Charge accumulation on a Luttinger liquid
The average charge Q on a quantum wire, modeled as a single-channel Luttinger liquid (LL), connected to metallic leads and coupled to a gate is studied theoretically. We find that the behavior of the charge as the gate voltage V_G varies depends strongly on experimentally adjustable parameters (length, contact transmission, temperature, …). When the intrinsic backscattering at the contacts is weak (i.e., the conductance is close to 2e²/h at high temperature), we predict that this behavior should be described by a universal function. For short such wires, the charge increases roughly linearly with V_G, with small oscillations due to quantum interference between electrons scattered at the contacts. For longer wires at low temperature, Coulomb blockade behavior sets in, and the charge increases in steps. In both limits ∂Q/∂V_G, which should characterize the linear-response conductance, exhibits periodic peaks in V_G. We show that due to Coulomb interactions the period in the former limit is twice that of the latter, and describe the evolution of the peaks through this crossover. The study can be generalized to multichannel LL's, and may explain qualitatively the recent observation by Liang et al. [Phys. Rev. Lett. 88, 126801 (2002)] of a four-electron periodicity for electron addition in single-walled carbon nanotubes.
Additional Information© 2004 American Physical Society. (Received 9 December 2003; published 28 April 2004) We thank Smitha Vishveshwara for many illuminating discussions and for contributions to the initial stages of this work. J.A. gratefully acknowledges support from an NSF Graduate Research Fellowship. L.B. was supported by the NSF through Grant No. DMR-9985255, and by the Sloan and Packard foundations. M.P.A.F. was supported by the NSF under grants No. DMR-0210790 and PHY-9907949.
Published - PhysRevB.69.155332.pdf
Accepted Version - 0312212.pdf