Luttinger Liquid Behavior in Carbon Nanotubes

Luttinger Liquid Behavior in Carbon Nanotubes

| Marc Bockrath*, David H. Cobden*, Jia Lu*, Andrew G. Rinzler*, Richard E. Smalley*, Leon Balents# and Paul L. McEuen*
This study investigates the behavior of electrons in single-walled carbon nanotubes (SWNTs) and finds evidence of Luttinger liquid (LL) behavior. The researchers measured the conductance of individual SWNT ropes as a function of temperature and voltage, observing power-law behavior: G ∼ T^α and dI/dV ∼ V^α. These results align with theoretical predictions for tunneling into a LL. The experiments revealed that SWNTs can behave as 1D conductors, with transport dominated by a single nanotube in the rope. The charging energy and level spacing of the nanotubes were determined, and the conductance was found to depend on the temperature and bias voltage in a power-law manner. The study also examined the differential conductance dI/dV as a function of applied bias voltage, finding that it follows a power-law behavior at high biases. The exponents of these power laws were found to be consistent with LL theory, which predicts that the tunneling amplitude vanishes as a power law in E - E_F. The LL theory also predicts that the differential conductance follows a power law, with exponents depending on the number of 1D channels and whether the electron tunnels into the bulk or the end of the LL. The results suggest that the electrons in metallic carbon nanotubes constitute a Luttinger liquid, even at room temperature. The study also found that the differential conductance transitions from a constant to a power-law behavior at a certain energy scale, which is well described by the theory. The data were found to collapse onto a universal curve when scaled appropriately, supporting the LL theory. The study also discusses the possible origins of the observed power-law behavior, including the role of Coulomb interactions and the effects of disorder. The results provide strong evidence that the electrons in metallic carbon nanotubes behave as a Luttinger liquid.This study investigates the behavior of electrons in single-walled carbon nanotubes (SWNTs) and finds evidence of Luttinger liquid (LL) behavior. The researchers measured the conductance of individual SWNT ropes as a function of temperature and voltage, observing power-law behavior: G ∼ T^α and dI/dV ∼ V^α. These results align with theoretical predictions for tunneling into a LL. The experiments revealed that SWNTs can behave as 1D conductors, with transport dominated by a single nanotube in the rope. The charging energy and level spacing of the nanotubes were determined, and the conductance was found to depend on the temperature and bias voltage in a power-law manner. The study also examined the differential conductance dI/dV as a function of applied bias voltage, finding that it follows a power-law behavior at high biases. The exponents of these power laws were found to be consistent with LL theory, which predicts that the tunneling amplitude vanishes as a power law in E - E_F. The LL theory also predicts that the differential conductance follows a power law, with exponents depending on the number of 1D channels and whether the electron tunnels into the bulk or the end of the LL. The results suggest that the electrons in metallic carbon nanotubes constitute a Luttinger liquid, even at room temperature. The study also found that the differential conductance transitions from a constant to a power-law behavior at a certain energy scale, which is well described by the theory. The data were found to collapse onto a universal curve when scaled appropriately, supporting the LL theory. The study also discusses the possible origins of the observed power-law behavior, including the role of Coulomb interactions and the effects of disorder. The results provide strong evidence that the electrons in metallic carbon nanotubes behave as a Luttinger liquid.
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Understanding Luttinger-liquid behaviour in carbon nanotubes