal setups [15], which seem however difficult to implement in practice and also give only indirect evidence for e * . On the other hand, pronounced interaction effects in shot noise experiments arise from the Coulomb drag shot noise of two adjacent or crossed SWNTs, where we predict the remarkable effect of complete noise locking. In fact, the noise power P 1 in one SWNT induces a Coulomb drag s...

Very low shot noise in carbon nanotubes

“…The effect of inter-tubes correlations has been recently discussed theoretically by Trauzettel et al [10] in a more sophisticated experimental setup where coupled nanotubes can be independently addressed. These authors propose a scenario with a perfect locking of the noise in different tubes.…”

Intershell resistance in multiwall carbon nanotubes: A Coulomb drag study

“…52 Coulomb drag has been an extremely successful tool in studying interactions in coupled quantum wells [53][54][55][56][57][58] ͑notably in the quantum Hall regimes 53,59 ͒, and indeed it was realized very early that Coulomb drag between Luttinger liquids would be an important object to study. [60][61][62][63][64][65][66] These studies focused on Coulomb drag on either crossed or adjacent subsystems, and used very simple models for the Coulomb interaction. Several interesting theoretical predictions emerged from these papers, some of which may have been confirmed experimentally.…”

Conductance of one-dimensional quantum wires

“…Various authors have discussed the observability of those irrational excitations ge [1,32,[36][37][38][39]. The obvious suggestion is based on electric current noise measurements [1].…”