Charge accumulation on a Luttinger liquid

Abstract

The average charge Q on a quantum wire, modeled as a single-channel Luttinger liquid, 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 2e^2/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 $\partial Q/\partial V_G$, 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 multi-channel Luttinger liquids, and may explain qualitatively the recent observation by Liang et al (Phys. Rev. Lett. 88, 126801) of a four-electron periodicity for electron addition in single-walled carbon nanotubes.

10 pages, 9 figures

References in corpus (14)

• Luttinger Liquid Behavior in Carbon Nanotubes
• High-Field Electrical Transport in Single-Wall Carbon Nanotubes
• Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes
• Effective low-energy theory for correlated carbon nanotubes
• Quantum Effects in Coulomb Blockade
• Electrical transport through carbon nanotube junctions created by mechanical manipulation
• A Mechanism for Cutting Carbon Nanotubes with a Scanning Tunneling Microscope
• Fabry-Perot interference and spin filtering in carbon nanotubes
• Quantum Interference Effects in Electronic Transport through Nanotube Contacts
• The two-boundary sine-Gordon model
• Minimal Models with Integrable Local Defects
• Smearing of Coulomb Blockade by Resonant Tunneling
• External voltage sources and Tunneling in quantum wires
• Theoretical Studies of Quantum Interference in Electronic Transport Through Carbon Nanotubes

Cited by in corpus (2)

• Electron Transport in Very Clean, As-Grown Suspended Carbon Nanotubes
• Density of states of interacting quantum wires with impurities: a Dyson equation approach