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Register a new userLuttinger Liquid Behavior in Carbon Nanotubes
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An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a Luttinger liquid (LL) characterized by a power-law vanishing of the density of states at the Fermi level. Experiments on one-dimensional semiconductor wires and fractional quantum Hall conductors have been interpreted using this picture, but questions remain about the connection between theory and experiment. Recently, single-walled carbon nanotubes (SWNTs) have emerged as a new type of 1D conductor that may exhibit LL behavior. Here we present measurements of the conductance of individual ropes of such SWNTs as a function of temperature and voltage. Power law behavior as a function of temperature or bias voltage is observed: G~ T^a and dI/dV ~ V^a. Both the power-law functional forms and the inferred exponents are in good agreement with theoretical predictions for tunneling into a LL.
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The low-energy theory for multi-wall carbon nanotubes including the long-ranged Coulomb interactions, internal screening effects, and single-electron hopping between graphite shells is derived and analyzed by bosonization methods. Characteristic Luttinger liquid power laws are found for the tunneling density of states, with exponents approaching their Fermi liquid value only very slowly as the number of conducting shells increases. With minor modifications, the same conclusions apply to transport in ropes of single-wall nanotubes.
Transport properties of metallic single-wall nanotubes are examined based on the Luttinger liquid theory. Focusing on a nanotube transistor setup, the linear conductance is computed from the Kubo formula using perturbation theory in the lead-tube tunnel conductances. For sufficiently long nanotubes and high temperature, phonon backscattering should lead to an anomalous temperature dependence of the resistivity.
We show that the absorption spectrum in semiconducting nanotubes can be determined using the bosonization technique combined with mean-field theory and a harmonic approximation. Our results indicate that a multiple band semiconducting nanotube reduces to a system of weakly coupled harmonic oscillators. Additionally, the quasiparticle nature of the electron and hole that comprise an optical exciton emerges naturally from the bosonized model.
We have measured the temperature dependence of the conductance in long V-groove quantum wires (QWRs) fabricated in GaAs/AlGaAs heterostructures. Our data is consistent with recent theories developed within the framework of the Luttinger liquid model, in the limit of weakly disordered wires. We show that for the relatively small amount of disorder in our QWRs, the value of the interaction parameter g is g=0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Trying to fit such data with perturbation-theory models leads inevitably to wrong (lower) values of g.
Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap (~ 30K), which crosses over smoothly to the Luttinger liquid behaviour with increasing temperature.
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