Confining interacting particles in onedimension 1d changes the electronic behavior of the system fundamentally, which has been studied extensively in the past. 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. Luttingerliquid behaviour in carbon nanotubes nature. Transport properties of metallic singlewall nanotubes are examined based on the luttinger liquid theory. Pdf luttinger liquid behavior in carbon nanotubes paul. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires that may exhibit luttinger liquid behaviour. Spin gap and luttinger liquid description of the nmr relaxation in carbon nanotubes. Observation of a luttingerliquid plasmon in metallic singlewalled carbon nanotubes zhiwen shi1, xiaoping hong1,hansa. For singlewall nanotubes, the electronelectron interaction destroys the fermi liquid state and leads to luttinger liquid behavior. The electric resistivity of a clean multiwalled carbon nanotube mwnt mat sample was studied at temperatures t between 300 and 1900 k. In particular, correlations imply the breakdown of fermi liquid theory and typically lead to luttinger liquid behavior characterized by pronounced powerlaw suppression of the transport current and the density of states, and spincharge separation. Spin gap and luttinger liquid description of the nmr. As opposed to fermi liquid model where the interaction between electrons is turned on adiabatically from corresponding fermi gas model. Luttinger liquid behavior of heliumthree in nanotubes subject.
Luttingerliquid behavior of heliumthree in nanotubes j. Carbon nanotubes cnts provide an ideal medium for testing the behavior of onedimensional electron systems and are promising candidates for electronic applications such as sensors or fieldeffect transistors. Observation of a luttingerliquid plasmon in metallic. Sensing kondo correlations in a suspended carbon nanotube. Electrically conducting single walled carbon nanotubes swnts represent quantum wires710 that may exhibit luttingerliquid behaviour11,12. Letters measurement of the quantum capacitance of interacting electrons in carbon nanotubes s. Singlewall carbon nanotubes are truly onedimensional conductors and are thus expected to behave as lls. Luttinger liquid behavior in carbon nanotubes arxiv. Luttinger liquid behavior in carbon nanotubes nasaads. Carbon nanotubes are exceptionally interesting from a fundamental research point of view. A luttinger liquid, or tomonaga luttinger liquid, is a theoretical model describing interacting electrons or other fermions in a onedimensional conductor e. Metallic singlewalled carbon nanotubes swnts are considered to be ideal. A scaling approach allows us to encompass the different values of the critical exponent. Luttinger liquids university of illinois at urbana.
Singlewall carbon nanotubes cornell laboratory of atomic and. New devices and geometries while the above experiments demonstrate that many of the basic properties of singlewall carbon nanotubes are now. Coulomb interaction effects have pronounced consequences in carbon nanotubes due to their 1d nature. To unambiguously demonstrate the luttinger liquid behavior, one can combine the study of nanotube plasmon which can determine the luttinger liquid parameter g with electrical. Our observed quantum plasmon behaviour agrees quantitatively with the. Martin2, kenji watanabe3, takashi taniguchi3, yuenron shen1,4 and feng wang1,4,5 surface plasmons1, collective oscillations of conduction elec trons, hold great promise for the nanoscale integration of. Depending on diameter and helicity, singlewalled carbon nanotubes swnts have, at most, two conducting channels with minimum resistance in the absence of disorder predicted to be h4e 2 6. Coulomb blockade oscillations, luttinger liquid behavior,3 kondo. Abstract the electrical conduction behavior of singlewalled carbon nanotube networks was investigated. Luttinger liquid state expected for a 1d system of interacting electrons. Luttinger liquid theory as a model of the gigahertz. Luttinger liquid behavior of heliumthree in nanotubes. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Terahertz spectroscopy of individual singlewalled carbon.
Electronelectron interactions in such systems are predicted to give rise to nonfermi luttinger liquid behavior at low temperature. Tomonaga luttingerliquid behavior in singlewalled carbon. These experiments show evidence of this luttinger liquid behavior, in which the electronelectron interactions lead to a qualitatively different ground state. Focusing on a nanotube transistor setup, the linear conductance is computed from the kubo formula using perturbation theory in the leadtube tunnel conductances. Luttinger liquid theory of nanotubes predicts 1,2 that, since tube diameter is larger than carbon separation, the 1d electron coupling is mainly accounted for by the longrange electron. Recently, singlewalled carbon nanotubes swnts have emerged as a new type of 1d conductor that may exhibit ll behavior. Pdf crossover from marginal fermi liquid to luttinger. Finally, chapter 8 will discuss measurements on metallic samples with extremely long mean free paths. We analyze a recent nmr experiments by singer et al. Carbon nanotubes by stephanie reich overdrive rakuten.
Walled carbon nanotubes prober lab yale university. The history of luttinger liquid theory actually goes back to the work of. With minor modifications, the same conclusions apply to transport in ropes of singlewall nanotubes. We realized the realspace imaging of luttinger liquid plasmons in semiconducting singlewalled carbon nanotubes sswcnts and studied the effects of chemicaldopinginduced charge carrier density modulation on plasmons. Luttinger liquid behavior in multiwall carbon nanotubes. The lowenergy theory of metallic carbon nanotubes is derived by bosonization methods. Using scatteringtype scanning nearfield optical microscopy s. Toshiyuki ohashi, liming dai, in carbon nanotechnology, 2006. Such a model is necessary as the commonly used fermi liquid model breaks down for one dimension. By modeling the nanotube as a nano transmission line with.
Tian x 1, gu q, duan j, chen r, liu h, hou y, chen j. Luttinger liquid behavior in carbon nanotubes springerlink. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires 7,8,9,10 that may exhibit luttingerliquid behaviour 11, 12. The functional form is consistent with the powerlaw behaviour predicted for tunnelling into a. Pdf direct observation of tomonagaluttingerliquid state in. The lowenergy theory for multiwall carbon nanotubes including the longranged coulomb interactions, internal screening effects, and singleelectron hopping between graphite shells is derived and analyzed by bosonization methods. Luttinger liquid behavior in carbon nanotubes article pdf available. Mceuen department of physics, university of california and materials sciences division, lawrence berkeley national. Our results can be well fitted with a power law of t within the framework of one dimensional luttinger liquid theory with. Examples of 1d metallic systems include carbon nanotubes, quasi1d organic conductors, metal chains, and domain boundary defects in monolayer thick transitionmetal dichalcogenides such as mose2. Luttinger liquid behavior in carbon nanotubes core. Doping and sizedependent suppression of tunneling in. Supercurrents through singlewalled carbon nanotubes science. Luttinger liquid in carbon nanotubes capri spring school.
Power law behavior as a function of temperature or bias voltage is observed. The predictions of correlated electron behavior in carbon nanotubes treated as a 1d. A comprehensive theory for the magnetic field and temperature dependent nmr c spin. It is characterized by collective behavior of electrons in contrast to quasiparticle description of fermi liquid. Quantum confined tomonagaluttinger liquid in mo6se6.
The strength of electron interactions is described by the socalled luttinger param. Transition from a tomonagaluttinger liquid to a fermi. Electric resistivity of multiwalled carbon nanotubes at. Strong electronelectron interactions have been demonstrated with the charge transport in swnts, leading to many phenomena such as coulomb blockade 49, 50, kondo effects 51, 52, and luttinger liquid behavior 53, 54. Citeseerx luttinger liquid behavior in singlewall nanotubes. Transition from a tomonaga luttinger liquid to a fermi liquid in potassiumintercalated bundles of singlewall carbon nanotubes h. We study the effect of doping in the suppression of tunneling observed in multiwalled nanotubes, incorporating as well the influence of the finite dimensions of the system. Many concepts of onedimensional physics have been verified experimentally such as electron and phonon confinement or the onedimensional singularities in the density of states. Although the nanotubes were entangled with each other and multiple junctions were formed within the network, they showed an apparently strong tomonaga luttinger liquid tl liquid character, which seemed to be attributable to their quasi onedimensional structures. Electrically conducting singlewalled carbon nanotubes swnts represent quantum wires 7,8,9,10 that may exhibit luttinger liquid behaviour 11, 12. Luttinger liquid model describes the behavior of id interacting electron gases. Luttinger liquid behavior in metallic carbon nanotubes core.
In semiconducting nanotubes, the electron dispersion is hyperbolic and the fermi energy can be tuned across a large range with electrostatic gating. Crossover from marginal fermi liquid to luttinger liquid behavior in carbon nanotubes. Carbon nanotubes cnts have been considered as an ideal platform for. For sufficiently long nanotubes and high temperature, phonon backscattering should lead to an anomalous temperature dependence. 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. Improving luttingerliquid plasmons in carbon nanotubes by. Thermal emission spectra from individual suspended carbon.
Lobb, department of physics carbon nanotubes cnts provide an ideal medium for testing the behavior of. Consequently, the luttinger liquid behavior is rigorous in metallic nanotubes with a temperature up to thousands of kevin. Improving luttinger liquid plasmons in carbon nanotubes by chemical doping. Here we present measurements of the conductance of individual ropes of such swnts as a function of temperature and voltage. Mceuen laboratory of atomic andsolidstate physics, department of physics, cornell university, ithaca, newyork 14853, usa. Here, a comprehensive theory for the magnetic field and temperature dependent nmr. For individual multiwall nanotubes or a rope of singlewall nanotubes, correlations are also important and can imply luttinger liquid behavior again. Fermi level both exhibit powerlaw behaviour with almost identical exponents in good. In particular, correlations imply the breakdown of fermi. Mcm41 nanotubes at temperatures near the fermi degeneracytemperature,t.
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